When it comes to a spaceship moving through space, I suggested in an earlier post that the torrent of blue-shifted photons coming from the front of the spaceship would slow it down if its engine was turned off.
On further reflection, it is clear to me that this is not the case. Random photons coming from outside of the local reference frame does not affect the speed of the spacecraft.
The reason for this becomes clear when we consider what would happen if we moved a two sided mirror through space in such a way that it reflects photons coming from the front and back.
At rest, such a mirror will reflect photons perfectly from both sides. Nothing happens to the photons as they hit the mirror. They change their direction. That's all.
However, as the mirror speeds up, the photons hitting the mirror from the front receive energy from the mirror. Returning back into space, the photons are blue-shifted.
From this alone, it is tempting to conclude that the mirror must slow down. However, the photons coming from the back will compensate by yielding energy to the mirror.
This is because the photons coming from the back hit the mirror in such a way that they would have slowed down if they were made of ordinary matter. But photons cannot slow down. They must therefore red-shift in order to keep their speed.
A mirror moving through space shifts energy from photons hitting it from behind over to photons hitting it from the front. In the process, there is no net gain or loss of energy for the mirror. It neither slows down nor speeds up. It continues unaffected.
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