Wednesday, February 23, 2005

GUITAR Predictions of Muon Mass

Previously I disclosed that GUITAR leads to precise prediction of neutron to electron mass ratio, accurate to 10 decimal places and agrees with the experimental value completely. See:
http://quantoken.blogspot.com/2005/02/proton-and-neutron-mass-from-guitar.html

The same reasoning connecting decay lifetime to particle mass can be applied to Muon as well, and it also leads to amazingly precise results.

Before we start let me emphasis again that I am using the natural unit set where hbar = c = 1, and electron mass Me = alpha. In the natural unit, one time unit is
T0 = 9.399637148x10^-24 seconds

Also, recall that the observational "age" of the universe is:
Tu = PI*N
with
N = PI * exp(2/(3*alpha)) = 1.4898x10^40

First, the Muon decay lifetime is:
ln (Tau) = 40 - alpha, with alpha = fine structure constant.
Which gives:
Tau = exp(40-alpha) = exp (40 - 1/137.03599911) = 2.3367383x10^17
Certainly, keep in mind our results are in natural unit set, to convert back to MKS unit:
Tau = 2.3367383x10^17 * T0 = 2.3367383x10^17 * 9.399637148x10^-24 seconds
Tau = 2.19645 x10^-6 seconds
That agrees excellently wiht experimental value of Tau = 2.19703x10^-6 seconds.

Now let's calculate the Muon mass:

Mu = beta,
with
beta^2 = ln (Tu)/ln(PI*Tau)
beta^2 = ln (PI*N) /ln (PI*2.3367383x10^17)
beta^2 = ln (PI*1.4898253x10^40)/ln(PI*2.3367383x10^17)
beta^2 = 2.27645
So
beta = sqrt(2.27645) = 1.5088
So
Mu = 1.5088

That is it. That is the result. We have found the Mu mass to be 1.5088.

How come? remember we are using the natural unit set, in which Me = alpha.
So:
Mu/Me = 1.5088/alpha = 1.5088 * 137.03599911 = 206.760

The most precise experimental value of muon to electron mass ratio is:
Mu/Me = 206.768
(See: http://physics.nist.gov/cgi-bin/cuu/Value?mmusmesearch_for=muon+mass)

So my theoretical value of muon mass has at least 6 effective decimal places. Not bad at all.

Quantoken