Relativity and Covariance

Abstract

Following the inception of General Relativity, a dialogue ensued between A. Einstein and E. Kretschmann concerning the status of the Principle of General Covariance. Einstein supposed it to have physical content whereas Kretschmann proved that all lawlike statements of physics are expressible in generally covariant form. Einstein finally concurred with Kretschmann. Subsequently, M. Bunge argued that all covariance principles are metatheoretical, i.e. their referents are not physical patterns but theories. However, recently, J. L. Anderson argued that the imposition of covariance requirements restricts the possible forms of the laws of a given theory, indicating that they do have physical content. We show that there is an element of truth in both positions. However, the dispute has rested on a confusion between principles of covariance and principles of relativity, the former being formal and the latter being physical. We distinguish between the covariance group and the relativity group of several theories in support of our contention.