An exact expression for the fine structure constant

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The discussion presents an exact expression for the fine structure constant, stating that α^(-1/2) + α^(1/2)μ = e^(π^2/4), where α is approximately 1/137.03599911 and μ represents a term related to the electron's magnetic moment anomaly. Substituting the value of α leads to an approximation of π that closely matches its true value, differing only in the tenth digit. Additionally, using the exact value of π yields a refined fine structure constant of 1/137.03599952837, which falls within the measurement range. The significance of these findings remains uncertain, prompting curiosity about their implications. The discussion invites further exploration of potential meanings behind these mathematical relationships.
Hans de Vries
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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
 
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