When is a hidden variable theory compatible with quantum mechanics?
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This paper is devoted to a study of some of the basic conditions which have to be satisfied by a hidden variable theory in order that it can reproduce the quantum mechanical probabilities. Of course one such condition, which emerges from the important theorem of Bell, is that a hidden variable theory has to be non-local. It is shown that a hidden variable theory is also incompatible with the conventional interpretation of mixed states and the mixing operation in quantum theory. It is therefore concluded that, apart from being non-local, a hidden variable theory would also necessarily violate the usual assumption of quantum theory that the density operator provides an adequate characterization of any ensemble of systems, pure or mixed.
KeywordsHidden variable theories complete specification of the state of a system compatibility with quantum mechanics local causality density operators mixed ensembles quantum mechanics
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- Belinfante F J 1973A survey of hidden variable theories (Oxford: Pergamon)Google Scholar
- Bell J S 1964Physics 1 195Google Scholar
- Bell J S 1971a inFoundations of quantum mechanics, (ed.) B d’Espagnat (New York: Academic Press)Google Scholar
- Bell J S 1971b On the hypothesis that the Schrodinger equation is exact (CERN Preprint Ref. TH 1424)Google Scholar
- Bell J S 1975 The theory of local beables (CERN Preprint Ref. TH 2053)Google Scholar
- Bell J S 1980 Bertlmann’s socks and the nature of reality (CERN Preprint Ref. TH 2926)Google Scholar
- Bub J 1974The interpretation of quantum mechanics (Dordrecht: Reidel)Google Scholar
- de Broglie L 1948, La Revue Scientifique No. 3292 fasc. 5,87 259Google Scholar
- d’Espagnat B 1976Conceptual foundations of quantum mechanics 2nd Ed. (Reading: Benjamin)Google Scholar
- d’Espagnat B 1979Sci. Am. 241 128Google Scholar
- Fine A 1976 inLogic and probability in quantum mechanics (ed.) P Suppes (Dordrecht: Reidel)Google Scholar
- Jammer M 1974The philosophy of quantum mechanics (New York: John Wiley)Google Scholar
- Mugur-Schächter M 1977 inQuantum mechanics a half century later (eds.) J Leite-Lopes and M Paty (Dordrecht: Reidel)Google Scholar
- Roy S M 1980Phys. News 11 Google Scholar
- Srinivas M D 1982,The Wave-particle Dualism (eds.) S Dineret al (Dordrecht: Reidel)Google Scholar
- Vandana Shiva 1978Hidden variables and locality in quantum mechanics Ph.D. Thesis (unpublished) (University of Western Ontario)Google Scholar
- Virendra Singh 1980 inGravitation, quanta and the universe, (eds) A R Prasanna, J V Narlikar and C V Visheveshvara (New Delhi; Wiley Eastern)Google Scholar
- Wigner E P 1971 inPerspectives in quantum theory (eds) W Yourgrau and T van der Merwe (Cambridge: MIT Press)Google Scholar