Wednesday, October 26, 2011

Theoretical calculation of Feynman's damn mystery number



Richard P. Feynman (a Nobelist on Physics) once said, "There is a most profound and beautiful question associated with the observed coupling constant, e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!"

Note:  Info on Electron Fine Structure Constant  is available at  (http://en.wikipedia.org/wiki/Fine-structure_constant )


In fact, this Feynman's damn mystery number cannot be derived theoretically in any traditional physics theory, the Standard Model or the whatnot. However, it can be easily derived in this Fictitious Universe (FU) physics as below.

Beta = 1/alpha = 64 ( 1 + first order sharing + sum of the higher order sharing)
        = 64 (1 + 1/Cos A(2) + .00065737 + …) = 137.0408704 …

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

The A(2) = 28.75 'degrees' is the result from the previous post, “Theoretical calculation of Cabibbo and Weinberg angles” (at http://prebabel.blogspot.com/2011/10/theoretical-calculation-of-cabibbo-and.html ). That is, this calculation is consistent in the FU physics.


There is a 0.0036% difference between this theoretical number from the measured value. The A(2) =28.75 degrees is calculated with the universe having the zero mass, and it could be compressed a bit after the universe gained its mass. When A(2) = 28.743, Beta = 137.035999679…, exactly the same as the measured value.  In many measurements, the value of the fine structure constant is about 1/137.036 at zero energy.  This difference can be a way to estimate the mass of the current universe.

Whether this FU physics is correct or not is not an issue here. The issue here is about which one can do better. With the FU physics, the calculation for alpha is straightforward while there is no way of any kind to derive it in Standard Model or its variants (Supersymmetry, String theory, etc.) .



Signature:
Tienzen (Jeh-Tween) Gong
The book “Super Unified Theory” (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325)

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