Let us rephase the $R_2$ factors for the CKM matrix, so that each factor is a nice matrix of determinant $\pm 1$. That is, one parameter appears in a factor of the form

The correct phase for the triplet of such factors is

where the numerator and denominator each contribute a phase of $\pi/12 + x$ for $x = 0.003$ a small parameter. In this form, the triple product is more clearly associated to triality. Note that the numerator of $\phi$ cancels the phasing of each factor, so we have simply modified the complex matrix by the phase $\pi/12 + x$.

6 years ago

Note that to divide the phase between the $2 \times 2$ block and the single $1$, we really need a phase of $\sqrt{\phi}$ rather than $\phi$. This phase is very close to $\pi /24$.

ReplyDeleteWell, the numerator and denominator are close to $\pi /24$. The full phase $\sqrt{\phi}$ is again $\pi / 12 + x$.

ReplyDeleteIn CKM is one factor implicit? The time. You need time to get the space. Time IS the computation.

ReplyDeleteAnother way to say Zero Energy Ontology.

Then you need to arrange these with the first row in the middle, and you get an oscillation around time +/-

Ulla, the three factors = one for each row arrangement. Triality has many highly mathematical elements. We are taking the three factors to correspond to generations 1,2,3. Usually, measurement time is associated to the process of doing the operation, but in this context I agree that may be a little misleading.

ReplyDeleteOn second thoughts, I like your way of putting it, since $24$ is naturally a dimension (like time steps).

ReplyDelete