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Modern Physics > Quantum Physics > Quantum Mechanics > General Quantum Mechanics v



Bell's Inequalities
    

An infinite class of inequalities formulated by Bell (1964) which seemed to be a physically reasonable condition of locality imposing restrictions on the maximum correlations of the measurements of a pair of spin 1/2 particles formed in the singlet state and moving freely in opposite directions, as considered in the Einstein-Podolsky-Rosen paradox.

Bell's inequalities can be tested in a laboratory experiment (under certain assumptions) because the statistical predictions of quantum mechanics are incompatible with any local hidden variables theory apparently satisfying only the natural assumptions of "locality," as shown by the predictions of Bell's inequality. However, at present there are no "clean" experiments unambiguously verifying the inequalities.

Einstein-Podolsky-Rosen Paradox, Entanglement, Hidden Variables




References

Aspect, A.; Grangier, P.; and Roger, G. "Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities." Phys. Rev. Let. 49, 91-94, 1982.

Aspect, A.; Dalibard, J.; and Roger, G. "Experimental Test of Bell's Inequalities Using Time-Varying Analyzers." Phys. Rev. Let. 49, 1804-1807, 1982.

Basdevant, J.-L. and Dalibard, J. "Hidden Variables and Bell's Inequalities." Ch. 15 in The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics. Berlin: Springer-Verlag, pp. 109-118, 2000.

Bell, J. S. "On the Einstein-Podolsky-Rosen Paradox." Physics 1, 195-200, 1964.

Elm, D. A. http://www.tiac.net/users/davidelm.

Grometstein, A. A. "The Bell Thunderbolt (1964)." Ch. 18 in The Roots of Things: Topics in Quantum Mechanics. New York: Kluwer, pp. 491-513, 1999.

Pitowsky, I. Quantum Probability--Quantum Logic. Berlin: Springer-Verlag, 1989.

Werner, R. F. and Wolf, M. M. "All Multipartite Bell Correlation Inequalities for Two Dichromatic Observables per Site" 5 Feb 2001. http://xxx.lanl.gov/abs/quant-ph/0102024/.

Wheeler, J. A. and Zurek, W. H. Quantum Theory and Measurement. Princeton, NJ: Princeton University Press, 1983.







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