General-Relativistic Covariance

Abstract

This is an essay about general covariance, and what it says (or doesn't say) about spacetime structure. After outlining a version of the dynamical approach to spacetime theories, and how it struggles to deal with generally covariant theories, I argue that we should think about the symmetry structure of spacetime rather differently in generallycovariant theories compared to non-generally-covariant theories: namely, as a form of internal rather than external symmetry structure.

Geometrical Constructivism and Modal Relationalism: Further Aspects of the Dynamical/Geometrical Debate

“…[45, §5.2.1]). 14 Indeed, the same account will go through if such spacetime is construed as a modal constraint of the kind discussed above; it will, indeed, go through (I claim) on any reasonable absolutist account of spacetime structure. Indeed, in a sense such constructive explanations are 'one level deeper' than the constructive explanations offered by advocates of the dynamical approach: they explain why the fundamental laws governing matter have certain symmetries, and in turn explain why special relativistic effects are observed.…”

“…For example: which symmetries are relevant-'internal' or 'external'? (For discussion of this issue, see[14].) Second: how is this ontological reduction supposed to work?…”

“…[22, p. 179] Frisch is correct here, if we read Einstein as identifying constructive and fundamental explanations. We have, however, already seen that these two notions can be teased apart 14. In the context of universally coupled massive scalar gravity (see[35,36,34,37]), or bimetric theories more generally, one might be able to point to one metric field (say η ab ) to explain some aspects of the laws-but perhaps not all of them, in light of the coupling of the other metric field.…”

New Perspectives on the Hole Argument

“…Finally, in his paper "General-Relativistic Covariance," Dewar [12] comes at a closely related set of issues-concerning the hole argument, symmetries, and structure-from a different direction. He develops an account of the "general covariance" often attributed to general relativity.…”

Newtonian Equivalence Principles

“…But this does not go all the way to addressing the concerns raised in e.g. (Dewar 2020;Fletcher 2020;Weatherall 2021): that, however, will have to wait for a future piece.…”