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 Maxwell's equations. As a byproduct, the growth of the intensity of the jumps in (partial derivative E/partial derivative t, partial derivative H/partial derivative 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 Maxwell's equations in one space variable.