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can you accelerate a photon?

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1) Depends on what you call "accelerate". Light can be bent. In a sense, you could call that acceleration. In a sense, you could say that therefore photons can be accelerated.

2) I'd be careful with the statement "like any other elementary particle". Defining an acceleration for an electron may be rather straightforward (just treat it like a classical point-sized particle with charge), whereas defining an acceleration for a gluon sounds way more tricky than for a photon (defining a gluon already sounds pretty tricky to me).

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