CKM Recipe
Take the following real unitary magic matrix. 
Take the square root of each entry to form another real matrix. The bottom right $2 \times 2$ corner is the real part of the Fourier transform of the CKM matrix. The top left corner is very close to the real part of the row sum for the cubed root of the CKM matrix, which itself has a row sum with real part $26/27$. That is, the following approximate relation holds:
$\textrm{cos}(\frac{1}{3} \textrm{cos}^{-1}(\frac{26}{27})) \simeq \frac{\sqrt{723}}{\sqrt{729}}$
The norms of the Fourier transform blocks were previously observed to be 1. This fixes the imaginary part of the $1 \times 1$ piece. We will then consider another unitary magic matrix for the imaginary component.
Take the square root of each entry to form another real matrix. The bottom right $2 \times 2$ corner is the real part of the Fourier transform of the CKM matrix. The top left corner is very close to the real part of the row sum for the cubed root of the CKM matrix, which itself has a row sum with real part $26/27$. That is, the following approximate relation holds:$\textrm{cos}(\frac{1}{3} \textrm{cos}^{-1}(\frac{26}{27})) \simeq \frac{\sqrt{723}}{\sqrt{729}}$
The norms of the Fourier transform blocks were previously observed to be 1. This fixes the imaginary part of the $1 \times 1$ piece. We will then consider another unitary magic matrix for the imaginary component.
posted by Kea | 9:36 PM
2 Comments:
Your math posts are always enjoyable. Thanks for the previous post, especially the word "patiently." Patience contributess to success more than intelligence or looks.
Carl and you are right--a changing rate of time is mathematically equivalent to a changing speed of light!
So right, Louise. One day I would like to spend time thinking about solar system tests of a varying speed of light.
Remote Kea
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