What is the role of topos theory in the topos models for quantum theory asused by Isham, Butterfield, Doring, Heunen, Landsman, Spitters and others? Inother words, what is the interplay between physical motivation for the modelsand the mathematical framework used in these models? Concretely, we show thatthe presheaf topos model of Butterfield, Isham and Doring resembles classicalphysics when viewed from the internal language of the presheaf topos, similarto the copresheaf topos model of Heunen, Landsman and Spitters. Both thepresheaf and copresheaf models provide a `quantum logic' in the form of acomplete Heyting algebra. Although these algebras are natural from a topostheoretic stance, we seek a physical interpretation for the logical operations.Finally, we investigate dynamics. In particular we describe how an automorphismon the operator algebra induces a homeomorphism (or isomorphism of locales) onthe associated state spaces of the topos models, and how elementarypropositions and truth values transform under the action of this homeomorphism.Also with dynamics the focus is on the internal perspective of the topos.
展开▼
