Background-Independence

TL;DR

This paper clarifies the concept of background-independence in classical field theories, emphasizing its dependence on interpretation and proposing a criterion based on the correspondence between physical possibilities and spacetime geometries.

Contribution

It offers a formal explication of background-independence, linking it to the interpretative framework and proposing a criterion based on the mapping of possibilities to geometries.

Findings

Background-independence depends on interpretation.

A theory is fully background-independent if each physical possibility has a unique spacetime geometry.

The paper provides a criterion to assess background-independence based on the correspondence between possibilities and geometries.

Abstract

Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.