You have a perfect ball of mirrors with no gaps, and a lightbulb inside. If you turned the lightbulb off, would it still be light inside?
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As the photons get reflected from the perfect mirror, some momentum, and therefore energy, will be coupled into the sphere as a mechanical force. Some of this transfer will cancel out (as the sphere will 'bounce back', and give the next reflected photon an extra kick)
However, these vibrations in the material of the sphere, will cause mechanical work and therefore heat up the sphere, which will radiate that heat from its outside surface.
Explanation:
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Yes. It would be there.
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