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Photons are considered mass-less particle with a specific velocity but according to the electromagnetic theory, a photon is considered to have both energy and momentum. So what happen when they are emitted, do they accelerate to reach the speed of light or is it somehow instantaneous?

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Photons do not accelerate, they either move at the speed of light or not at all, in which case they do not exist. Special relativity tells us that massless particles cannot move at velocities below the speed of light. So if a photon is created, it instantaneously moves at full speed.