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What does it mean when somebody, let's say a random person on the crosswalk waiting for the sign to go green, say that a "photon is a propagator of the Electromagnetic field"? I don't know if it's a dumb question, I just stumbled upon that sentence and wondered what it really meant.

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Most physicists wouldn’t say that. Instead, they’d say that photons are quanta of the electromagnetic field. There’s only one EM field, throughout the universe, and all photons are quanta of this one field. You can crudely think of quanta as particle-like excitations of the field.

A “propagator” in physics is a mathematical function of two points that gives the probability amplitude for a particle to go from A to B. So there is a “photon propagator” function, but saying that the photons themselves are propagators is nonstandard terminology.

Sometimes photons are said to “mediate” or “carry” the electromagnetic interaction between charged particles. In classical electrodynamics, this is what the electromagnetic field does. In quantum electrodynamics, this is what the field’s quanta —- “real” and “virtual” photons — do. (Or at least they do Feynman’s perturbative approach to QED.)

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