Empirical Equivalence, Artificial Gauge Freedom and a Generalized Kretschmann Objection

TL;DR

This paper explores the concept of artificial gauge freedom in physical theories, proposing a generalized procedure to install gauge symmetries and analyzing their substantive versus formal nature, with implications for understanding general covariance.

Contribution

It introduces a generalized method for installing artificial gauge freedom that unifies and extends existing procedures like parametrization and BFT, clarifying the distinction between substantive and formal gauge symmetries.

Findings

A generalized gauge installation procedure that is more Lagrangian-friendly.

Analysis of the Kretschmann objection in the context of artificial gauge freedom.

Insights into the distinction between substantive and formal gauge symmetries.

Abstract

Einstein considered general covariance to characterize the novelty of his General Theory of Relativity (GTR), but Kretschmann thought it merely a formal feature that any theory could have. The claim that GTR is "already parametrized" suggests analyzing substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar "clock fields," much as Einstein construed general covariance as the lack of preferred coordinates. Physicists often install gauge symmetries artificially with additional fields, as in the transition from Proca's to Stueckelberg's electromagnetism. Some post-positivist philosophers, due to realist sympathies, are committed to judging Stueckelberg's electromagnetism distinct from and inferior to Proca's. By contrast, physicists identify them, the differences being gauge-dependent and hence unreal. It is often useful to install gauge freedom in theories with broken gauge symmetries (second-class constraints) using a modified Batalin-Fradkin-Tyutin (BFT) procedure. Massive GTR, for which parametrization and a Lagrangian BFT-like procedure appear to coincide, mimics GTR's general covariance apart from telltale clock fields. A generalized procedure for installing artificial gauge freedom subsumes parametrization and BFT, while being more Lagrangian-friendly than BFT, leaving any primary constraints unchanged and using a non-BFT boundary condition. Artificial gauge freedom licenses a generalized Kretschmann objection. However, features of paradigm cases of artificial gauge freedom might help to demonstrate a principled distinction between substantive and merely formal gauge symmetry.