A note on the physical interpretation of Weyl gauging

Abstract

A possible physical justification of the Weyl gauge procedure is proposed. It is argued that in the case of a general affine connection geodesic parameters have a nontrivial functional relation to metric interval. Since geodesic parameters can also define a notion of interval (via Schild's ladder), we appear to have an inconsistency at the very foundation of any theory which incorporates a nonmetric-compatible connection. This inconsistency can be removed by postulating the Weyl transformations as a valid symmetry of nature, at least at the appropriate energy scale. The method would appear to work even in theories containing shear, provided that it too acquires a mass as a result of (or prior to) the breaking of Weyl symmetry.