  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 $H \sim \kappa F$, with the constitutive tensor $\kappa$. 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.
