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> The paradox claims that the sky should appear bright, which I take to mean that a detector should be receiving light from each point in the sky at each moment in time.

I don't think this is required for the paradox. All that is required is that the average flux of radiation received from the sky as a whole should be constant, and equal, roughly speaking, to the flux corresponding to the surface brightness of a star. That will still be true, under the specified conditions of the paradox (a universe in steady state and infinitely old) even if quantization is taken into account.




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