The most stringent test of quantum electrodynamics theory (QED) is a test of the QED formula that relates the measured value of the electron magnetic moment in Bohr magnetons (called g/2) to the measured value of the fine structure constant, α . The most accurate calculated values for the constants are tabulated in a recent review (of determinations of α). A very small value of the additional standard model correction a_{hadronic} must be included, but it is small enough that this relation between g/2 and α comes essentially from QED theory.
The QED test comes from comparing the g/2 that we measure to the g(α)/2 value that we calculate using an independently measured α in the QED formula. The most up-to-date result is in a different review (of electron g/2 measurements).. The difference the magnitudes of these two values is
at the one standard deviation level. The standard model of particle physics, which includes QED theory, is thus able to predict the electron magnetic moment in Bohr magnetons to a remarkable level of precision.
The accuracy of our measured electron magnetic moment is already high enough to make tests that are 12 times more stringent. Two developments are required. First, an independent determination of the fine structure constant that is as accurate as the one that we report must be made, rather than being 12 or more times less accurate as at present. Second, the effort underway by QED theorists Kinoshita and Nio must succeed in calculating C_{10}.