Wednesday, May 24, 2006

New values of "g" and the fine-structure constant

Gerry Gabrielse, an experimenter from Harvard University, and his collaborators are going to announce new, more accurate values of the fundamental constants. Using their single-electron quantum cyclotron, they can see that the new magnetic moment of the electron is
  • g/2 = 1.001 159 652 180 85 (76).
As you can see, there are 13 significant figures or so - the value is six times more accurate than ever before. Using the cyclotron result for "g" above plus QED theorists from other universities, they can also deduce the value of the fine-structure constant. The theoretical calculation, starting with the terms
  • g/2 = 1 + alpha / 2 pi,
requires to calculate 891 diagrams with up to four loops, and the result for the fine-structure constant
  • 1 / alpha = 137.035 999 710 (96)
is ten times more accurate than the results from atom-recoil measurements. In fact, it is the first improvement of the accuracy in roughly 20 years. The precise value is sensitive on new physics at 130 GeV. All skillful numerologists are welcome to interpret the new data.

Update: Thanks to Alejandro Rivero: the correct sequence in 1/alpha is indeed "999" instead of the previous typo "997".


  1. Incidentally, this progress in the measurement of g/2 can be used to do some exersice on one of the favorite themes of Lubos' blog: frequentist versus bayesian. Remember that the notation .xxxxXX (yy) in the results is supossed to mean that the central value of the measurement is .xxxxXX and the gaussian width is two times .0000yy


    1) if a measurement was .xxxxXXX (yyy), calculate the probability of a new measurement .zzzzzzzqq (QQ). For instance take the old measurement of g/2 to calculate the probability of the new one

    2) If a theoretical result was inside the 50% interval of the old measurement, which is the probability for it to be still in the 50% interval of the new one?

    3) suggest your own question and solve it

  2. corrects the estimate for the four loops and then uses new measurement of Gabrielse, so that know the fine structure constant is at
    1/137.035 999 084 (51)

    I guess they suspected someone was wrong when they compared 999 710 (96) to the old 999 108 (450); the result was out for almost 2 sigma. Now on the contrary the new result is astonishingly near of the center of the oldest. Perhaps the error estimate is conservative, or perhaps they are fine tuning the math, knowing in advance the new results of Gabrielse?

    In any case here you have:
    1/137.035 999 084 (51)

  3. Now a funny thing is that other prediction of my favorite seer, the one I left out of papers, is still, four years later, inside the 1-sigma, because it was inside the old and it has survived the new digit. It is
    137.035 999 095 829
    to be compared with
    137.035 999 084 (51)

    The ansatz of De Vries for this prediction is amusing, and I am not sure if it could have some meaning. It is
    alpha^1/2+alpha^-1/2 = exp((pi^2)/4)
    and then he proceeds to further corrections.

    A thing that amazes me, now, is that both sides of the ansatz stink to duality. The LHS is e plus 1/e, so a sum of electric plus magnetic charge, and it is invariant under alpha-->1/alpha. The RHS, i^ln(i), is the integration of a gaussian energy lump, except that a peculiar one, \int exp(-x^2)*(cos x + i sin x). But close to all the stuff of solitons, instantons, monopoles etc.