In discussing this question about propelling a spacecraft with photons and their relativistic momentum, the author asked that I restate my comment as another question.
If photons can really be used for propulsion, could two mirrors be affixed between two objects, focused well and continually adjusting their respective 'where they will be at the time of light arrival', and use the same photons bouncing back and forth between the two objects for perpetual thrust after the initial photon generation?
The initial question was on an assignment problem:
"A rocket of mass $m_0$ is propelled by a giant monochromatic laser mounted on the back of the rocket. The laser emits a beam with a power of $P_0$ watts and a frequency $f_0$, both measured in the rest frame of the rocket. When the beam is turned on, the rocket is driven in the opposite direction by the recoil."