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A Suggested Classical Model for an Up (Positive) Quark

Useful Values:

q=2e/3=1.06812e-19

According to the Equivalence Principle,

minert =|mgrav| = m = 1.7826-30

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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 rq, concentric with a spherical shell of gravitational mass mgrav, with radius rm. 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:

Eq+Em=0.                (1)

The work expended to assemble the sphere of charge is theoretically

Eq=q2/6peorq.          (2)

Since in general E=mc2, we can define the mass as

m=Eq/c2        (3)

or

m=q2/6peoc2rq.        (4)

Rearranging (4) we find that

rq = q2/6peoc2m = 4.2667e-16         (5)

and

Eq = q2/6peorq = 1.6021e-13.        (6)

Now according to gravitomagnetic theory a companion equation to Eq. 6 can be formed by substituting the imaginary quantity mgrav for q, and G for 1/4peo: 

Em=2mgrav2G/3rm.            (7)

Note that since mgrav is theoretically imaginary, Em is negative.   

Em=-Eq=-1.6021e-13.        (8)

Rearranging (7) we find that

rm=2mgrav2G/3Em=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>rq, the electric repulsive force is

Felec=q2/4peoR2.

And the gravitational attractive force would be

Fgrav=Gmgrav2/R2.

Thus Felec>>Fgrav, and for most practical purposes the quarks (e.g. the ones in a proton) simply repel one another electrically.