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Non-contextuality, finite precision measurement and the Kochen-Specker theorem

par Barrett, Jonathan ;Kent, Adrian
Référence Studies in history and philosophy of modern physics, 35, 2, page (151-176)
Publication Publié, 2004-06

Article révisé par les pairs

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Résumé :

Meyer originally raised the question of whether non-contextual hidden variable models can, despite the Kochen-Specker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental precision (Phys. Rev. Lett. 83 (1999) 3751). Meyer's result was extended by Kent (Phys. Rev. Lett. 83 (1999) 3755). Clifton and Kent later presented constructions of non-contextual hidden variable theories which, they argued, indeed simulate quantum mechanics in this way (Proc. Roy. Soc. Lond. A 456 (2000) 2101).These arguments have evoked some controversy. Among other things, it has been suggested that the Clifton-Kent models do not in fact reproduce correctly the predictions of quantum mechanics, even when finite precision is taken into account. It has also been suggested that careful analysis of the notion of contextuality in the context of finite precision measurement motivates definitions which imply that the Clifton-Kent models are in fact contextual. Several critics have also argued that the issue can be definitively resolved by experimental tests of the Kochen-Specker theorem or experimental demonstrations of the contextuality of Nature.One aim of this paper is to respond to and rebut criticisms of the Meyer-Clifton-Kent papers. We thus elaborate in a little more detail how the Clifton-Kent models can reproduce the predictions of quantum mechanics to arbitrary precision. We analyse in more detail the relationship between classicality, finite precision measurement and contextuality, and defend the claims that the Clifton-Kent models are both essentially classical and non-contextual. We also examine in more detail the senses in which a theory can be said to be contextual or non-contextual, and in which an experiment can be said to provide evidence on the point. In particular, we criticise the suggestion that a decisive experimental verification of contextuality is possible, arguing that the idea rests on a conceptual confusion. © 2003 Elsevier Ltd. All rights reserved.