To consider the electromagnetic field as fundamental, and the metric only as a subsidiary field

Abstract

In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant and metric-independent way. The electromagnetic field is then given in terms of the excitation $H=(H,D)$ and the field strength $F=(E,B)$. Additionally, a local and linear ``spacetime relation'' is assumed between $H$ and $F$, namely $H \sim κF$, with the constitutive tensor $κ$. The propagation is studied of electromagnetic wave fronts (surfaces of discontinuity) with a method of Hadamard. We find a generalized Fresnel equation that is quartic in the wave covector of the wave front. We discuss under which conditions the waves propagate along the light cone. Thereby we derive the metric of spacetime, up to a conformal factor, by purely electromagnetic methods.