2009/11/28 by J. Brian Pitts, Pitts, J. Brian
Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph) #Quantum Mechanics and Applications #Relativity and Gravitational Theory #gr-qc #hep-th #physics.hist-ph
paper · pdf · doi:10.48550/arxiv.0911.5400
54 pages
arxiv created 2009/11/28 · openalex publication_date 2009/11/28 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.