Diffeomorphism Invariance and Background Independence

TL;DR

The paper investigates the relationship between $Diffeomorphism ext{ Invariance}$ ($DI$) and $Background ext{ Independence}$ ($BI$), arguing that $DI$ is a mathematical criterion whose relation to $BI$ is nuanced and not universally equivalent. It surveys influential positions by Teitel, Smolin, Stachel, and Pooley, highlighting that $BI$ lacks a single universal definition and that reformulations can render non-$DI$ theories $DI$-compliant, as shown for SR. The analysis clarifies that $DI$ represents a degree of background independence rather than a complete account, with $DI$-compliant theories like GR, AGT, and TEGR possessing nonfixed manifold structure but still harboring fixed background features. The discussion of haecceity, via Stachel's maximal permutability, shows that while $DI$ entails lack of haecceity, the converse fails, underscoring a nuanced landscape for background conceptualization in gravitational theories and their reformulations.

Abstract

This paper answers examines the relationship between Diffeomorphism Invariance and Background Independence. First, a review of the relationship between Background Independence, General Relativity (GR) and pre-GR theories are given. Then, a wide range of other conceptions of background independence is discussed. It is shown that the definition of Background Independence is fluid and can mean different things to different philosophers and/or physicists. Most pertinently, the paper addresses the question of what kind of background independence is implied by a mathematical criterion of diffeomorphism invariance or in what sense is diffeomorphism invariance background independence. Lastly, the concept of haecceity in relation to diffeomorphism invariance is discussed.