  Extraneous motion of optical elements in an interferometer lead to excess
noise. Typically, fluctuations in the effective path length lead to phase
noise, while beam-pointing leads to apparent amplitude noise. For a
transmissive optic moving along the optical axis, neither effect should exist.
However, relativity of motion suggests that even in this case, small
corrections of order $v/c$ ($v$ the velocity of the optic), give rise to phase
and amplitude noise on the light. Here we calculate the effect of this
relativistic mechanism of noise coupling, and discuss when such an effect would
limit the sensitivity of optical interferometers.
