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Negations and Meets in Topos Quantum Theory

Kitajima, Yuichiro

Foundations of physics, 2022-02, Vol.52 (1), Article 12 [Periódico revisado por pares]

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Título:
Negations and Meets in Topos Quantum Theory
Autor: Kitajima, Yuichiro
Assuntos: Algebra ; Boolean algebra ; Classical and Quantum Gravitation ; Classical Mechanics ; History and Philosophical Foundations of Physics ; Lattices (mathematics) ; Philosophy of Science ; Physics ; Physics and Astronomy ; Quantum Physics ; Quantum theory ; Relativity Theory ; Statistical Physics and Dynamical Systems
É parte de: Foundations of physics, 2022-02, Vol.52 (1), Article 12
Descrição: The daseinisation is a mapping from an orthomodular lattice in ordinary quantum theory into a Heyting algebra in topos quantum theory. While distributivity does not always hold in orthomodular lattices, it does in Heyting algebras. We investigate the conditions under which negations and meets are preserved by daseinisation, and the condition that any element in the Heyting algebra transformed through daseinisation corresponds to an element in the original orthomodular lattice. We show that these conditions are equivalent, and that, not only in the case of non-distributive orthomodular lattices but also in the case of Boolean algebras containing more than four elements, the Heyting algebra transformed from the orthomodular lattice through daseinisation will contain an element that does not correspond to any element of the original orthomodular lattice.
Editor: New York: Springer US
Idioma: Inglês

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