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If photons have no mass, and yet have energy, how is that compatible with $E=mc^2$? Anything having mass should have energy (and the opposite should be true as well no)?

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$E=mc^2$ is a statement about energy in the rest frame. The photon rest frame does not exist but one can approach it in principle by moving along with a photon at near light speed. The photon will be red shifted and its energy will approach zero. In this limit $E=mc^2=0$.

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    $\begingroup$ Very helpful, thanks a lot! $\endgroup$
    – GaelF
    Apr 21, 2020 at 9:36

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