[Richard777 (OP)]

Fundamental energies of mass and electric charge may be considered to be different forms of particle energies. Maybe they will combine with wave energy to give wave-particle energies.

Wave-particle energies may be considered to be different forms of potential energy.

Two massive objects are assumed to interact by an intersection of their potential energies. Can two charged objects also interact according to their potential energies?

[yor_on]

" Two massive objects are assumed to interact by an intersection of their potential energies. "

How would you go about proving that one? To me a 'potential energy' is nowhere, until you have a interaction that actually is measurable, aka a collision for example.

The way I think of it is that a single object can be said to have a immeasurable amount of different 'potential energies' at a same time, depending on what you define this energy versus. It's equivalent to uniform motion in where you also can be said to have a immeasurable amount of different 'uniform motions' at a same time, depending on from where you compare.

That you can count on your mass etc to give yourself a energy doesn't solve it.
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The point I'm getting stuck on is that a potential energy, although connected to relative motion, accelerations, mass and other forces is locally not there (measurable) until something really happens, just as a uniform motion can be seen to be.

To make it you need to introduce a 'universe', something 'enclosed' in some way, and then postulate something to be there that we can't measure locally.
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The only way I make sense of such a statement is when I think of geodesics actually. There it can be said that mass influence SpaceTime and vice versa. But I'm not sure that this is what you think of? Geodesics doesn't state that it need a 'enclosure' to exist, but the idea of potential energy might?
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What I mean is that you need a universe to get to the idea of 'potential energy' whereas a geodesic is a path of 'no/least resistance' that just as easily exist without a universe, well, sort of, playing with the thought :)

[Bored chemist]

Fundamental energies of mass and electric charge may be considered to be different forms of particle energies. Maybe they will combine with wave energy to give wave-particle energies.

Wave-particle energies may be considered to be different forms of potential energy.

Two massive objects are assumed to interact by an intersection of their potential energies. Can two charged objects also interact according to their potential energies?

That  post seems to contain a whole lot of novel terms that are not really defined.
What do you mean by these phrases?

 forms of particle energies.
 wave energy
Wave-particle energies
 an intersection of their potential energies.