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PHYSICAL STATES ON A C*-ALGEBRA
- Publisher
- Springer Journals
- Copyright
- Copyright © 2005 by Springer Science + Business Media, Inc.
- Subject
- Physics; Physics, general; Quantum Physics; Elementary Particles, Quantum Field Theory; Theoretical, Mathematical and Computational Physics
- ISSN
- 0020-7748
- eISSN
- 1572-9575
- DOI
- 10.1007/s10773-005-1490-6
- Publisher site
- See Article on Publisher Site
Abstract
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 ∞. Afterwards, we give a proof of the Kochen–Specker theorem for an arbitrary von Neumann algebra $${\cal R}$$ without summands of types I 1 and I 2, using a known result on two-valued measures on the projection lattice $${\cal{P(R)}}$$ . Some connections with presheaf formulations as proposed by Isham and Butterfield are made.
Journal
International Journal of Theoretical Physics – Springer Journals
Published: Jan 1, 2005