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American Journal of Physics

A lecture demonstration of the incompatibility of quantum predictions with those of a local realistic theory

G E Stedman

Published Dec 1, 1985• 2 citations
Publisher

Abstract

A logic circuit is used to light bulbs in accordance with quantum predictions and in violation of the predictions of a local realistic theory. This makes Mermin’s gedanken experiment, in which the Einstein–Podolsky–Rosen paradox (as sharpened by Bell) is presented with the minimum of technicalities, a feasible and instructive lecture demonstration. We give circuit details, a useful order of presentation, the reactions of a class of nonscience majors, and a simple general proof of the incompatibility.

DOI
10.1119/1.14070

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A logic circuit is used to light bulbs in accordance with quantum predictions and in violation of the predictions of a local realistic theory. This makes Mermin’s gedanken experiment, in which the Einstein–Podolsky–Rosen paradox (as sharpened by Bell) is presented with the minimum of technicalities, a feasible and instructive lecture demonstration. We give circuit details, a useful order of presentation, the reactions of a class of nonscience majors, and a simple general proof of the incompatibility.
The purpose of this lecture is to give a self-contained demonstration of a version of Bell's theorem and a discussion of the significance of the theorem and the experiments which it inspired. The lecture should be comprehensible to people who have had no previous acquaintance with the literature on Bell's theorem, but I hope that explicitness about premisses and consequences will make it useful even to those who are familiar with the literature. All versions of Bell's theorem are variations, and usually generalizations, of the pioneering paper of J. S. Bell of 1964, entitled “On the Einstein–Podolsky–Rosen Paradox.” All of them consider an ensemble of pairs of particles prepared in a uniform manner, so that statistical correlations may be expected between outcomes of tests performed on the particles of each pair. If each pair in the ensemble is characterized by the same quantum state φ, then the quantum mechanical predictions for correlations of the outcomes can in principle be calculated when the tests are specified. On the other hand, if it is assumed that the statistical behavior of the pairs is governed by a theory which satisfies certain independence conditions (always similar to the Parameter and Outcome Independence conditions stated below, though the exact details vary from version to version of Bell's theorem), then it is possible to derive a restriction upon the statistical correlations of the outcomes of tests upon the two particles.
This chapter begins with a review of the ideas of locality and realism which provide the basis for the Einstein–Podolsky–Rosen paradox. The general conditions defining a local, realistic theory are stated, and then used to prove Bell's theorem, which yields — for any local, realistic theory — an inequality satisfied by certain linear combinations of correlations. It is shown that this inequality is violated by quantum theory and by experiment. The chapter ends with a discussion of possible experimental loopholes and the alternative Greenberger–Horne–Zeilinger (GHZ) state, which would, in principle, make the use of statistical correlations unnecessary.
Chapter 7 discusses the Bell theorem and its demonstration using Mermin’s machine. The Bell theorem proves that a theory based on local realism (one with hidden variables) must satisfy certain inequalities; quantum mechanics predicts these are violated. Mermin designed a gedanken experiment having a double-particle source and two detectors each having three settings, which can correspond to measurements along three spin orientations. A simple hidden-variable assumption is shown to violate quantum predictions. The CHSH inequality, a form of the general Bell inequality, is proved. This relation has been shown to be violated experimentally in quantum experiments, implying that quantum mechanics indeed has “spooky action at a distance.” Many experiments over the years had loopholes, ways used to explain away the data in order to preserve local reality, but recent experiments have been able to eliminate most of these.
Although considerable discussion about the completeness of quantum mechanics followed the publication in 1935 of the Gedanken experiment of Einstein, Podolsky, and Rosen (EPR), it was not until Bell's work, published in 3 965, that it was realized that the issue could be rigorously formulated and put to experimental test. An even more provocative demonstration of the incompatibility of quantum mechanics with local realism was recently discovered by Greenberger, Horne, and Zeilinger (GHZ) in a Gedanken experiment employing more than two particles.1 Typical of EPR experiments that have been proposed to date, one has a metastable system that decays into n particles.
A few years ago I described a simple device that reveals in a very elementary way the extremely perplexing character the data from the Bohm–Einstein–Podolsky–Rosen experiment assumes in the light of the analysis of J. S. Bell. There is a second, closely related form of that gedanken demonstration, which I would like to examine for several reasons. It is simpler: there are only two (not three) settings for each switch. The gedanken data resemble more closely the data collected in actual realizations of the device. None of the possible switch settings produce the perfect correlations found in the first version of the gedanken demonstration, where the lights always flash the same color when the switches have the same setting. Since absolutely perfect correlations are never found in the imperfect experiments we contend with in the real world, an argument that eliminates this feature of the ideal gedanken data can be applied to real data from real experiments. (If you believe, however, along with virtually all physicists, that the quantum theory gives the correct ideal limiting description of all phenomena to which it can be applied, then this is not so important a consideration.) Because the ideal perfect correlations are absent from this version of the gedanken demonstration, one is no longer impelled to assert the existence of impossible instruction sets. To establish that the new data nevertheless remain peculiar, it is necessary to take a different line of attack, which has again intriguing philosophical implications, but of a rather different character. The modified demonstration In the modified gedanken demonstration there are only two switch settings (1 and 2) at each detector.