Relativity without miracles

Abstract

It has been claimed, recently, that the fact that all the non-gravitational fields are locally Poincaré invariant and that these invariances coincide, in a certain regime, with the symmetries of the spacetime metric is miraculous in general relativity (GR). In this paper I show that, in the context of GR, it is possible to account for these so-called miracles of relativity. The way to do so involves integrating the realisation that the gravitational field equations (the Einstein field equation in GR) impose constraints on the behaviour of matter in a novel interpretation of the equivalence principle, which dictates the determination of local inertial frames through gravitational interaction. This proposed explanation of the miracles can also deal with the problematic cases for attempts at explaining them in the context of the standard geometrical perspective on relativity theory.

Miracles persist: a reply to Sus

“…In a recent article in this journal Sus (2021) argues that what Read et al (2018) dub the 'two miracles' of general relativity-that (1) the local symmetries of all dynamical equations for matter fields coincide, and (2) the symmetries of the dynamical equations governing matter fields coincide locally with the symmetries of the metric field-are after all derivable from innocuous assumptions on the matter sector of that theory. In Sus' words, the Einstein field equation constrains the equations for the non-gravitational fields by imposing that, insofar as such fields are sources for the gravitational fields, such equations must be locally Poincaré invariant, and the motion of force-free bodies is approximately geodesic.…”

“…One might legitimately raise the concern that all work on the 'two miracles' of general relativity is stymied by the lack of precision in these discussions-in particular, regarding the notion of 'local symmetries' which these discussions deploy (See, for example, Weatherall (2021, Section 3.1) for a pointed critique in this regard). Although in our view appeal to recent work such as that of Fletcher (2020) can go some way to resolving these issues, for the purposes of this note we do not engage with these discussions: rather, our focus lies solely on Sus' argument, as presented in Sus (2021), and we accept the shared premises of Read et al and Sus-in particular, regarding the meaningfulness of the centrally-employed notion of 'local symmetry' in the sense of form-invariance of mathematical structures defined at each point of the manifold under specific coordinate transformations, such as those of the Poincaré group. 1…”

“…Read et al (2018),Sus (2021), and ourselves all make use of the notion of a fixed field presented by Pooley in(Pooley 2017, p. 115)-such an object is a field fixed identically in all kinematical possibilities of a theory. In addition, all three parties can be taken to accept the understanding of diffeomorphism invariance presented inPooley (2017, p. 117), for which the salient transformations are those which transform dynamical fields, but not fixed fields.…”

What spacetime does: ideal observers and (Earman's) symmetry principles

“…For a defence of the 'miracles' view, see(Read et al, 2018;Read, 2019;Read, 2020) for a critical perspective on it:(Sus, 2021;Weatherall, 2021).5 Myrvold (2017) provides an explicit defence of this perspective, while(Acuña, 2016;Knox, 2019;Read et al, 2018) can also be taken as partially endorsing such a view. See(Sus, 2019(Sus, , 2020 for critical takes on this (Norton, 2008;Hagar and Hemmo, 2013).…”