Rothman, Tony ; Sudarshan, E. C. G. (2001) Hidden variables or positive probabilities? International Journal of Theoretical Physics, 40 (8). pp. 1525-1543. ISSN 0020-7748
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Official URL: http://www.springerlink.com/content/ur851577473743...
Related URL: http://dx.doi.org/10.1023/A:1017565730083
Abstract
Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption that local hidden-variable theories produce a set of positive-definite probabilities for detecting a particle with a given spin orientation. The standard argument is that because quantum mechanics assumes that particles are emitted in a superposition of states the theory cannot produce such a set of probabilites. We examine a paper by Eberhard, and several similar papers, which claim to show that a generalized Bell inequality, the CHSH inequality, can be derived solely on the basis of the locality condition, without recourse to hidden variables. We point out that these authors nonetheless assumes a set of positive-definite probabilities, which supports the claim that hidden variables or "locality" is not at issue here, positive-definite probabilities are. We demonstrate that quantum mechanics does predict a set of probabilities that violate the CHSH inequality; however these probabilities are not positive-definite. Nevertheless, they are physically meaningful in that they give the usual quantum-mechanical predictions in physical situations. We discuss in what sense our results are related to the Wigner distribution.
Item Type: | Article |
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Source: | Copyright of this article belongs to Springer. |
ID Code: | 51147 |
Deposited On: | 27 Jul 2011 13:01 |
Last Modified: | 27 Jul 2011 13:01 |
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