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The change in speed of a photon with respect to time is 0 as photons travel at $c$ forever. If no change in speed exists, how can photons have momentum and acceleration? I guess they don't work like classical mechanics particles.

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    $\begingroup$ Duplicate of physics.stackexchange.com/q/2229/50583 $\endgroup$
    – ACuriousMind ♦
    Commented Sep 22, 2016 at 22:11
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    $\begingroup$ Why do you think a change in speed (or a non-zero acceleration) is necessary to have momentum? (Technically, only a change in velocity is necessary to have a non-zero acceleration. Speed is only the scalar length of the velocity vector. If the velocity changes direction, but not magnitude, the body is still accelerating.) $\endgroup$
    – wnoise
    Commented Sep 22, 2016 at 23:01
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    $\begingroup$ @wnoise sorry, I incorrectly believed that momentum equals mass* change in velocity. So photons have no momentum change, but have a momentum. I believe that the sum of force times the time elapsed equals mass times change in velocity, so force times time equals change in momentum $\endgroup$
    – user130451
    Commented Sep 22, 2016 at 23:08
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    $\begingroup$ Even for massive particles $m \,\Delta \vec{v}$ represents a change in momentum. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Sep 22, 2016 at 23:27

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Everything has momentum, even when acceleration is zero. Photons do not accelerate, they pop in and out of existence instantaneously and immediately travel at the speed of light. Their momentum and energy are proportional to their frequency.

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