Kochen-Specker theorem for von Neumann algebras

  • The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type I_n factor as algebra of observables, including I_infinity. Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von Neumann algebra R without summands of types I_1 and I_2, using a known result on two-valued measures on the projection lattice P(R). Some connections with presheaf formulations as proposed by Isham and Butterfield are made.

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Author:Andreas Döring
ArXiv Id:http://arxiv.org/abs/quant-ph/0408106
Document Type:Preprint
Date of Publication (online):2005/05/21
Year of first Publication:2004
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/06/17
Tag:Kochen-Specker theorem; von Neumann algebras
Page Number:22
Preprint, International Journal of Theoretical Physics volume 44.2005, S. 139–160
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht