An exact expression for the fine structure constant

[Hans de Vries]

Just for the record:


$$\ \alpha^{-\frac{1}{2}}\ +\ \alpha^\frac{1}{2}\mu\ =\ e^{\pi^2/4}$$


Where $\alpha$, the fine-structure constant = 1/137.03599911 (46)
and $\mu=1+\frac{\alpha}{2\pi}$ is Schwingers first term of the electrons
magnetic moment anomaly which is a function of $\alpha$ as well.

$\alpha^\frac{1}{2}$ is the probability for an electron to emit or absorb a photon.

Fill in 1/137.03599911 for $\alpha$ and you'll get for pi:

3.14159265263 which only differs in the 10th digit with the real value:
3.14159265358...

Using the exact value for pi results in a value for the fine structure
constant of: 1/137.03599952837 which is within the measurement range.

Does it mean anything? maybe, maybe not.

Regards, Hans

 

[Greg Bernhardt]

@Hans de Vries curious if you ever did find any meaning to this?