Pure Derivation Of The Exact Fine-structure
Constant & As A Ratio Of Two Inexact Metric Constants
Author: Sean Sheeter
Theorists at the Strings Conference in July of 2000 were asked
what mysteries remain to be revealed in the 21st century.
Participants were invited to help formulate the ten most
important unsolved problems in fundamental physics, which were
finally selected and ranked by a distinguished panel of David
Gross, Edward Witten and Michael Duff. No questions were more
worthy than the first two problems respectively posed by Gross
and 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 these millennial mysteries expressed
some interesting comments about the #1 question. Perhaps
Einstein indeed "put it more crisply: Did God have a choice in
creating the universe?" - which summarizes quandary #2 as well.
While certainly the Eternal One `may' have had a `choice' in
Creation, the following arguments will conclude that the reply
to Einstein's question is an emphatic "No." For even more
certainly a full spectrum of unprecedented, precise fundamental
physical parameters are demonstrably calculable within a single
dimensionless Universal system that naturally comprises a
literal "Monolith."
Likewise the article went on to ask if the speed of light,
Planck's constant and electric charge are indiscriminately
determined - "or do the values have to be what they are because
of some deep, hidden logic. These kinds of questions come to a
point with a conundrum involving a mysterious number called
alpha. If you square the charge of the electron and then divide
it by the speed of light times Planck's (`reduced') constant
(multiplied by 4p times the vacuum permittivity), all the
(metric) dimensions (of mass, time and distance) cancel out,
yielding a so-called "pure number" - alpha, which is just over
1/137. But why is it not precisely 1/137 or some other value
entirely? Physicists and even mystics have tried in vain to
explain why."
Which is to say that while constants such as a fundamental
particle mass can be expressed as a dimensionless relationship
relative to the Planck scale or ratio to a somewhat more
precisely known or available unit of mass, the inverse of the
electromagnetic coupling constant alpha is uniquely purely
dimensionless as the `fine-structure number' a ~ 137.036. On the
other hand, assuming a unique, invariantly discrete or exact
fine-structure numeric exists as a "literal constant," the value
must still be empirically confirmable as a ratio of two
inexactly determinable `metric constants,' h-bar and electric
charge e (light speed c being exactly defined in the 1983
adoption of the SI convention as an integer number of meters per
second.)
So though this conundrum has been deeply puzzling almost from
its inception, my impression upon reading this article in a
morning paper was utter amazement a numerological issue of
invariance merited such distinction by eminent modern
authorities. For I'd been obliquely obsessed with the fs-number
in the context of my colleague A. J. Meyer's model for a number
of years, but had come to accept it's experimental determination
in practice, pondering the dimensionless issue periodically to
no avail. Gross's question thus served as a catalyst from my
complacency; recognizing a unique position as the only fellow
who could provide a categorically complete and consistent answer
in the context of Meyer's main fundamental parameter. Still, my
pretentious instincts led to two months of inane intellectual
posturing until sanely repeating a simple procedure explored a
few years earlier. I merely looked at the result using the 98-00
CODATA value of a, and the following solution immediately struck
with full heuristic force.
For the fine-structure ratio effectively quantizes (via h-bar)
the electromagnetic coupling between a (squared) discrete unit
of electric charge (e) and a photon of light; in the same sense
an integer is discrete or 'quantized' compared to the
`fractional continuum' between it and 240 or 242. One can easily
see what this means by considering another integer, 203, from
which we subtract the 2-based exponential of the square of 2pi.
Now add the inverse of 241 to the resultant number, multiplying
the product by the natural log of 2. It follows that this pure
calculation of the fine-structure number exactly equals
137.0359996502301…- which here (/100) is given to 15, but is
calculable to any number of decimal places.
By comparison, given the experimental uncertainty in h and e,
the NIST evaluation varies up or down around the mid 6 of `965'
in the invariant sequence defined above. The following table
according gives the values of h-bar, e, their calculated ratio
as and the actual NIST choice for a in each year of their
archives, as well as the 1973 CODATA, where the standard two
digit +/– experimental uncertainty is in bold type within
parentheses.
year: h-bar=Nh*10^-34 Js e = Ne*10^-19 C h/e^2 = a = NIST value
&±(SD):
2006: 1.054571.628(053) 1.602176.487(040) 137.035999.661
137.035999.679(094)
2002: 1.054571.680(18x) 1.602176.530(14x) 137.035999.063
137.035999.11o(46x)
1998: 1.054571.596(082) 1.602176.462(063) 137.035999.779
137.035999.76o(50x)
1986: 1.054572.66x(63x) 1.602177.33x(49x) 137.035989.558
137.0359895xx(61xx)
1973: 1.0545887xx(57xx) 1.6021892xx(46xx) 137.036043335
137.036.040(11x)
So it seems the NIST choice is roughly determined by the
measured values for h and e alone. However (as explained at
http://physics.nist.gov/cuu
interest shifted to a new approach that provides a direct
determination by exploiting the quantum Hall effect, as
independently corroborated with both theory and experiment of
the electron magnetic-moment anomaly, thus reducing its already
finer tuned uncertainty. Yet it took 20 years before an improved
measure of the magnetic moment g/2-factor was published in mid
2006, where this group's estimate for a was (A:)
137.035999710(96) - explaining the much reduced uncertainty in
the new NIST list, as compared to that in h-bar and e. However,
recently (B:) a numeric errorHowever, recently (B:) a numeric
error
(http://hussle.harvard.edu/
in the initial QED calculation (A:) was discovered which shifted
that value of a to (B:) 137.035999070(98).
Though it reflects a nearly identically small uncertainty, this
assessment is clearly outside the NIST value concordant with
estimates for h-bar and elementary charge, which are
independently determined by various experiments. The NIST has
three years to sort this out, but meantime face an embarrassing
irony in that at least the 06-choices for h and e seem to be
slightly skewed toward the expected fit for a! For example,
adjusting the last three digits of the 06-data for h and e to
accord with our pure a-number yields an unperceivable adjustment
to e alone into the ratio h628/e487.065. Had the QCD error been
corrected prior to the actual NIST publication in 2007, it
rather easily could have been evenly adjusted to h626/e489;
though questioning its coherency in the last 3-digits of a with
respect to the comparative 02 and 98 data. In any case, far
vaster improvements in multiple experimental designs will be
required for a comparable reduction in error for h and e in
order to settle this issue for good.
But again, even then no matter how `precisely' metric measure
is maintained, it's still infinitely short of `literal
exactitude,' while our pure fs-number fits the present values of
h628/e487quite precisely. In the former regard, I recently
discovered a mathematician named James Gilson
(http://www.maths.qmul.ac.uk/
pure numeric = 137.0359997867... nearer the revised 98-01
standard. Gilson contends he's also calculated numerous
parameters of the standard model such as the dimensionless ratio
between the masses of a W and Z weak gauge boson. I know he
could never construct a single `Proof' employing equivalencies
capable of deriving both Z and/or W masses per se from, so thus
proven, precise masses of heavy quarks, Higgs fields or hadrons
(http://ezinearticles.com/?The
which themselves result from a single over-riding dimensionless
tautology.
For the numeric discreteness of the fraction 1/241 allows one
to construct physically meaningful dimensionless equations. If
one instead took Gilson's numerology, or the refined empirical
value of Gabreilse et. al., for the fs-number, either would
destroy this discreteness, precise self-consistency and ability
to even write a meaningful numeric equation! By contrast,
perhaps it's then not too surprising that after I literally
looked for and/or found the integer 241, and then derived the
exact fine-structure numerical constant from the resultant
Monolith Number, it took about only 2 weeks to calculate all six
quark masses utilizing real dimensionless analysis and various
fine-structured relations.
But as we now aren't really talking about the fine-structure
number per se any more than the integer 137, the result
definitively answers Gross's question. For those "dimensionless
parameters that characterize the physical universe" (including
alpha) are ratios between selected metric parameters that lack a
single unified dimensionless system of mapping from which all
metric parameters like particle masses are derivable from set
equations. The standard model gives one a single system of
parameters, but no means to calculate or predict any one and/or
all within a single system – thus the experimental parameters
are put in by hand arbitrarily. Final irony: I'm doomed to be
demeaned as a `numerologist' by the `experimentalists' who can't
recognize a hard empirical proof for quark, Higgs, or hadron,
masses that are used to exactly calculate the present standard
for the most precisely known and heaviest mass in high energy
physics. So contraire foolish ghouls: empiric confirmation is
just the final cherry the chef puts on top before he presents a
Pudding Proof no sane man can, or should, resist just because he
could never assemble it himself, so instead makes a mimicked
mess the real deal doesn't resemble - for the base of this
pudding is made from melons I call Mumbers, which are really
just numbers, pure and simple!
About The Author: Sean Sheeter is an independent theorist,
geometer and author of 241-Mumbers: The Definitive Data for
Fundamental Physics and Cosmology. Interested parties are
encouraged to visit http://www.241mumbers.com and also explore
our Sample Data & Proofs page that includes the body of the
above reference.
