Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Friday, February 29, 2008

Damned Numbers

Carl and kneemo, amongst others, like to think about that damned number, otherwise known as the phase angle determining the charged lepton mass matrix, which is

$\phi = 0.22222204717$

to within experimental precision: notably close to $\frac{2}{9}$. The $3 \times 3$ MUB problem says nothing about this phase. Since phases usually involve factors of $\pi$, one wonders if there are any well known numbers that, when multiplied by $\pi$, also give numbers very close to $\frac{2}{9}$. For example, consider the first zero of the Riemann zeta function, namely $\gamma_{1} = 14.134725142$. Observe that

$\frac{\pi}{\gamma_{1}} = 0.222260611(5)$

which differs from $\frac{2}{9}$ by a factor of 1.000172751(75). So we didn't really need to look far to find a number satisfying this curiosity. Are there better ones?


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