Natural Science Forum / Physics / General Physics / July 2008

Frank says;

Your equation is in obselete cgs units, Frank.

The International MetricSystem (SI) is the modern language of science,
and I find it more intuitive.

See the following link I gave you, Figure 4, left panel bottom
calculation.

The fine structure constant can be derived from a number of different
math equations but all are traceable to the geometry, as demonstrated
by the derivation shown.

Alpha= (Flux x 2 x e)/ h

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Let me give you the equation:

Lets define,

1) 1/alphaPrime=((180*Phi)^2)/(20*pi^3)

2) For period doubling, as the limit approching infinity in chaos
theory:
Feigenbaum constant delta:
deltaF=delta Feigenbaum constant=4.66920....

3) For period doubling reduced from one doubling to the next,
converges to:
Feigenbaum constant alpha:
alphaF=alpha Feigenbaum constant=2.50290...

then,

1/alpha=1/alphaPrime+alphaF/10+sqrt(10/deltaF)

Rearranging the alphaPrime shows that its in fact a product of radians
and the golden ratio.

Regards,
Jay Bala.

That's the low energy asymptotic value. As you ramp up the energy in a
scattering process and probe deeper into the field of a source, the
effective value of alpha increases. This occurs because the source
being probed by a scatting process actually deviates from Coulomb, as
you probe deeper into it. For electromagnetism, the effective
potential goes faster than 1/r, though it's 1/r when far-removed from
the source. There's a huge industry that is (and has long been around)
dedicated to the question of the inverse scattering problem
(reconstructing an image, here, the profile of the potential
surrounding a source, from the results of scattering done off the
source). One actually sees the effective alpha go up at high energies.

It's widely believed (but not a complete consensus) that theory
predicts, in fact, that it would approach infinity at a finite
positive radius. That's called the Landau Pole.

To some extent this may be classically modelled. On general
principles, one would expect an effective dynamics for the dielectric
coefficient epsilon to be given by an equation of the form
  [] log(epsilon_0) = -K epsilon_0 (E^2 - B^2 c^2)
for some positive constant K. This translates directly into an
equation d^2(log alpha)/d(1/r)^2 = k alpha, for some constant k. From
this you can get any of a wide variety of phases, including one that
replicates the features of the Landau Pole.

Other solutions, interestingly, include a phase where the effective
field E approaches a constant as r -> infinity, and alpha -> 0 as r ->
0. These features are called, respectively, "infrared slavery" and
"asymptotic freedom". For non-Abelian gauge fields (SU(3), here) it's
the basis of confinement that rules out the existence of monopole
sources. In this phase, sources with bounded fields can only exist as
dipoles or higher order multipoles (which includes, in SU(3), the 3-
body neutral sources with 3 charges bound to each other).

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