The basis on which Weyl’s unified theory of gravitation and electromagnetism was rejected is reconsidered from a new perspective. It is argued that while Weyl’s theory, as indeed any classical theory, is incapable of explaining atomic phenomena, this does not nullify the geometric interpretation of the exterior electromagnetic field; it simply reflects the fact that some form of quantization is needed to account for atomic standards of length. In support of this argument the Gauss-Mainardi-Codazzi formalism is employed to demonstrate that it is possible to construct a bubble in Weyl space where the exterior geometry is conformally invariant and the electromagnetic field can be given a geometric interpretation, while at the same time a standard of length can be introduced into the theory by breaking the conformal invariance in the interior of the bubble.

• Received 8 August 1991

DOI:https://doi.org/10.1103/PhysRevD.45.3617