“Photons don’t experience time” is a consequence of something called the Lorentz Transformation, which is a consequence of Einsteinian Relativity.
The idea is that time dilates as you approach the speed of light. That means that the closer you get to c, the slower you feel time move. (in comparison to whatever clock you define as stationary.)
But this effect approaches 0 as speed approaches c, so the only logical conclusion is that things traveling *at* c perceive 0 time. We of course cannot know what photons or other massless particles perceive, but there isn’t much of an option to say that they do experience time.
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