Extracting energy from a static electric field with capacitors

Suppose that we have a pointlike charge static in space.

                         _____________

                  ___|___

                  _______    capacitor

                       |_____________

          

                       ● negative charge

We can extract energy from the static field of the charge with a capacitor. In the diagram, the charge will repel electrons to the upper plate of the capacitor. If we put a resistor to the wire connecting the plates, we get energy in the form of heat.

Does this show that energy is contained locally in the electric field of the charge?

The charge might be far away and would not even know that we connected the capacitor plates and started extracting energy.

If we explain the process with Coulomb forces, then the charge will not know about the extraction after some time, because of the finite speed of light. This is called retardation.

Let us make a thought experiment. We put so many capacitors so close to the charge that we can extract more energy than is the mass-energy of the charge itself. That would break conservation of energy.

We do not believe that conservation can be broken. The capacitors have to "negotiate" with the electron if there is still mass-energy available which they could take.

If there is no more mass-energy available, Nature solves the problematic situation with annihilation.

We see that the huge energy density close to the charge cannot be utilized without asking the charge first - in this sense we may claim that the huge energy really is "located" inside the pointlike charge.

Transactional interpretation of quantum mechanics

https://en.wikipedia.org/wiki/Transactional_interpretation

In a Feynman diagram, the time order of close encounters, emissions, and absorptions is insignificant. As if Nature would perform transactions. Inside a single transaction, the time order of various operations does not matter. The crucial thing is that either all operations succeed, or none at all.

The Wheeler-Feynman absorber theory tries to extend the transactional paradigm to cover an emission of a photon today to the absorption of the same photon a trillion years from now (in a Big Crunch, for example). That is counter-intuitive, and the absorber theory has gained little acceptance.