The classical electron radius
The "classical electron radius" arose from the analogy with charged macroscopic hollow spheres, and it describes a
charged hollow sphere with the distribution of the elementary charge on the sphere surface. The classical electron radius is
derived from the context of the capacity of a spherical surface and the rest energy of the electron.
Here, we do not talk about a normal radius of a particle or the electron, but it is described the relationship between the
charge distribution on a spherical surface and the self-energy of the electron. The designation of "electron radius" is
misleading because it does not concern the actual radius of the "particle" electron.
The equation for the classical electron radius is:
Since, for the Maxwell's formula with applies, for the classical electron radius we obtain in abbreviated (short) form:
and this corresponds exactly to the following relationship:
The classical electron radius thus describes the relationship between the interactions of the elementary charge to the mass
of the electrons. When we replace the variables with their quantized sizes and , we do obtain the following:
With this formula we can explain the interaction of the charge distribution on a spherical surface instead of the electron
mass with the Planck mass.
In this formula we add the modified elementary charge from Chapter 2.2, with the value and the electron mass derives in
the last Chapter is replaced with and we do obtain the classical electron radius with the following value:
Or with and we do obtain:
With the classical electron radius and the quantized sizes we can also calculate the electron charge:
In my analysis, I have found the following relationships whereby the Planck length has been omitted for clarity.