One way of thinking about it is that light has zero mass.
Neutrino’s also have almost zero mass, they are tiny, about 500,000 times less massive than an electron. They also always move at essentially the speed of light. In fact, so fast do neutrinos move, I don’t think we’ve ever measured it accurately enough to confirm they move slower than the speed of light. For a long time we weren’t sure if they had any mass or not, because they always appeared to move at the speed of light, within the precision of our ability to measure their speed. We now know that they do have a tiny mass, from other methods. I think it took 40 years after discovering neutrinos, to discover they did have non-zero mass.
If having no mass confuses you, it shouldn’t. In Quantum Field Theory, mass is just another field (the Higgs), so having no mass is really no different to having no electric charge, and thus not interacting with the Electromagnetic Field at all.
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