(Henry Spencer) wrote:

(If the mirror is held stationary -- relative to the observer who is
measuring the details -- by some means, then there can be no Doppler shift.
But there is also no work done on the mirror, since work is thrust times
*distance*, and hence there is no added kinetic energy.)

I don't understand the above statements.
The mirror will definitely still be accelerated even if an arbitrary
observer is attached to it.
Also, there'll be a Doppler shift to the photons in any
non-accelerating reference frame.