Background Independence, Diffeomorphism Invariance, and the Meaning of Coordinates

TL;DR

The paper challenges common beliefs by arguing that background dependence and diffeomorphism invariance do not necessarily imply different physical magnitudes, and that background-dependent theories can be formulated in a background-independent manner.

Contribution

It demonstrates that background-dependent theories can be reformulated to be diffeomorphism-invariant, clarifying misconceptions about the nature of physical observables in such theories.

Findings

Background-dependent theories can be formulated in a diffeomorphism-invariant way.

The difference in physical magnitudes between background-dependent and independent theories is less fundamental than commonly thought.

Misunderstanding of spacetime coordinates leads to misconceptions about background dependence.

Abstract

Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the "observables") of background-independent theories and those of background-dependent (non-diffeomorphism-invariant) theories are essentially different in nature. I argue against both claims. Background-dependent theories can be formulated in a diffeomorphism-invariant manner. This suggests that the nature of the physical magnitudes of relevantly analogous theories (one background free, the other background dependent) is essentially the same. The temptation to think otherwise stems from a misunderstanding of the meaning of spacetime coordinates in background-dependent theories.