Quantum mechanics are at the basis of many semiconductive effects, and so, are the basis of current electronics.
Photons may be massless, but its not void of momentum. The equation E^2 = (m0 * c^2) + (p^2 * c^2) , which is the actual general equation for energy in relativity (from which it can be simplified in many cases to the E=mc^2 equation) gives us a little hint at why. That is how light sails can propel themselves.
I am aware of how Solar sails work; I referenced them in the original post with an (admittedly vague) explanation.
Quantum mechanics are offered as an explanation of how electronics work, but the mechanics themselves are not necessary knowledge. Even so, it would not follow the mechanics we use as a model are complete or fully accurate: Newton is all the evidence you need of that.