Recall that the two factor mixing products corresponded to a new kind of magic matrix. For example, the tribimaximal values may be rearranged as where the number $6$ replaces the zero entry of the matrix. Such magic squares have both sum and product rules. For example, the tribimaximal values give us

$\frac{2}{3} \times \frac{1}{2} = \frac{1}{3} $

$\frac{1}{2} \times \frac{1}{3} = \frac{1}{6} $.

Similarly, the CKM values give us the product rules

$(ud) \times (tb) = (cs) $

$(us) \times (cb) = (td)$.

The probability matrices are obtained from these magic squares by rearranging only a few values. One way that we might draw such a magic square is:

7 years ago

Good luck with this, but remember the cases of failure in physics by mathematical physics inventors. Levi-Civita and tensors, Riemann and geometry, Weyl and gauge theory, etc. etc. None of them got past making tools. Later generations found them useful by fluke really

ReplyDeleteThat's a funny sort of warning because everything you list actually was useful to physics in the long run. Maybe that wasn't an accident after all?

ReplyDelete