Empirical Equivalence, Artificial Gauge Freedom and a Generalized Kretschmann Objection

摘要

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