Substantive general covariance: Another decade of dispute

Abstract

John Earman's recent proposal that a substantive version of general covariance consists in the requirement that diffeomorphism invariance be a gauge symmetry is critically assessed. I argue that such a principle does not serve to differentiate general relativity from pre-relativistic theories. A model-theoretic characterization of two formulations of specially relativistic theories is suggested. Diffeomorphisms are symmetries of only one such style of formulation and, I argue, Earman's proposal does not provide a reason to deny diffeomorphisms the status of gauge transformations relative to this formulation. Carlo Rovelli's distinction between passive and active diffeomorphism invariance is also clarified. © 2010 Springer Science+Business Media B.V.