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.
Author: | Andreas Döring |
---|---|
URN: | urn:nbn:de:hebis:30-11183 |
ArXiv Id: | http://arxiv.org/abs/quant-ph/0408106 |
Document Type: | Preprint |
Language: | English |
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 |
Note: | Preprint, International Journal of Theoretical Physics volume 44.2005, S. 139–160 |
HeBIS-PPN: | 134976606 |
Institutes: | Informatik und Mathematik / Mathematik |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Licence (German): | Deutsches Urheberrecht |