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 I1 and I2, 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.
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Döring, A. Kochen–Specker Theorem for von Neumann Algebras. Int J Theor Phys 44, 139–160 (2005). https://doi.org/10.1007/s10773-005-1490-6
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DOI: https://doi.org/10.1007/s10773-005-1490-6