2019-06-27: Kevin Dunne

Tue, 14 Oct 2025 16:51:42 +0000

Kevin Dunne

Isbell Duality, Stone Duality, and Physical Theories

Abstract

Isbell duality is an adjunction between a category of "generalised algebras" and a category of "generalised spaces", and is an abstraction of Stone duality. Broadly speaking, a Stone duality is an equivalence between some category of commutative algebras, and some category of spaces, for example: Boolean algebras and Stone spaces; or, commutative C*-algebras and Hausdorff spaces.

There is a Stone duality which applies in the setting of Newtonian mechanics, between the category of smooth manifolds and a category of commutative algebras, and this equivalence of categories admits an extremely elegant and intuitive interpretation from the perspective of physics.

I am going to discuss how to build an analogous interpretation for quantum theory using the machinery of Isbell duality, in such a way that directly generalises Newtonian mechanics, with the ultimate aim being to resolve some of the conceptual problems of quantum theory.

2019-06-27 16:00:00 UTC
LT1310