Review of the Topos Approach to Quantum Theory

TL;DR

This paper reviews the topos approach to quantum theory, which reformulates quantum mechanics using topos theory to address interpretational issues and promote a more realist perspective.

Contribution

It provides a comprehensive overview of the topos approach, highlighting its conceptual innovations and how it overcomes traditional interpretational problems in quantum physics.

Findings

Replaces Boolean logic with multivalued/intuitionistic logic in quantum theory

Addresses interpretational issues by reformulating quantum mechanics in topos theory

Promotes a more realist interpretation of quantum phenomena

Abstract

Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of physics is and what its conceptual framework looks like. The motivation of using topos theory to express quantum theory lies in the desire to overcome certain interpretational problems inherent in the standard formulation of the theory. In particular, the topos reformulation of quantum theory overcomes the instrumentalist/Copenhagen interpretation thereby rendering the theory more realist. In the process one ends up with a multivalued/intuitionistic logic rather than a Boolean logic. In this article we shall review some of these developments.