Hard part of this concept is that how these fiels are acting on each others. We already know most of the theory. You cannot hit the electro-magnetic field. Who can change it is only the time. Thus, you which is a mass like a stone does not act on the electro-magnetic field, but the time.
Answer can be only one.
The electro-magnetic field, together they create the mass. We know that the electric field can induce the magnetic field as time goes by, and we know the mass induces the electro- magnetic field as time goes by. So, I wonder why nobody could solve the problem. Reason was quite simple. It was commutative version of Hamiltonian.