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Analysis of Wigner’s Set Theoretical Proof for Bell-Type Inequalities
Center for Advanced Study, University of Illinois, Urbana, IL, USA
Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany RWTH Aachen University, Aachen, Germany
- 1 Center for Advanced Study, University of Illinois, Urbana, IL, USA
- 2 Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
- 3 Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany RWTH Aachen University, Aachen, Germany
Journal of Modern Physics·Volume 08 (2016)·Pages 57–67·Published 7 December 2016·DOI10.4236/jmp.2017.81005
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Abstract
We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein’s local realism, but instead, without justification, to the existence of certain joint probability measures for possible and actual measurement outcomes of Einstein-Podolsky-Rosen (EPR) experiments. His conclusions about Einstein’s local realism are, therefore, not applicable to EPR experiments and the contradiction of the experimental outcomes to Wigner’s results has no bearing on the validity of Einstein’s local realism.
KeywordsBell InequalityLocal RealismNonlocality
- Einstein, A., Podolsky, A. and Rosen, N. (1935) Physical Review, 47, 777-780. https://doi.org/10.1103/PhysRev.47.777
- Bell, J.S. (1993) Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge.
- Wigner, E.P. (1970) American Journal of Physics, 38, 1005-1009. https://doi.org/10.1119/1.1976526
- Khrennikov, A.Yu. (2008) Entropy, 10, 19-32. https://doi.org/10.3390/entropy-e10020019
- Rosinger, E.E. (2014) Quantum Matter, 3, 499-504. https://doi.org/10.1166/qm.2014.1153
- Geurdes, J.F. (1998) Australian Journal of Physics, 51, 835-842. https://doi.org/10.1071/P97067
- Hess, K., De Raedt, H. and Michielsen, K. (2016) Journal of Modern Physics, 7, 1651-1660. https://doi.org/10.4236/jmp.2016.713150
- d’Espagnat, B. (1979) The Quantum Theory and Reality. Scientific American. https://doi.org/10.1038/scientificamerican1179-158
- Einstein, A. (1982) Ideas and Opinions. Three Rivers Press, New York.
- Aspect, A., Dalibard, J. and Roger, G. (1982) Physical Review Letters, 49, 1804-1807. https://doi.org/10.1103/PhysRevLett.49.1804
- Weihs, G., Jennewein, T., Simon, C., Weinfurther, H. and Zeilinger, A. (1998) Physical Review Letters, 81, 5039-5043. https://doi.org/10.1103/PhysRevLett.81.5039
- Fine, A. (1996) The Shaky Game: Einstein Realism and the Quantum Theory. University of Chicago Press, Chicago. https://doi.org/10.7208/chicago/9780226923260.001.0001
- Hess, K. (2015) Einstein Was Right! Pan Stanford Publishing, Singapore.
- Aguero, M.B., Hnilo, A.A., Kovalsksy, M.G. and Larotonda, M.A. (2009) European Physical Journal D, 55, 705-709. https://doi.org/10.1140/epjd/e2009-00261-y
- Adenier, G. (2012) AIP Conference Proceedings, 1508, 115-124. https://doi.org/10.1063/1.4773123
- Vistnes, A.-I. and Adenier, G. (2012) AIP Conference Proceedings, 1508, 326-333. https://doi.org/10.1063/1.4773143
- Zhao, S., De Raedt, H. and Michielsen, K. (2008 Foundations of Physics, 38, 322-347. https://doi.org/10.1007/s10701-008-9205-5
- De Raedt, H., Jin, F. and Michielsen, K. (2013) Data Analysis of Einstein-Podolsky-Rosen-Bohm Laboratory Experiments.