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The two fundamental ‘no go’ theorems for hidden variable reconstructions of the ► quantum statistics, the ► Kochen-Specker theorem [4] and ► Bell's theorem [1], can be formulated as results about the impossibility of associating a classical probability space (X,F, P ρ) with a quantum system in the state ρ, when certain constraints are placed on the probability measure P ρ. The Bub-Clifton theorem [2,3], by contrast, is a ‘go’ theorem: a positive result about the possibility of associating a classical probability space with a quantum system in a given state.

Keywords

Classical Probability Measurement Interaction Hide Variable Theory Modal Interpretation Quantum Mechanical Probability 
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Literature

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    J. Bub: Interpreting the Quantum World. Cambridge University Press, Cambridge, 1997.zbMATHGoogle Scholar
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    J. Bub, R. Clifton: A uniqueness theorem for no collapse interpretations of quantum mechanics. Studies in the History and Philosophy of Modern Physics. 27:181–219, 1996.CrossRefMathSciNetGoogle Scholar
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    S. Kochen, E. P. Specker: On the problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics. 17:59–87, 1967.zbMATHMathSciNetGoogle Scholar
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    K. Nakayama: Topos-theoretic extension of a modal interpretation of quantum mechanics. arXiv e-print quant-ph/0711.2200, 2007.Google Scholar
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    I. Pitowsky: George Boole's ‘conditions of possible experience’ and the quantum puzzle. British Journal for the Philosophy of Science. 45:95–125, 1994.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jeffrey Bub

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