Is it possible to apply force to a light particle? I know, the universal speed limit is the speed of light $c$.  So, is it possible to apply more force to a light particle?  What would happen to it if we could?
 A: A force is defined as a change in momentum over time. In the Newtonian limit, this means a mass times an acceleration. But when dealing with things like photons, the formal definition is applied.
Photons have no mass, only momentum. Therefore, if a force is applied to them, their momentum can be changed. This can happen in two important ways, a force can change the direction or the magnitude of the momentum. Changing the direction means the light is reflected, scattered, refracted, or curved. Changing the magnitude means that the frequency of the light is changed. Gravity can accomplish this as can a reflection off of a moving object (nothing can hit a photon from behind, so any momentum change from hitting the photon will have to reflect it).
Gravity can and does apply force to photons. When entering a gravity well, the photon falls in. It gains momentum, as most inward falling objects do, which blue-shifts the frequency. When leaving a gravity well, the photon loses momentum, which red-shifts the frequency.
