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:
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?
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