An exact expression for the fine structure constant

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SUMMARY

The discussion presents an exact expression for the fine structure constant, represented as α, which is defined as 1/137.03599911. The equation α^{-\frac{1}{2}} + α^{\frac{1}{2}}μ = e^{\pi^2/4 is introduced, where μ is Schwinger's first term of the electron's magnetic moment anomaly, calculated as 1 + α/(2π). Substituting the value of α into the equation yields a calculated value for π that closely approximates the known value, differing only in the 10th digit. This calculation results in a refined value for the fine structure constant of 1/137.03599952837, which falls within the measurement range.

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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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