Saturday, April 14, 2012

Alpha, Fine Structure Constant, mystery no more!

Alpha (Fine Structure Constant) was initially viewed as an observed coupling constant for the amplitude of a real electron to emit or absorb a real photon. Thus, the value for Alpha could vary depending upon the energy level. In the GUT (Grand Unified Theory) energy level, the Alpha should approach the same level as the strong force coupling value, and its observed value does approach 1/128 at interaction energies above 80 GeV.

However, the theoretical calculation equation for Alpha below can, indeed, encompass the above-said issue, as the A(2), the  Weinberg angle, in the equation is also varying as a function of the momentum transfer, Q. At Q = 0.16 GeV/c, the Weinberg angle is about ~30°. In fact, the Weinberg angle ranges from 28 to 30 degrees.

Beta = 1/alpha = 64 ( 1 + first order mixing + sum of the higher order mixing)
= 64 (1 + 1/Cos A(2) + .00065737 + …)
=  137.0359 …

A(2) is the Weinberg angle, A(2) = 28.743 degrees

The sum of the higher order mixing = 2(1/48)[(1/64) + (1/2)(1/64)^2 + ...+(1/n)(1/64)^n +...]
= .00065737 + …

However, when Alpha is defined as,

Alpha = e^2/c * h-bar

it is no longer a measured “coupling” constant. It is an anchor-lock which locks the three Nature constants [electric charge (e), light speed (c) and Planck constant (h-bar)]. That is, the Alpha must be a true constant, not a varying constant anymore. The measured value for this true constant (at low energy level) is 137.03597….

Again, my theoretical equation of Alpha does reproduce this value (137.03597…) when the Weinberg angle = 28.743 degrees. Obviously, this Weinberg angle (28.743 degrees) does fall in the range of the observed values (from 28 to 30 degrees). Yet, can this be a simple good luck? And, the theoretical equation for Alpha is still a numerological formula, isn’t it?

Today, the Weinberg angle is a pure observed parameter, and it has no theoretical base for its calculation. If I can provide a theoretical calculation for the Weinberg angle with the same physics which calculates the Alpha, will it still be a good luck numerological formula?

While both Cabibbo angle and Weinberg angle are the foundation for electro-weak symmetry breaking, there is no axiomatic linkage between the two. If I can show two points,

1. the Cabibbo angle can be calculated with the same physics which calculates both the Weinberg angle and the Alpha, (note --- today, Cabibbo is also a pure observed parameter without any theoretical base for its calculation in the Standard Model),

2. the Weinberg angle is actually derived with the Cabibbo angle,

then, will them still be good luck numerological formulas? If they are, they are “chain-linked” good luck numerological formulas.

These chain-linked formulas are available in the article “LHC and the knowledge-based physics, http://prebabel.blogspot.com/2012/03/lhc-and-knowledge-based-phyiscs.html “.

In the  “Introduction to The Common Sense” (page 3), Thomas Paine wrote, "Perhaps the sentiments contained in the following pages, are not yet sufficiently fashionable to procure them general favor; a long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom. But the tumult soon subsides. Time makes more converts than reason."

By agreeing with Paine 100%, I am not trying to convince anyone about this new physics which provides the theoretical chain-formulas as the final physics. I will simply give a short history of it here.

The theoretical calculations for the Cabibbo and Weinberg angles were done in 1980 and published in the book “Super Unified Theory” (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325) in 1984. This book is available in many university libraries around the world, and this info is available from the WorldCat (the world's largest library catalog).

They were also discussed online in 2001. A copy of Dr. Jason W. Hinson’s (Cornell University) email on this issue was published in the article “Playing with numbers??? “  at  http://www.prequark.org/think04.htm .

The theoretical calculation for Alpha was done in 1990 and was published online since 1997. However, the 1997 online page is no longer available. Now,  it is available at the following sites.

e. the Prequark site (http://www.prequark.org/pq04.htm ) since May 2005.

In the book (Rights of Man, by Thomas Paine, page 121), he wrote, "Ignorance of a peculiar nature: once dispelled, and it is impossible to re-establish it. It is not originally a thing of itself, but is only the absence of knowledge; and though man may be kept ignorant, he cannot be made ignorant."

Now, this information is here.

Update (January 24, 2014):
On January 5, 2014, Amir Mulic published an Alpha formula (4π^3+π^2+π). Although he gave it an M-string interpretation, it is still basically a numerological formula.

The fine-structure constant should be a running constant with (1/α) = 4π^3+π^2+π at low energy while it approaches 128 at energy higher than 90 Gev. . Thus, the 4π^3+π^2+π formula meets only one point of that spectrum. Furthermore, that formula can only be interpreted in terms of geometry or topology, hinting an eleven (11) dimension universe. But, my Alpha formula has the following points.

1.       It has a ‘physics’ parameter, the Weinberg angle.
2.       As this Weinberg mixing angle is a function depending on the energy, this formula encompasses the entire  (1/α) spectrum (from 4π^3+π^2+π to 128).
3.       It is also a formula for an eleven dimension universe.

My Alpha-formula above (with the Weinberg angle) is, in fact, the result of three points.
First,  ‘uncountable-infinity to finite’ concretization process, see "Multiverse bubbles are now all burst by the math of Nature (http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html )”. That is, the uncountable-infinity is concretized as a circle (or a pie).

Second, this pie (the highest infinity) is ‘divided’ by 64 kids (of this ultimate infinity) which consist of two groups; one group (16 kids) takes the energy (dark energy), the other (48 kids) takes the landmass as landlords.  See “Pimple Model; BARKED UP THE WRONG TREES (M-THEORY AND SUSY); (http://tienzengong.wordpress.com/2013/09/19/barked-up-the-wrong-trees-m-theory-and-susy/ )” and “DARK ENERGY, MYSTERY NO MORE! (http://tienzengong.wordpress.com/2013/09/25/dark-energy-mystery-no-more/ )”. Thus, the numbers (64, 48 and 24) play the key roles in my Alpha-formula. The whole point is about the ‘dividing’ the pie.

Third, the 64 and 48 are the result of a True-Ultimate-Symmetry (the real/ghost symmetry, see http://www.prequark.org/Gravity.htm ) breaking.

Yet, when Mulic’s formula is rewritten with the following equation, the physics significance is now all clear.

Let 2 π = the circumference of a unit disk (with radius = 1) = Pie
π = half Pie = HPie
Then, his formula can be written as,
(1/α) = (1/2) {Pie * [(Pie + 1/Pie)^2 + (HPie – 1/HPie) – ((1/Pie) – 1)^2]} … equation A

The equation A above is the topological (static) description of the three points above
(Pie + 1/ Pie), type 1 mixing (division); (Pie + 1/ Pie)^2, the first order mixing
(HPie – 1/HPie), type 2 mixing (division), the second order mixing
[(1/Pie) – 1]^2, the ‘remainder’ (indivisible) of the division

So, equation A = (1/2) Pie * (the first order mixing + the second order mixing - the ‘remainder’ of mixing)

Thus, although Amir Mulic’s formula (4π^3+π^2+π) is purely numerological, it can be rewritten with my physics. The fact that the Alpha is now written with two formulas (one static and one dynamic), the validity of this Alpha-physics is very much assured.

Note (added on August 28, 2016):

The current (2016) mainstream physics status is this: #PostCheckmateTTF (Post Checkmate temper tantrum fit).

Copyright © April 2012 by Tienzen (Jeh-Tween) Gong

1. Mr Tienzen, I had some intuition to ask this,

To make (or observe) the emergence of spacetime metric, from matrix, the origin of photons or realm of photons should be determined ?. Otherwise we have no possible instruments to measure particle duality - beyond that there is no empirical evidence.

Thus the 3D space of observed universe can create measurable geometry ?
The weinberg angle is a pure observed parameter, so the rotation of spontaneous symmetry breaking (lowest energy level), decides the realm of 3D metric and thus the realm of photons ?

In "particular" higher energy parameter, makes the same for symmetry breaking of gravity also, from electroweak and strong forces ?

2. @veeramohan:

Every article in this blog discusses only one topic. This article talks about the calculation of Alpha only.

3. /In the GUT (Grand Unified Theory) energy level, the Alpha should approach the same level as the strong force coupling value, and its observed value does approach 1/128 at interaction energies above 80 GeV.

The Weinberg angle, in the equation is also varying as a function of the momentum transfer, Q./

LHC energy increased the momentum – the bump is an observable high cosmological constant – otherwise at low energies, is an unObservable due to the very short life time.

This new low energy level implies high cosmological constant ?