Derivation of the Pure Precise Fine-Structure Number and as a Ratio of Two Inexact Metric Constants

By: Sean Sheeter
Submitted: 2008-07-25 17:49:53
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Theorists at the Strings 2000 Conference were asked what mysteries remain to be revealed in the 21st century. No questions were more worthy than the top two selections respectively posed by David Gross and Edward Witten. #1: Are all the (measurable) dimensionless parameters that characterize the physical universe calculable in principle or are some merely determined by historical or quantum mechanical accident and incalculable? #2: How can quantum gravity help explain the origin of the universe?

A newspaper article about expressed some pertinent comments regarding the #1 millennial question. Perhaps Einstein did "put it more crisply: Did God have a choice in creating the universe?" - which summarizes quandary #2 as well. While surely the Eternal One 'may' have had a choice in Creation, the following arguments firmly suggest the reply to Einstein’s question is "No." Indeed, the pending text "241-Mumbers" chronicles a full spectrum of precise fundamental parameters and solutions that are undoubtedly calculable in a unified dimensionless system representing a literal Universal "Monolith."As the article asked: "is the speed of light, Planck’s constant and electric charge indiscriminately determined, or do the values have to be what they are because of some deep, hidden logic. These questions reach a conundrum involving a mysterious number called alpha. If you square the electron's charge and then divide it by the speed of light times Planck’s constant, all (metric) dimensions (mass, time, distance) cancel out, yielding a so-called 'pure number' -alpha, which is just over 1/137."

Though Sheeter had come to accept alpha’s experimental determination, he'd periodically pondered the dimensionless issue to no avail within the context of colleague A.J. Meyer's model. Gross’s question thus served as catalyst to fully address this problem. Yet two months attempting intellectualized 'fits' to the refined 98/00-NIST value exposed plain vanity. But the frustration led him to repeat a simple procedure explored before learning any of this. Merely peeking at this result restored sanity as the following solution struck with full heuristic force.

For just as alpha quantizes (via h-bar) the electromagnetic coupling between a discrete charge (e) and a photon of light; in the same sense an integer like 241 is discretely quantized compared to the 'fractional continuum' between it and 240 or 242. To see this, take the integer 203 and then subtract the 2-based logarithm of the square of 2pi. Now add 1/241 to the result and multiply that by the natural-log of 2. This 'pure calculation' yields a "fine-structure number" a=1/alpha =137.035999.6502301.

Which coincides with the 98-02 NIST value 137.035999.76o(50o), so even better with their 2006-choice 137.035999.679(o94), where the 2-digit parenthetical uncertainties are normal numerals. Though either choice remains determined by the measured values of h and e alone, interest had shifted to a new approach exploiting the quantum Hall effect, independently corroborated with theory and measure of the electron magnetic-moment anomaly. An improved measure of the magnetic moment concluded in 2006, where this (Harvard) group’s estimate for a was (A:) 137.035999.710(o96); explaining the far reduced NIST uncertainty. However, an error in the QED-calculation (http://hussle.harvard.edu/~gabrielse/gabrielse/papers/2006/NewFineStructureConstant.pdf) was later discovered which shifted Harvard's value to (B:) 137.035999.070(o98).  

So the increased precision ironically leaves (B:) outside the NIST value concordant with estimates for h and charge, as independently determined by various experiments. The NIST has three years for re-evaluation, facing the possibility their choices for h and e may be slightly skewed toward the expected fit for a. But vast improvements in multiple experimental designs will be required for a comparable reduction in h&e error to settle this issue since h/e could have as easily been re-adjusted without controversy had the QED-error been caught.

Yet, however 'precise' the measure, it's still infinitely short of  'exactitude:' like the equally pure number 137.0359997867 devised by mathematician James Gilson (http://www.maths.qmul.ac.uk/~jgg/page5.html). Who has estimated other standard parameters such as the mass-ratio between the Z and W gauge bosons. But even if Z/W were 'purely calculable,' it'd pale by comparison to a "pudding proof" on the 241mumbers.com website. For the formulation derives the precisely-measured Z-mass from 'unmeasured,' yet just as "highly confirmed," masses of a Higgs field and two heavy quarks. Surprising? It's no less natural than after 'discovering' 1/241 and deriving 1/alpha from a well-defined Monolith-Number, taking two weeks to calculate all six quark masses utilizing its dimensionless scaling and various fine-structured sub-relations.

Then we aren't discussing just 'alpha,' but a full, confirmed answer to question-#1, however interpreted. Remember, it's 'discrete integer' in 1/241 that allows construction of physically meaningful equations. If one adopted Gilson's "'or/other" choice like (B:), it would destroy both self-consistency and ability to even write an equation. The "dimensionless parameters" characterizing Gross's phrasing are each just a ratio between metric parameters. But as with the "standard model," there's no calculable means to predict one, let alone all, within a unified dimensionless system. Which explains why there is only one source of "The Definitive Data for Fundamental Physics and Cosmology: 241-Mumbers."

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