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How My Dad became My Daddy.

An electron is almost, but not perfectly spherical. Anyway, a ball with its center at the origin O (which is the point (0,0,0)) and radius one is made up of a sphere whose equation is x^2 + y^2 + z^2 = 1 and an interior whose equation is x^2 + y^2 + z^2 < 1. A sphere is a hollow ball. Suppose that the electromagnetic vector is the sphere, moving around and reversing its direction as a standing curvilinear wave. The length of this wave would be 4pi, since it must travel 2pi and reverse itself coming back 2pi. Now suppose that the electromagnetic wave is 'peeled away' into a linear band, tangent to the interior of the ball at a single point. So choose (0,0,1) as the new center of the interior and (0,0,0) as the single point of attachment. Just translate the ball up one unit. Then the equation of the exploded positron would be the union of x^ + y^2 + (1-z)^2 < 1 with the line segment {(x,0,0) | 0 <= x <= 4pi}."

"But wait. The line segment {(0,y,0) | 0 <= y <=4pi} would work equally well. In fact, for any fixed real number u and each v where 0 <= v <= 4pi the line segment {(v*sin(u),v*cos(u),0) | 0 <= v <= 4pi} would work. So, in the xy plane we have equal likelihood of the line segment assuming any value u. (By periodicity of the trigonometric functions it, it suffices to say 0 <= u <= 2pi.) We have a disk spun out with center (0,0,0) and radius 4pi. This is like spinning the xy plane around the z-axis. Remember that the x-axis faces into you from the origin, the y-axis goes from left to right and the z-axis is down to up."

Andra records and passes over the techno-babble. Odd, it does seem to make sense; but, if the physics eggheads all say "no," then who's to argue?

"Would Master like a back rub?" Andra asks. She is preparing to undress and let her warm, soft synthetic skin massage away the tension that the hoary old curmudgeon is spouting. For sure there are mental processes at work, all those silly equations and numbers.

Undaunted and unable to fully appreciate the warm massage, Harry continues: "We could spin likewise about the x-axis and the y-axis, giving a perfect ball (solid sphere) of radius 4pi. I call this anomaly the Ur-proton. But there is a problem about spinning about the x-axis. The interior ball of the positron spins out an inner disk of radius 2. (This would be 2r if we let r = radius of positron or electron.) Double that problem about the y-axis as there are two disks spun out in the xz plane. What about this matter?"

Andra constructs a 3D plot displaying the Ur-proton and the infrastructure. Could this indicate a fundamental difference between the proton and electron?

Harry suggests a solution: "Map away the open ball of the positron. Use the inversion of the spheres on the yz plane. 2*2 = (4pi)*t. Where t is the inner radius. Now we see that an interior ball of radius 1/(pi) is deleted. Double that for the xz plane. This gives values for each of the three degrees of freedom: 4pi(4pi-1/pi)(4pi-2/pi). It is not surprising that the value is 1836.15..."

Andra pauses her neuro-circuitry. She cannot derive or comprehend the final step. This is disconcerting and frustrating for a gynoid many times more intelligent than any living human. She queues a query to Master Control for guidance.

Harry then feels the need to explain even to a non-human, soulless sentient being the theory. Exhausted from mental exertion he finished by deriving the value of the neutron to electron mass ratio. The neutron-proton isospin is = proton-electron mass ratio + ln(4pi). Here ln is the natural logarithm and pi is, of course 3.1415926534...

Before drifting into his morning torpor, Harry gives the final derivation. In the neutron, the electron drifts in the neighborhood (0,4pi). But it has radius one. So it's likelihood is 1/rho, where rho varies from 1 to 4pi. Integrate: The integral from 1 to 4pi of (d rho)/rho = ln(4pi) -- ln(1) = ln(4pi) = 2.531024247...

Andra is communicating with Master Control.

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