  The goal of this article is to establish general principles for high
frequency dispersive estimates for the $p$-form Laplacian with relative
boundary conditions on co-closed forms. In dimension $3$ for the case $p=1$, we
show that the propagator corresponding to Maxwell's equations on compactly
supported co-closed forms satisfies the same dispersive estimates as in
$\mathbb{R}^3$ for the corresponding wave equation in the exterior of a ball --
but only for certain polarizations. In particular we show that some, but not
all, polarizations of electromagnetic waves scatter at the same rate as the
usual wave equation and this rate is not expected to hold in general. The
Dirichlet Laplacian wave equation $L^1-L^{\infty}$ scattering rate does not
hold true for the $1-$form Laplacian with relative boundary conditions by
itself in the exterior of a sphere, or any smooth obstacle for that matter. We
also do not expect it to hold in general for Maxwell's equations because of the
presence of $L^2$ harmonic $1$ forms.
