A topos perspective on the Kochen-Specker theorem: I. Quantum States as Generalized Valuations

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dc.creatorIsham, C. J.
dc.creatorButterfield, J.
dc.date1998-03-20
dc.date1998-10-13
dc.date.accessioned2026-07-07T06:14:53Z
dc.date.available2026-07-07T06:14:53Z
dc.descriptionThe Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalized valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalized valuation.
dc.descriptionClarification of situation for situation for operators with continuous spectra
dc.identifierhttps://arxiv.org/abs/quant-ph/9803055
dc.identifierhttp://arxiv.org/abs/quant-ph/9803055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93633
dc.subjectQuantum Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA topos perspective on the Kochen-Specker theorem: I. Quantum States as Generalized Valuations
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