__A
Suggested Stable, Classical Model for the Electron__

__Useful
Values:__

q=-1.60218e-19

m_{inert}=|m_{grav}|=9.10938e-31

__Recommended
reading:__

https://www.feynmanlectures.caltech.edu/II_28.html

____________

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 gravitational
*mass* m_{grav}, with radius r_{m}. The idea is that the
model will be * stable* if the *negative*
work, expended to assemble the shell of gravitational mass, plus the *positive* work, expended
to
assemble the shell of charge, sum to zero:

E_{q}+E_{m}=0.
(1)

The work
expended to assemble the sphere of *charge*
is theoretically

E_{q}=q^{2}/6pe_{o}r_{q}.
(2)

Since in
general E=mc^{2}, we can define a real *inertial* mass as

m_{inert}=E_{q}/c^{2}
(3)

or

m_{inert}=q^{2}/6pe_{o}c^{2}r_{q}.
(4)

Rearranging (4) we find that

r_{q}=1.87864e-15
(5)

and

E_{q}=8.18711e-14.
(6)

Now
according to gravitomagnetic theory a companion equation to Eq. 2 can be formed
by substituting (a) the * imaginary* quantity m_{grav} for q, and (b) G for 1/4pe_{o}:

E_{m}=2m_{grav}^{2}G/3r_{m}.
(7)

Note that
since m_{grav} is theoretically *imaginary*, E_{m}
is *negative**:*

E_{m}=-E_{q}=-8.18711e-14.
(8)

Rearranging (7) we find that

r_{m}=4.51031e-58.
(9)

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 would 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 electric* 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* attractive *electric*
force toward the other (due to the neutron's lack of 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 in the sense that they are constituted of multiple particles (quarks) with powerful binding forces, etc.