NDLI: A Categorial Semantic Representation of Quantum Event Structures

Content Provider	Springer Nature Link
Author	Zafiris, Elias Karakostas, Vassilios
Copyright Year	2013
Abstract	The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches.
Starting Page	1090
Ending Page	1123
Page Count	34
File Format	PDF
ISSN	00159018
Journal	Foundations of Physics
Volume Number	43
Issue Number	9
e-ISSN	15729516
Language	English
Publisher	Springer US
Publisher Date	2013-08-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quantum event structures Boolean algebras Topos subobject classifier Kochen-Specker theorem Quantum truth values Adjoint functors Sheaves Grothendieck topos Realist account History and Philosophical Foundations of Physics Quantum Physics Classical and Quantum Gravitation, Relativity Theory Statistical Physics, Dynamical Systems and Complexity Mechanics Philosophy of Science
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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