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Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact.
There is a better question, IMV, how do you prove em waves actually travel through a vacuum? After all, a photon moves at the speed of light relative to an observer so to a photon it doesn't travel through anything, it just is. Instantly. Alec Cawley, A very rusty first degree in Physics. But I have kept up with the subject at ...