I have some confusion about potential energy in Newtonian mechanics and field energy in classical Field mechanics. I have many questions but they are all strongly related.
In Newtonian mechanics, we analyze a system of two particles A & B attracted to each other by a conservative force, and say that there is kinetic energy and potential energy. Kinetic energy depends on their masses and velocities, and potential energy depends on their distance.
Is it correct to say that particle A has kinetic energy? I think so, since it depends solely on properties of that particle.
If so, is it correct to say that such kinetic energy is located within particle A?
Is it correct to say that particle A has potential energy? Maybe not, since it depends of the distance between both particles. On the other hand, we can assign a part of the potential energy to particle A and the rest to B. And by taking those derivatives we obtain the force that acts on each one, separately. So I'm not sure if it's a property of the system as a whole, or of each separate particle.
If so, is it correct to say that such potential energy is located within particle A?
On the other hand, there is Field mechanics for that same system. We say that there is an attractive field. And that this field has energy.
If we introduce fields and field energy, then we must discard potential energy, right? They are alternate expressions of the same thing?
Does each point in space has some field energy located within it? Or is that just for calculating purposes, and the field energy is considered to be just a property of the whole system?
Finally, is it any more correct to talk about field energies than to talk about potential energies? Or are they completely equivalent models?