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Kochen-Specker theorem for von Neumann algebras | | Andreas Doering
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16 Aug 2004 | | Subject: | Quantum Physics; Mathematical Physics; Operator Algebras | quant-ph math-ph math.MP math.OA | | 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 $I_{infty}$. Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von Neumann algebra $mathcal{R}$ without summands of types $I_{1}$ and $I_{2}$, using a known result on two-valued measures on the projection lattice $mathcal{P(R)}$. Some connections with presheaf formulations as proposed by Isham and Butterfield are made. | | Source: | arXiv, quant-ph/0408106 | | Services: | Forum | Review | PDF | Favorites | |
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