The role of representational conventions in assessing the empirical significance of symmetries

TL;DR

This paper investigates the direct empirical significance of symmetries in gauge theories, proposing a rigorous, general definition that clarifies previous ambiguities and relates to representational conventions and gauge invariance.

Contribution

It introduces a new, general definition of direct empirical significance of symmetries that applies to all states, clarifying previous approaches and their limitations.

Findings

Provides a rigorous, state-independent definition of DES in gauge theories.

Clarifies the role of representational conventions in assessing symmetry significance.

Dispenses with the need for generic states in analyzing DES.

Abstract

This paper explicates the direct empirical significance (DES) of symmetries in gauge theory, with comparisons to classical mechanics. Given a physical system composed of subsystems, such significance is to be awarded to physical differences of the composite system that arise from symmetries acting solely on its subsystems. So my overarching main question is: can DES be associated to the local gauge symmetries, acting solely on subsystems? In local gauge theories, any quantity with physical significance must be a gauge-invariant quantity. To attack the question of DES from this gauge-invariant angle, we require a split of the state into its physical and its representational content: a split that is relative to a representational convention, or a gauge-fixing. Using this method, we propose a rigorous definition of DES, valid for any state. This definition fills the gaps in influential previous construals of DES. In particular, Wallace's need to specialize to `generic' states is explained and dispensed with.