For example, suppose our mirrors are one atom wide and distanced one light-second apart. Initially, our ship is "stationary" (purely inertial) and a photon is emitted from one of the (half-silvered or what have you) mirrors. Two seconds elapse, and the photon returns to strike the emitter, just as expected. Now a second photon is emitted, but immediately thereafter the engines are throttled up and the ship lurches forward some distance. Clearly, the returning photon must necessarily miss it's mark. Shut off the engines (whatever the speed) and the results of the experiment once again demonstrate straight-line propagation; "being stationary" and "moving at a constant speed" are equivalent (and thus completely indistinguishable) states.
Ergo, a photon emitted from an inertial reference frame is somehow "resonant" to that frame, in the sense that it acts much like an ordinary particle would by obeying straight-line paths with respect to that frame. Conversely, non-inertial frames (including gravitational fields) bend or deflect the path of light.