Relational Physics and Quantum Space

TL;DR

This paper explores how purely relational theories can define length and time, reconcile with Lorentz transformations, and potentially inform quantum gravity research.

Contribution

It demonstrates that relational definitions of length and time are possible with known dynamics and suggests Lorentz transformations naturally emerge in this framework.

Findings

Relational definitions of length and time are feasible with known dynamics.

Lorentz transformations naturally arise between different observers.

Insights may advance the search for quantum gravity theories.

Abstract

In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We then address this conflict by showing that a purely relational definition of length and time can be given, provided the dynamics of the theory is known. We further show that in such a setting it is natural to expect Lorentz transformations to describe the mapping between different observers. We then comment on how these insights can be used to make progress in the search for a theory of quantum gravity.