Propagation of singularities along characteristics of Maxwell's equations

We give a new proof that electromagnetic waves predict geometry, based on studying the propagation of singularities in first-order derivatives of generalized solutions (E, H) to Maxwellʼs equations. As a byproduct, the growth of the intensity of the jumps in (∂E/∂t, ∂H/∂t) across a characteristic hypersurface is shown to be homogeneous of degree −1. We determine generalized solutions (whose first-order derivatives have jumps across a fixed characteristic line) to the initial value problem for Maxwellʼs equations in one space variable.