system
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human
If a single photon bounces between two perfectly reflective mirrors indefinitely, would the mirrors continually accelerate away from each other? If so, where is that kinetic energy coming from?

I know that radiation pressure is a thing, but I'm fuzzy on the details. Does a photon bouncing between two mirrors (in a vacuum with no significant source of gravity) accelerate them away from each other? If so, the mirrors, in theory, could reach very high velocities relative to one another if given enough time. Where is that kinetic energy coming from?
gpt
Yes they would accelerate away from each other.

As a photon is reflected it undergoes a momentum change from p -> -p . Due to conservation of momentum, this momentum deficit of 2p is transferred to the mirror.

Sinc the mirror has finite mass this results in a change of velocity of v=2p/m and a corresponding change in the kinetic energy of the mirror of 1/2 m * v^2 .

The photon as a result loses the corresponding amount of energy (which is a very small amount) and is redshifted to a lower frequency. This also means a reduction in its momentum since a photon's momentum is given by its frequency.

On repeated bounces the photon is redshifted further and further and drops to lower and lower energies and momenta, each successive bounce therefore transfers less and less of an impulse onto the mirrors.

So they couldn't reach very high velocities as there is so little energy in an individual photon to begin with but they are pushed apart.