The many classical faces of quantum structures

TL;DR

This paper explores how quantum mechanics can be reformulated in classical terms using algebraic quantum theory, addressing interpretational issues through a focus on empirically accessible information.

Contribution

It provides a survey of the mathematical approach to reformulating quantum mechanics in classical language via algebraic quantum theory.

Findings

Reformulation of quantum mechanics in classical terms clarifies interpretational problems

Algebraic quantum theory offers a framework for this reformulation

Focus on empirically accessible information is central to the approach

Abstract

Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme in terms of algebraic quantum theory.