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Imagine you have a photon with momentum $p$ which hits a mirror $M$ and is reflected back.

Since $M$ is at rest in your frame of reference the total momentum of the system pre-reflection is $p$ and post reflection is $-p$.

This seems quite odd to me and a clear violation of conservation of momentum.

How this can be resolved:

The mirror begins to move/absorbs some momentum after being hit by the photon, but if the photon was reflected with momentum $p$ then we end up having conservation of kinetic energy being violated.

The only conclusion that's reasonable is the photon being reflected back has a different (probably lesser) momentum after hitting the mirror and the mirror then picks up some positive momentum, so that the sum of the momenta remains constant and the sum of their kinetic energies remains constant.

Is this actually what happens? And if so does that mean that almost all mirrors are heating up when they are reflecting photons?

Qmechanic
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Sidharth Ghoshal
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  • yep it does answer it – Sidharth Ghoshal Dec 11 '20 at 21:54
  • I think your question is different from the proposed question. In general of course the loss of energy during any energy conversation (in your case from photon to momentum on the mirror and back into a photon) takes place because of the energy dissipation (phonons and so on). But maybe you want take a closer view of how the momentum works. see here https://upload.wikimedia.org/wikipedia/commons/thumb/6/68/Lasercooling_Streuvorgang.svg/2000px-Lasercooling_Streuvorgang.svg.png. – HolgerFiedler Dec 12 '20 at 09:05
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    It is a really nice sketch because it shows that the re-emissioned photon could be emitted in a different direction as zh incoming one. THIS is the reason for the phonons (vibrations inside the mirror, leading to infrared radiation at the end). An ideal mirror simply does not exist. To your question: The conservation of energy is not violated. The conservation of momentum is not violated if you include the momentum of the photons and phonons and all the other exitations. – HolgerFiedler Dec 12 '20 at 09:10

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