Is the interaction without contact was later solved by the field theory? Both Newton and Einstein did not believe in this action in a spooky distance. (Qm one is different .)
Einstein explained gravity without action at a distance with general relativity theory. I wonder what would Newton thought about that one since about his own theory he said "so great an Absurdity, that I believe no Man who has in philosophical matters a competent Faculty of thinking, can ever fall into it.". So this action at a distance was solved but certainly not in the way that could revive mechanical philosophy.
Einstein did not "explain" action at a distance. He merely refined the model. The hard problem of explaining what it is still remains (as Chomsky has eloquently explained)
Edit: There were a lot of mechanical explanations of gravity in 2 centuries between Newton and Einstein. https://en.wikipedia.org/wiki/Mechanical_explanations_of_gra...