I don’t know that we can explicitly state they don’t experience time. However, the experience of time for an object relates to the frame of reference in which it is stationary. Massless objects don’t have a stationary reference frame, they move at c in all frames of reference. So a stationary frame of reference is undefined.
In other words, if you’re in a train going at 60mph, we can pick a frame of reference where you’re stationary and the earth is going past you at 60mph, and we can talk about what time means to you in it. A massless particle has no such frame of reference.
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