Sometimes I wonder if it actually possible to prove the action-reaction principle. I do know that Newtons laws are empirical but then if you think about the third law it says that in interaction between two bodies they exert equal and opposite forces on each other. Now what happens in the collision between two classical bodies is purely determined by the laws of electromagnetism and in Coulombs law, the action reaction principle is built in directly. The same can be said about interactions which involves gravity - here the action-reaction principle is also just a purely mathematical thing in the law of gravitation. So was Newtons observation of action-reaction not just a manifestation of these two laws?