the classical electron radius is from math not from physics! In so fare as physics behind the r_e does not work physically (see Feynman). Math works without sense. This alone can not vivid physically.
S=m*c*r_G=1/2*h_bar
Spin_electron is a constant vivid physically. So r_G is a radius from physics, not from math. (I call it Compton_radius, related to the Compton Wavelength)
But there is a very promising new method for physics to increasingly use mathematics starting with a possible new equation for the Rydberg constant via the classical electron radius and then with a possible new equation for the radius of the atom of hydrogen in connection with Rydberg and the classical electronic radius.
Many thanks for the documents. Thanks to the results of measurements on hydrogen and deuterium, both muonic, there is a new physics that uses a lot of mathematics but people do not understand these results. For example the radius of the hydrogen atom is a function of a muonic ratio. I will post prepints on my RG pages soon therefore people can find similarity because I continu to work with the known constants of physics but I rejected the Rydberg and the Bohr radius classical equations. for me theses two constants it is time that they take retired!!! they blocked physics toward to uses more mathematics!!!! that is my opinion.