  The dependence of macroscopic radiation pressure on the velocity of the
object being pushed is commonly attributed to the Doppler effect. This need not
be the case, and here we highlight velocity dependent radiation pressure terms
that have their origins in the mixing of s and p polarizations brought about by
the Lorentz transformation between the lab and the material rest frame, rather
than in the corresponding transformation of frequency and wavevector. The
theory we develop is relevant to the nano-optomechanics of moving bodies.
