Light interacts with matter all the time. Blue skies, green leaves, and the colors of the rainbow all come about because of the scattering of light. But light doesn’t scatter off itself. In fact, under Maxwell’s equations, which originally defined electromagnetism, light can’t scatter off itself.
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As with many other things, however, quantum mechanics showed that what we thought was impossible is possible: a photon can, technically, scatter off another photon. But that was recognized back in the 1930s, and we’ve not been able to confirm that it actually happens.
Until now, that is.