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An exact(?) expression for the fine structure constant

  1. Sep 20, 2004 #1

    Hans de Vries

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    Just for the record:

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

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

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

    Fill in 1/137.03599911 for [itex]\alpha[/itex] and you'll get for pi:

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

    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
  2. jcsd
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