It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two‐particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin‐correlation and multiparticle interferometry examples are given of suitable three‐ and four‐particle arrangements, both at the gedanken and at the real experiment level.
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December 1990
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December 01 1990
Bell’s theorem without inequalities
Daniel M. Greenberger;
Daniel M. Greenberger
Department of Physics, City College of the City University of New York, New York, New York 10031
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Michael A. Horne;
Michael A. Horne
Department of Physics, Stonehill College, North Easton, Massachusetts 02357
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Abner Shimony;
Abner Shimony
Departments of Philosophy and Physics, Boston University, Boston, Massachusetts 02215
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Anton Zeilinger
Anton Zeilinger
Atominstitut der Österreichischen Universitäten, Schüttelstrasse 115, A‐1020 Vienna, Austria
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Am. J. Phys. 58, 1131–1143 (1990)
Article history
Received:
June 10 1990
Accepted:
July 30 1990
Citation
Daniel M. Greenberger, Michael A. Horne, Abner Shimony, Anton Zeilinger; Bell’s theorem without inequalities. Am. J. Phys. 1 December 1990; 58 (12): 1131–1143. https://doi.org/10.1119/1.16243
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