Empirical Equivalence, Artificial Gauge Freedom and a Generalized Kretschmann Objection

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 covari-ance as formal general covariance achieved without hiding preferred coor-dinates as scalar “clock fields, ” much as Einstein construed general covari-ance 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 philoso-phers, 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 bro-ken gauge symmetries (second-class constraints) using a modified Batalin-Fradkin-Tyutin (BFT) procedure. Massive GTR, for which parametriza-tion 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 parametriza-tion and BFT, while being more Lagrangian-friendly than BFT, leaving any primary constraints unchanged and using a non-BFT boundary con-dition. Artificial gauge freedom licenses a generalized Kretschmann ob-jection. However, features of paradigm cases of artificial gauge freedom might help to demonstrate a principled distinction between substantive and merely formal gauge symmetry. Key words: general covariance, gauge freedom, clock fields, constrained dy-namics, theory equivalence, Kretschmann objection