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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/3941
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dc.contributor.authorSurya, Sumati-
dc.contributor.authorWallden, Petros-
dc.date.accessioned2010-07-22T09:21:54Z-
dc.date.available2010-07-22T09:21:54Z-
dc.date.issued2010-06-
dc.identifier.citationFoundations of Physics, 2010, Vol.40, p585en
dc.identifier.issn1572-9516 (Online)-
dc.identifier.issn0015-9018-
dc.identifier.urihttp://hdl.handle.net/2289/3941-
dc.descriptionRestricted Access. An open-access version is available at arXiv.org (one of the alternative locations)en
dc.description.abstractSorkin’s recent proposal for a realist interpretation of quantum theory, the anhomomorphic logic or coevent approach, is based on the idea of a “quantum measure” on the space of histories. This is a generalisation of the classical measure to one which admits pair-wise interference and satisfies a modified version of the Kolmogorov probability sum rule. In standard measure theory the measure on the base set Ω is normalised to one, which encodes the statement that “Ω happens”. Moreover, the Kolmogorov sum rule implies that the measure of any subset A is strictly positive if and only if A cannot be covered by a countable collection of subsets of zero measure. In quantum measure theory on the other hand, simple examples suffice to demonstrate that this is no longer true. We propose an appropriate generalisation, the quantum cover, which in addition to being a cover of A, satisfies the property that if the quantum measure of A is non-zero then this is also the case for at least one of the elements in the cover. Our work implies a non-triviality result for the coevent interpretation for Ω of finite cardinality, and allows us to cast the Peres-Kochen-Specker theorem in terms of quantum coversen
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urihttp://arxiv.org/abs/0809.1951en
dc.relation.urihttp://dx.doi.org/10.1007/s10701-010-9419-1en
dc.relation.urihttp://adsabs.harvard.edu/abs/2010FoPh...40..585Sen
dc.rights2010 Springeren
dc.subjectquantum interpretationen
dc.subjectquantum measure theoryen
dc.subjectquantum topologyen
dc.subjectlattice theoryen
dc.titleQuantum covers in quantum measure theoryen
dc.typeArticleen
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