On page 4 of "Naturally Speaking" by G.F. Giudice, after a short list of numerological formulas for the fine-structure constant α, one finds a formula for α according to physical orthodoxy, i.e. grand unification. I reproduce it here for the edification of passing numerologists:
α = { αs sin2θW (b1−b3)+3/5 cos2θW (b3−b2) } / (b1−b2) + higher-order terms.
"Here, the fine-structure constant α, the strong coupling constant αs and the weak mixing angle θW are evaluated at the same renormalization scale and b1,2,3 are the gauge β-function coefficients. Higher-order terms cannot be neglected to achieve a prediction that matches the experimental accuracy."
Somewhat off topic, another interesting numerological hypothesis is the Gatto-Sartori-Tonin relation.
ReplyDeleteSee also this paper discussing that relation among others: http://arxiv.org/abs/1607.07898
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ReplyDelete(Alpha)^-1~137 + ln(137)/137 =137.035912269532
ReplyDeleteln(137)/137~(Pi(137))^-1
Prime number theorem: x/ln(x)~Pi(x)