Abstract
In the early 1950s, a physics student in Northern Ireland of unusual critical ability noticed a puzzling situation. Einstein, the student knew, had claimed quantum mechanics gave an inadequate account of atoms, and he had read about von Neumann’s “impossibility proof” in a popular book. But then was not one of these geniuses wrong?
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Notes
Bell was profiled by physicist and New Yorker staff writer Jeremy Bernstein in Quantum Profiles (1991). His collected papers on quantum philosophy are in Speakable and Unspeakable in Quantum Mechanics (1987), except for “Against ’measurement” (his final work), a scathing critique of the current situation in quantum physics (see Chapter 18, “Principles”).
The popular book Bell read was Max Born’s Natural Philosophy of Cause and Chance, 1949. Von Neumann’s book had not yet been translated from the German.
“44 countries on a grain of rice”: see the section on miniature writing in the 1989 Guinness Book of World Records.
Bell’s theorem appeared in Physics 1 no. 3, (1964), pp. 195–200, reprinted in Bell (1987). The story of this journal is interesting in its own right. Its full title was Physics Physique Fizika (it accepted papers in three languages), and its subtitle was “An International Journal for Selected Articles Which Deserve the Special Attention of Physicists in All Fields.” In an editorial foreword, P. W. Anderson (then at Bell Labs, now at Princeton) and B. T. Matthias (U. of California at San Diego) described their unusual serial as analogous to “a journal of literature and general information, such as Harper’s,” for the benefit of physicists who have stopped reading articles even in closely related subfields, “as perforce most of them have long since… in the other sciences.” Writers submit articles to Harper’s, they noted, partly because they will be paid (and one might also remark that the rejection rate at Harper’s or the New Yorker is at least 99 percent). By contrast, many scientific journals, despite lofty goals and high standards, are essentially vanity presses. “Page charges” at these journals can run as high as a hundred dollars a page. Bell recalled sending his paper to Physics at least partly to avoid such charges—he was too embarrassed to ask his American hosts to pay for his unusual submission.
Philip Anderson, who won the Nobel Prize in 1977 for developing the quantum theory of electrons in disordered materials, read Bell’s paper and accepted it, partly because he thought it refuted Bohmism.* Physics Physique Fizika lasted only four years. It is sad that Anderson’s and Matthias’s idea did not catch on.
The proof of Bell’s theorem given here seems the simplest and is in general circulation among Bell aficionados; I do not know whom to credit. Bell proved his inequality (“Bell’s inequality” has since become a generic label for any inequality ruling out local realism) by conventional probability calculus. The angles chosen are not optimal for violating Bell’s inequality; with better choices the violation can become \( 2\sqrt {2} \). Other proofs can be found in Clauser and Horne, Phys. Rev. D 10 (1974), p. 526;
Wigner, Am. J. Phys. 33 (1970), pp. 1005–1009;
Stapp, Phys. Rev. D 3 (1971), pp. 1303–1320;
Eberhard, Nuovo Cimento B 38, (1977), p. 75–80,
Eberhard, Nuovo Cimento B (1978), pp. 392–419;
Mermin, Physics Today (April 1985), p. 38, and there are many others (peruse the back issues of Found. Phys., for instance). Bell’s theorem entered popular culture with Gary Zukav’s The Dancing Wu-Li Masters (1979), where it is called, somewhat hyperbolically, “the most important single work, perhaps, in the history of physics.” Unfortunately, Zukav continues, it is also “indecipherable to the non-mathematician.”
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Wick, D. (1995). Bell’s Theorem. In: The Infamous Boundary. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4030-3_11
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