Thursday, December 30, 2010

Theory Update 27

For the CKM matrix
three phases of the complex matrix are given by
so that the new value $\sin 2 \beta = -0.649$ follows from the phase $- 0.7063$ radians. All phases are fixed by the three real parameters of the triple factors.


  1. Hi,

    I am not sure if it has relevance to your CKM matrix applications... But I saw a pattern between Conway's Matrix and perhaps non-standard uses of these decay ideas.
    Please see today's post and scroll to the last photo entry.

    The PeSla

  2. Thanks for your post, ThePeSla. Interesting.

  3. I can't help wondering why $0.0388$ is so close to $\pi / 81$ ...

  4. Kea

    I found it interesting the Egyptians, I think, approximated pi by 256/81. 2^4/3^3 which fit their needs.

    You probably know all this. Of course the sum of the subcells of a hypercube = 81 as the fourth level of the expansion (2+1)^n is of course 3^4. The Orthogons (and anti-orthogons).

    But such things still are in the realm of some sort of modern numerology for me. In general if we think of points all connected to each other it is a simplex space- but I find it interesting you in later posts treat 81 as 81 dimensions. It was not easy to eventually see the chessboard as 6 dimensional, that is = 64.

    Once reviewing a thesis for just a look at repeated lines and spelling and so on for a string theory professor (wow, I learned a lot doing it but did not know much of the theory). He eventually got me aside to show him all this algebra of the Pascal analogs. Alas, he did not get tenure here.

    Such algebra is indeed as important as any of our ideas from the geometry viewpoint.


  5. Very nice of you to help out some string theorists. They are not all bad. Numbers happen to BE dimensions in quantum algebra. It helps to get the two things mixed up, and think of sets as being a lot like vector spaces.

  6. Kea,

    Your comment on 81 and near realtion to pi inspired me, that and seeing parts of an analog to Pascal's triangle applied. Tonight I add a post called On Kea's Observation.

    I googled a little and found you are familiar with Peter Rowlands book and work of which I have made many comments while my reading.

    Of course my creative posting makes no claims beyond raw speculation but perhaps one more trained can see what I cannot.

    Numbers, and classes of numbers can be dimensions- but that is one of our terms not defined so well at the foundations.

    The PeSla

    ps I love Cambridge what time I was there briefly in the 60's in the air force. It was a thrill to walk Newton's philosophers walk and eat in places Crick and Watson may have, or just go punting on the backs of the Granta.


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