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On a purported local extension of the quantum formalism

Melia, J. and Redhead, M. (1999) On a purported local extension of the quantum formalism. Journal of Mathematical Physics, 40 (9). pp. 4290-95. ISSN 1089-7658

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Abstract

Since the early days of quantum mechanics, a number of physicists have doubted whether quantum mechanics was a complete theory and wondered whether it was possible to extend the quantum formalism by adjoining hidden variables.1 In 1952, Bohm answered this question in the affirmative2 and in doing so refuted von Neumann’s influential yet flawed proof that no such extension was possible.3 However, Bohm’s hidden variable theory has not won wide support partly because the theory is nonlocal: there is instantaneous action at a distance. Since there is an obvious problem reconciling such nonlocal theories with Relativity, hidden variable theories would look much more promising if they also satisfied locality. Accordingly, the question as to whether or not local hidden variable theories are possible assumes great significance. In 1964 Bell appeared to prove that this question had a negative answer:4 He showed that any local hidden variables theory is incompatible with certain quantum mechanical predictions. Since these predictions have been borne out by the experiments of Aspect and others5 the prospects for hidden variable theories have looked grim. Angelidis disagrees.6 He claims to have done to Bell what Bohm did to von Neummann: He has found a theory which is local and which generates a family of probability functions converging uniformly to the probability function generated by quantum mechanics. If this were true, then Angelidis’ theory would be a counterexample to Bell’s theorem and a promising path would once again be open to hidden variable theorists. Unfortunately, Angelidis’ theory fails to live up to his claims: As formulated, the theory does not make the same predictions as quantum mechanics, and while there is a natural extension of his theory which does make the same predictions, the extension is not local. Bell’s Theorem stands.

Item Type: Article
Copyright, Publisher and Additional Information: © 1999 American Institute of Physics. Reproduced in accordance with the publisher's self-archiving policy.
Academic Units: The University of Leeds > Faculty of Arts (Leeds) > School of Humanities (Leeds) > School of Philosophy (Leeds)
Depositing User: Leeds Philosophy Department
Date Deposited: 11 Oct 2007 17:20
Last Modified: 08 Feb 2013 16:55
Published Version: http://dx.doi.org/10.1063/1.532966
Status: Published
Publisher: American Institute of Physics
Refereed: Yes
Identification Number: 10.1063/1.532966
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/3252

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