We propose two feasible experimental studies of the interaction of lig
ht with linearly accelerating media. First, sidebands are induced in t
he output spectrum of a Mach-Zehnder interferometer when a dielectric
in one arm is oscillated parallel to the beam. Second, linear accelera
tion of a dielectric in a.ring cavity will induce asymmetry in the nea
r-resonant optical response profile. Both experiments probe the intera
ction of photons with inertia by testing the covariant formulation of
Maxwell's equations used here and so the related assumption that the l
ocal optical properties of a medium are unaffected by acceleration. Th
e second experiment is explicitly sensitive to a Doppler shift induced
when light propagates through linearly accelerating media, predicted
by Tanaka [Phys. Rev. A 25, 385 (1982)]. Observation of this Doppler s
hift would confirm a manifestation of the coupling between radiation a
nd matter in a noninertial context.