Constructive Axiomatics in Spacetime Physics Part III: A Constructive Axiomatic Approach to Quantum Spacetime

TL;DR

This paper extends the EPS constructive axiomatisation of general relativity to incorporate quantum mechanical inputs, aiming to develop a constructive axiomatic approach to quantum spacetime, with implications for the epistemology and metaphysics of spacetime theories.

Contribution

It introduces a quantum extension of the EPS axiomatic framework, bridging classical and quantum spacetime structures in a constructive manner.

Findings

Proposes a quantum axiomatic framework for spacetime

Extends classical EPS axioms to quantum context

Highlights implications for quantum gravity theories

Abstract

The Ehlers-Pirani-Schild (EPS) constructive axiomatisation of general relativity, published in 1972, purports to build up the kinematical structure of that theory from only axioms which have indubitable empirical content. It is, therefore, of profound significance both to the epistemology and to the metaphysics of spacetime theories. In this article, we consider extensions of the EPS axiomatisation towards quantum general relativity based upon quantum mechanical inputs (Part III). There are two companion papers, in which we provide a pedagogical walkthrough to the EPS axiomatisation (Part I), and discuss the significance of constructive approaches to spacetime structure more generally (Part II).