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 model
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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Metadaten
Author:Andreas Döring
URN:urn:nbn:de:hebis:30-11183
Document Type:Preprint
Language:English
Date of Publication (online):2005/06/17
Year of first Publication:2004
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/06/17
Tag:Kochen-Specker theorem; von Neumann algebras
HeBIS PPN:134976606
Institutes:Mathematik
Dewey Decimal Classification:510 Mathematik
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

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