The atoms refused to fit one simple value
At Columbia University, Polykarp Kusch and Henry Foley compared how several atomic states responded to a magnetic field. Their 1947–48 work found a small, consistent mismatch with the leading picture of the electron. The 1948 report, The Magnetic Moment of the Electron, compared gallium, indium and sodium through resonance frequencies measured in a constant magnetic field.
The mismatch was about one part in a thousand in the electron’s spin response. Small as that sounds, it mattered: the same electronic property had to account for different atoms, each packaging the electron’s magnetic contributions in a different way.
Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstract
A resonance turns an energy gap into a frequency
An atom placed in a magnetic field has several nearby energy levels. An oscillating field can make it change levels when the driving frequency matches their energy gap. Scanning that frequency finds a resonance, a response that marks the transition.
The electron contributes magnetism associated with its orbital motion and with its intrinsic spin. Spin is an intrinsic quantum property; the electron need not be pictured as a rotating ball. Different atomic states combine these contributions in different proportions. Their magnetic factors describe how strongly the total energy responds to the field.
Comparing resonances in one shared field helps reduce reliance on its absolute calibration. The rest of the inference comes from the atomic structure: identify the levels, calculate how their contributions combine, and ask whether one set of electron factors explains all the measured ratios.
Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstractP. A. M. Dirac (1928), The Quantum Theory of the Electron, Proc. R. Soc. A 117, 610–624 — UC San Diego scan
Several comparisons pointed in the same direction
A single displaced resonance might come from a complication of that particular atom. Kusch and Foley’s comparisons instead gave a consistent correction across states with different electronic weightings. Their 1948 abstract used that agreement, together with theoretical arguments, to reject a perturbation explanation for the observed ratios. The key was the pattern shared by the comparisons.
Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstract
Read the number with its date attached
The expression below is the 1948 result, with the orbital factor taken as one apart from the residual effects discussed by the authors. The spin factor is written as a positive magnitude. Because the electron is negatively charged, its magnetic moment points opposite to its spin.
Dividing this factor by two gives a value about 0.00119 above one. That fractional excess is called the anomaly: the small extra response beyond Dirac’s leading value. The uncertainty belongs to the historical estimate quoted here. Keep the 1947 announcement, the 1948 number and later measurements separately dated when following how the precision improved.
Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstractP. A. M. Dirac (1928), The Quantum Theory of the Electron, Proc. R. Soc. A 117, 610–624 — UC San Diego scan
Later experiments gave the electron a simpler home
Kusch and Foley reached the electron through atoms. Later Penning-trap experiments kept one electron and compared its spin resonance with its circling motion in the same magnetic field. The field largely cancels from the frequency ratio, while the cavity and trap bring new instrumental corrections. Fan and colleagues’ 2023 paper is one separately dated example of this route.
The anomaly also became a precise target for theory. Quantum electrodynamics calculates how the electron’s interaction with the electromagnetic field modifies its magnetic response; at sufficiently high precision, other interactions enter too. Comparing a modern prediction with the measurement requires an independently known fine-structure constant as well as the theoretical calculation. The early atomic comparisons supplied the experimental puzzle that such calculations had to explain.
Read the evidence: X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801P. A. M. Dirac (1928), The Quantum Theory of the Electron, Proc. R. Soc. A 117, 610–624 — UC San Diego scan