Is Newton's third law merely a consequence of the laws of universal gravitation and Coulomb?

Question

Can it be said that Newton's third law is simply the fact that gravity and electromagnetism do obey an action/reaction principle (as per $\vec{f}_{grav,12}=G\frac{mm'}{r^2}\vec{e}_{12}$ and $\vec{f}_{elec,12}=\frac{qq'}{4\pi\varepsilon_0}\vec{e}_{12}$ which are experimental facts, at least in classical physics), and that at the all the forces that we consider in Newtonian mechanics (if one rules out magnetic and time-dependant electric phenomena) originate from these two? This would certainly explain why the third law fails for magnetic forces (see Newton's Third Law Exceptions?). In this picture the 'correct third law' would be the conservation of momentum, field momentum included, from which one could retrieve action/reaction under certain hypotheses (in the static regim for instance).

Answer 1

Newton's third law expresses conservation of momentum and is of general validity. It only requires that the system is translation invariant. Force is defined as rate of change of momentum, thus the sum of all forces is zero. An exception is the magnetic force, which is not the derivative of momentum.