__A
Suggested Classical Model for an Up (Positive) Quark__

__Useful Values:__

q=2e/3=1.06812e-19

According to the
Equivalence Principle,

m_{inert} =|m_{grav}|
= m = 1.7826-30

___________

In this article the
objective is to demonstrate that an up quark might be modeled as a spherical
shell of *charge* q=2e/3, 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 the mass as

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

or

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

Rearranging (4) we find
that

r_{q }= q^{2}/6pe_{o}c^{2}m =_{ }4.2667e-16
(5)

and

E_{q }= q^{2}/6pe_{o}r_{q} = 1.6021e-13.
(6)

Now according to
gravitomagnetic theory a companion equation to Eq. 6 can be formed by
substituting the *imaginary* quantity m_{grav} for q, and 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}=-1.6021e-13.
(8)

Rearranging (7) we find
that

r_{m}=2m_{grav}^{2}G/3E_{m}=8.82446e-58
(9)

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

Given two up quarks whose
centers are separated by R>r_{q}, the electric repulsive force is

F_{elec}=q^{2}/4pe_{o}R^{2}.

And the gravitational
attractive force would be

F_{grav}=Gm_{grav}^{2}/R^{2}.

Thus F_{elec}>>F_{grav},
and for most practical purposes the quarks (e.g. the ones in a proton) simply repel one another
electrically.