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The Urantia Book statement remained nonsensical until the 1990's when Nobel prize winner, Hans Dehmelt, found a way to confine a single electron to a trap semi-permanently. This achievement allowed actual measurements to be made that assigned the radius of the electron to fall into the range of 10-19 m to 10-22 m.
This estimate was noticed by physicist Stefan Talqvist, a Urantia Book student who had previously checked the calculation using the Urantia Paper's version of Swann's earlier work. A few years later at Dehmelt's laboratory1, refining of their techniques allowed them to settle for the electron radius being in the order of 10-22 m, so even closer to the 2 x 10-21 that is calculated for the Urantia Papers' modified version of Swann's comparison.
There was a second part to Swann's comparison that went:
"Then we have the proton--the fundamental unit of positive charge--a thing 1800 times as heavy as the electron, but 1800 times smaller in size, so that if you should magnify it to the size of a pin's head, that pin's head would, on the same scale of magnification, attain a diameter equal to that of the earth's orbit around the sun."
[Note: Swann's estimate of the size of the proton as 1800 times smaller than the electron came from using r = e2/mc2, where e is the charge of the electron. The charge to mass ratio for the electron was known accurately by the early 1900 period. The charge was determined by Millikan in 1909. Its mass was then determined as 9.11 x 10-28 g.]
The Urantia Paper's author did not use this equation, changing the comparison to:
"If the volume of a proton--eighteen hundred times as heavy as an electron--should be magnified to the size of the head of a pin, then, in comparison, a pin's head would attain a diameter equal to that of the earth's orbit around the sun." (P.477)
Stefan Talqvist was again responsible for doing the calculations and drawing attention to this remarkable piece of prophetic material in the Papers.
Taking the radius of the Earth's orbital around the sun as 1.5 x 1014 mm and the radius of the pinhead as 1 mm, the magnification factor (k) is obtained by dividing the Earth's orbital radius by the pinhead radius, so 1.5 x 1014 / 1.0, which is 1.5 x 1014 (k)
The radius of the proton times the magnification factor (k) is equal to the radius of the pinhead, hence:
Proton radius x 1.5 x 1014 = pinhead radius (1.0 mm), so
Proton radius = 1.0 /1.5 x 1014, which is 6.7 x 10-15 mm, or 6.7 x 10-18m.
The classical radius for the proton was given as 0.85 x 10-15m so again the Urantia Paper's comparison looked to be nonsensical.
In later years it was realized that the proton consisted of three subunits called quarks and this component accounts for only about 50% of the proton's measured momentum, the remainder being accounted for by virtual particles that flip in and out from the vacuum. The current estimate of what is now termed the Bohr radius, a measurement of the 'real' part of the proton was given in Physics Today of November 1993, as 7.7 x 10-18m.--the same order of magnitude as that for the Urantia Paper's estimate.
When we take into consideration that Swann's details were deliberately modified in both estimates in order that they produce these results, it becomes impossible to support the notion that this was simply a lucky guess. Any rational interpretation must surely allow that it is a most remarkable prophecy, impossible to explain as by pure chance. So what is left?
[Please note that Swann's work, where correct, was used verbatim by the authors of the Urantia Papers. But where erroneous, it was either ignored or modified.]
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