In this forum we are concerned about potential energy, so let us take Coulombs force law and look at the integral from r to r = (infinity) and one can clearly see that something is wrong.

*Eq1. Electrical potential energy as a function of radius*

As we can see this equation predicts all matter should have infinite energy, because protons with a charge of +1 and electrons with a charge of -1 are clearly a finite distance apart, and somehow had to get from zero to some distance r, without using an infinite amount of energy. Therefore we are looking for a minimum radius at which individual charges first come into play, beyond which this equation holds true.

So how do we determine this radius, and is this minimum radius a konstant, or is it a function of something else?

Well let us consider pair production, experiment shows that pairs are created when the energy of a photon exceeds 1022 keV, or 2 * 511 KeV per particle. It is surely no coincidence that this also happens to be the energy of an electron.

I think we can safely draw the conclusion that the minimum radius for the above equation is the radius where the potential energy equals 511 keV. Now if we are to believe Ground Potential theory, then this radius is a variable, and will be a function of the observers potential.

*Eq.2 Electron radius based on electron energy*

What this says, is that the minimum radius between two charged particles is when the potential energy is equal to the energy of the electron, which just happens to 511 keV at this moment in time.

We can write a more general equation as follows;

*Eq3. General extpression for electron radius (∂ø = difference between proton potential and ground potential)*

The interpretation of this result is that potential energies lower than the potential of the electron lies outside the observers domain, and are therefore not observable. This is consistent with Ground Potential theory, which postulates a minimum and maximum potential for any observer.

We can test this equation in Wolfram Alpha as follows;

(Coulombs Constant * (elementary charge)^2)/(8.18712225*10^-14 joules)

Which gives the result;

Which agrees with the classical electron radius.

http://en.wikipedia.org/wiki/Classical_electron_radius

Steven