Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity

TL;DR

This paper explores how topos theory, a branch of category theory, can be applied to interpretative issues in quantum theory and quantum gravity, proposing potential frameworks and applications.

Contribution

It introduces topos theory concepts and discusses potential applications to interpretative problems in quantum physics and quantum gravity.

Findings

Topos theory offers new interpretative frameworks for quantum physics.

Potential applications include reformulating quantum and gravity theories within topos structures.

The paper suggests directions for future research in applying topos theory to foundational physics.

Abstract

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory, especially the idea of a topos of presheaves. In Section 3, we discuss several possible applications of topos theory to the problems in Section 1. In Section 4, we draw some conclusions.