Topos theory and `neo-realist' quantum theory

TL;DR

This paper introduces topos theory as a mathematical framework for quantum physics, highlighting its logical structure and how it assigns truth-values to propositions within quantum systems.

Contribution

It provides an overview of topos theory's application to quantum theory, emphasizing the logical aspects and detailed implementation for algebraic quantum systems.

Findings

Topos theory offers a new logical perspective on quantum physics.

It demonstrates how topos-based models assign truth-values to quantum propositions.

The approach bridges category theory and quantum logic.

Abstract

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves as a `mathematical universe' with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.