A Suggested Stable, Classical Model for the Electron

J. J. Thomson, discoverer of the electron

Recommended reading:

1. The Feynman Lectures on Physics, Vol. 2, Chap 28

In this article the objective is to demonstrate that an electron might be modeled as a spherical shell of charge q, with radius r_q, concentric with a spherical shell of mass m, with radius r_m. The idea is that the model will be stable if the negative work, expended to assemble the shell of mass, plus the positive work, expended to assemble the shell of charge, sum to zero:

E_q+E_m=0.           (1)

Since in general E=mc² and, in the case of the electron m= 9.109328e-31, we have

E_q= 8.18706e-14. (2)

Now the work expended to assemble the sphere of charge is theoretically:

E_q=q²/8πε_or_q.⁽¹⁾                   (3)

Hence

r_q=q²/8πε_oE_q (4)

    =1.40898e-15.

According to gravitomagnetic theory, a companion equation to Eq. 4 can be formed by substituting (a) the imaginary quantity m_grav for q, and (b) G for 1/4πε_o: 

r_m=m_grav²G/2(-E_m)             (5)

    =3.382366e-58

Note that since m_grav is theoretically imaginary, r_m is positive.

Our model, then, consists of a miniscule sphere of mass, concentric with a much larger sphere of charge.

Let us now consider how such an electron might interact with some other particles.

Given two electrons, each would experience a repulsive force from the other (due to the like-signed spheres of charge), plus a much smaller, attractive gravitational force (due to the identical spheres of gravitational mass). 

Given an electron and a proton, each would experience an attractive force toward the other (due to the electron’s negative sphere of charge and the proton’s positive charge). And again there would be a much smaller, attractive gravitational force (due to the electron’s sphere of imaginary gravitational mass and the proton’s imaginary gravitational mass).

Given an electron and a neutron, each would experience no electric force toward the other (due to the neutron’s lack of net electric charge). But here again there would be a small, attractive gravitational force.

Of course such examples beg models for the proton and neutron. However, these models would presumably be more complicated than the electron’s simple model suggested above. For protons and neutrons are not elementary particles; they are constituted of multiple elementary particles (quarks).