This was one of the first two great successes of quantum electrodynamics, the other one being the Lamb shift.
In youtu.be/UKbp85zpdcY?t=52 from freeman Dyson Web of Stories interview (1998) Dyson mentions that the original key experiment was from Kusch and Foley from Columbia University, and that in 1948, Julian Schwinger reached the correct value from his calculations.
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Published on Physical Review by Polykarp Kusch and Foley.

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The electron magnetic moment is a fundamental property of electrons that describes their behavior in a magnetic field. It can be thought of as a measure of the strength and orientation of an electron's intrinsic magnetic field, which is linked to its spin and charge. ### Key points about the electron magnetic moment: 1. **Intrinsic Property**: The electron magnetic moment arises from two key factors: the electron's electric charge and its spin. It is a quantum mechanical property that does not depend on the electron's motion.