Bounce light back and forth between mirrors forever?

[hxtasy]

[Mentors' note - this post was forked off from this thread because it's an interesting question in its own right]

I would also like clarification on this. if you throw a rubber ball at concrete, it will "bounce off". if you throw the rubber ball at mud, the mud will absorb it and it will stay there.

however both the mud and the concrete have absorbed some of the rubber balls energy, just different amounts. is this the same with photons? could you reflect light indefinitely..

 

[Nugatory]

is this the same with photons? could you reflect light indefinitely..

No. No matter how perfect the reflection, some small amount of energy has to be transferred to the mirror - this is required by conservation of momentum as the reflected light is reversing direction with each bounce. Thus the bouncing light loses a bit of energy with each bounce, just as does the bouncing ball. The big difference is that when the ball loses energy it slows down and eventually stops; light must always travel at $c$ so it doesn't slow down. Instead it's redshifted down to thermal wavelengths which are absorbed and turned into waste heat instead of being reflected - so as with the bouncing ball it all ends up as waste heat eventually.

It's a good exercise to calculate how long each "bounce" takes for a light signal moving between two mirrors a few meters apart. "Eventually" happens very quickly indeed.

 

[russ_watters]

Are you sure that's true? Seems to me that conservation of energy and momentum should just produce a container that shakes back and forth in place, whether it is a photon or a hypothetical perfectly elastic rubber ball bouncing back and forth in it.

Your description also suggests the light gradually redshifts out of existence.

My understanding was that imperfect reflection just means a certain fraction of photons are absorbed instead of reflected.

 

[nasu]

If it's in a box, the second wall will move towards the incoming particle for the second bouncing. So the particle will gain some energy after this second collision.

 

[Nugatory]

You're both right.