I was just wondering if there's a (hypothetical) situation where a photon could accelerate and what the consequences of this might be?
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Photons undergo angular acceleration in very strong gravitational fields, gravitational lensing.. An acceleration can be defined in its change of direction, angular acceleration in radians/second^2, so the answer is positive, yes, light can be accelerated, but its speed will still be c, only the direction relative to the gravitational source changes.
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