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American Journal of Physics

Quantum mysteries refined

N. David Mermin

Published Oct 1, 1994• 147 citations
Publisher

Abstract

A gedanken experiment discovered by Lucien Hardy is translated into a very direct black-box gedanken demonstration of quantum nonlocality with red and green lights, using only two far apart detectors each of which operates in only two modes. The quantum mechanical underpinnings of the gedanken demonstration are quite simple. (This paper provides a text for the Klopsteg Memorial Lecture to the American Association of Physics Teachers at Notre Dame University, August 11, 1994.)

DOI
10.1119/1.17733

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Once upon a time everybody knew why measurements in quantum mechanics don't reveal pre-existing properties. It was because the act of acquiring knowledge unavoidably messes up the object being studied. What you learn is not intrinsic to the object, but a joint manifestation of the object and how you probe it to get your knowledge. In 1935 this state of happy innocence was forever dispelled by Einstein, who with Boris Podolsky and Nathan Rosen discovered how to learn about an object by messing up only some stuff it left behind in a faraway place. They concluded that knowledge acquired in this way was indeed about pre-existing properties of the object, revealed—not created—by the act of probing the stuff left behind. Bohr, however, insisted their conclusion was unjustified, and 30 years later John Bell proved that no assignment of such pre-existing properties could agree with the quantitative predictions of quantum mechanics. A couple of years ago Lucien Hardy [1] gave this tale an unexpected twist, by finding a charming variation of the Bell–EPR argument. Hardy's theorem is even simpler than the argument of Daniel Greenberger, Michael Home, and Anton Zeilinger that I enthused about in this column four years ago. The reason he was able to pull the trick off, and the reason, I suspect, nobody had noticed so neat an argument for so long, is that Hardy's analysis applies to data that are not correlated strongly enough to support the argument of EPR. But they do give rise to an argument every bit as seductive, which Hardy is then able to demolish with surprising ease. Parts of the formulation I give here of Hardy's gedankenexperiment are similar to those of Henry Stapp [2] and Sheldon Goldstein [3]. We consider two particles that originate from a common source and fly apart to stations at the left and right ends of a long laboratory. At the left station we can experimentally determine the answer to one of two yes–no questions, A or B . There is a choice of two other yes–no questions, M or N , to be answered by experiment on the right. Hardy provides questions A , B , M , and N , and a two-particle state |Ψ〉 for which the answers to the questions have the following features: […]

Cambridge University Press eBooks•Jan 5, 2016•0 citations
A gedanken experiment discovered by Lucien Hardy is translated into a very direct black-box gedanken demonstration of quantum nonlocality with red and green lights, using only two far apart detectors each of which operates in only two modes. The quantum mechanical underpinnings of the gedanken demonstration are quite simple. (This paper provides a text for the Klopsteg Memorial Lecture to the American Association of Physics Teachers at Notre Dame University, August 11, 1994.)
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.
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.
Once upon a time everybody knew why measurements in quantum mechanics don't reveal pre-existing properties. It was because the act of acquiring knowledge unavoidably messes up the object being studied. What you learn is not intrinsic to the object, but a joint manifestation of the object and how you probe it to get your knowledge. In 1935 this state of happy innocence was forever dispelled by Einstein, who with Boris Podolsky and Nathan Rosen discovered how to learn about an object by messing up only some stuff it left behind in a faraway place. They concluded that knowledge acquired in this way was indeed about pre-existing properties of the object, revealed—not created—by the act of probing the stuff left behind. Bohr, however, insisted their conclusion was unjustified, and 30 years later John Bell proved that no assignment of such pre-existing properties could agree with the quantitative predictions of quantum mechanics. A couple of years ago Lucien Hardy [1] gave this tale an unexpected twist, by finding a charming variation of the Bell–EPR argument. Hardy's theorem is even simpler than the argument of Daniel Greenberger, Michael Home, and Anton Zeilinger that I enthused about in this column four years ago. The reason he was able to pull the trick off, and the reason, I suspect, nobody had noticed so neat an argument for so long, is that Hardy's analysis applies to data that are not correlated strongly enough to support the argument of EPR. But they do give rise to an argument every bit as seductive, which Hardy is then able to demolish with surprising ease. Parts of the formulation I give here of Hardy's gedankenexperiment are similar to those of Henry Stapp [2] and Sheldon Goldstein [3]. We consider two particles that originate from a common source and fly apart to stations at the left and right ends of a long laboratory. At the left station we can experimentally determine the answer to one of two yes–no questions, A or B . There is a choice of two other yes–no questions, M or N , to be answered by experiment on the right. Hardy provides questions A , B , M , and N , and a two-particle state |Ψ〉 for which the answers to the questions have the following features: […]