Symmetries, Indexicality and the Perspectivist Stance

Abstract

I critically examine the assumption that the theoretical structure that varies under theoretical symmetries is redundant and should be eliminated from a metaphysical picture of the universe, following a "symmetry to reality" inference. I do so by analysing the status of coordinate change symmetries taking a pragmatic approach. I argue that coordinate systems function as indexical devices, and play an important pragmatic role for representing concrete physical systems. I examine the implications of considering this pragmatic role seriously, taking what I call a perspectivist stance. My conclusion is that under a perspectivist stance, all symmetries (including local gauge symmetries) potentially have a direct empirical status: they point to dynamical aspects that are invariant under changes of operationalisation, and they constitute a guide not to reality, but to nomology and kinship.Note, however, that the authors concerned with the debate on DES present their case using the traditional formulation of physical theories, with all their "surplus structure." And that for a good reason: a reduced theory has no symmetry, so trivially, no symmetry of this theory can have DES. Galileo's ship would be represented by the same model in a reduced theory, or by the same sub-structure of a model, whether it is moving or not; a distinct part of a model encompassing the shore and the ship, representing the distance (or the region) between the two, would vary in the two situations, but the part that represents the ship would be identical. Arguably, reduced theories still explain why one cannot tell whether Galileo's ship is moving from the inside, but without appealing to symmetries: the explanation is simply that Galileo's ship is in the same state in both cases. Friederich (2015) draws the same conclusion with regards to local symmetries (in non-reduced theories), after arguing that they have no DES: "what appear to be two physically distinct yet empirically indistinguishable subsystem situations [. . . ] turns out to be one single physical subsystem situation." This conclusion comes out naturally with reduced theories.However, scientists do not use reduced theories either when representing concrete physical systems. This could be because reduced theories are more difficult to handle. But most of the time, they do not even use coordinate-free formulations of non-reduced theories, except in foundational discussions (Wallace 2019b). As remarked by Belot ( 2018), the received view, among scientists, is that translations and rotations applied to a model do represent a genuine physical change (or at least they can represent such a change).So, part of our original puzzle remains: if what is real is what is invariant under symmetry, and if the aim of science is to describe reality, why aren't scientists and philosophers doing away with coordinate systems or gauges when representing physical systems, or the universe as a whole? And why should we assume that any symmetry has empirical significance if, ultimately, theories without symmet...

Symmetries and Representation

“…The plurality of admissible interpretations associated with a model are then those states of affairs such that, for some context, the character of the model maps that context to one of those states of affairs. For a recent article on the connection between indexicality and symmetries in the context of physical theories see Ruyant (2021). from models to admissible interpretations is correct will depend on which theory we are talking about and the norms that the users of that theory employ.…”