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Sandbox Physics
Quantum physics: reading the evidence

Nobel A · Evidence and control · 1897–2022

Kusch and Foley: a small mismatch between magnetic factors

Sandbox Physics ·

How can atomic resonance reveal a property of the electron?

The instrument measures an atom, not an isolated electron

An atomic-beam resonance frequency depends on the energy difference between selected magnetic sublevels. Those levels combine electronic orbital and spin contributions, with hyperfine structure as well. A precise frequency is therefore the beginning of an inference about the electron, not a direct display of its magnetic moment.

Kusch and Foley compared magnetic factors of gallium, indium and sodium states through hyperfine transition frequencies in a constant magnetic field. Comparing different states changes the relative weight of the electronic contributions. The usefulness lies in their shared constraints, not merely in locating one sharp resonance.

Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstract

A reference field helps, but does not remove atomic physics

A ratio measured in a common field can reduce dependence on an absolute field calibration. Yet it still requires identifying the transitions and connecting atomic magnetic factors to orbital and spin factors. State mixing or an omitted interaction can bias that conversion.

The authors’ 1948 abstract emphasizes agreement among several comparisons in arguing against a perturbation explanation. That is stronger than repeating one transition many times: a common electronic correction must remain compatible with differently weighted atomic states. Precision within one comparison and consistency across comparisons answer different questions.

Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstract

Keep the date attached to the number

The expression below is the summary quoted in the 1948 paper, taking the orbital factor as unity apart from the residual effects discussed by the authors. The spin factor is the positive magnitude convention. The electron’s negative charge still makes its magnetic moment oppose its spin.

The corresponding anomaly is about a thousandth of the Dirac reference after the factor of two is removed. This is a historical estimate with the stated uncertainty, not today’s recommended constant. Nor is it automatically the value reported in the first 1947 announcement.

gS=2(1.00119±0.00005),ae≡gS−22g_S=2(1.00119\pm0.00005),\qquad a_e\equiv\frac{g_S-2}{2}

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

A later experiment changes the route to the same property

Fan and colleagues’ 2023 experiment used a single trapped electron rather than extracting its moment from several atomic species. Spin and cyclotron frequencies in the same apparatus provide a comparison in which the magnetic field largely cancels. Cavity and trap effects still require careful treatment.

That change of method matters scientifically. Removing an atomic-structure inference introduces different instrumental corrections, so agreement is not simply a longer repetition of Kusch and Foley’s experiment. The 2023 paper also distinguishes measurement uncertainty from the uncertainty of a theoretical comparison involving the fine-structure constant.

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, 071801

An anomaly is an observable, not a cartoon mechanism

The Dirac baseline fixes a leading magnetic response. A reproducible departure demands additional physics in the comparison. Modern calculations include radiative contributions and, at sufficient precision, other interactions. A picture of an electron surrounded by a cloud does not perform that calculation.

This article follows the experimental inference. It does not derive quantum electrodynamics or attribute the entire modern prediction to one historical correction. The Lamb shift is a related precision challenge, but it is a different measured quantity and needs its own evidence.

Read the evidence: P. A. M. Dirac (1928), The Quantum Theory of the Electron, Proc. R. Soc. A 117, 610–624 — UC San Diego scanX. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801

What the teaching spectra can establish

Changing an effective Hamiltonian in the linked Lab shows how level shifts alter transition frequencies. Rabi calibration explores coherent drive and readout. Neither model estimates the historical electron anomaly from gallium, indium and sodium records.

A convincing magnetic-moment reconstruction would preserve assigned lines, field comparisons, calibration and atomic corrections before reporting a fitted electron factor. Entering the historical value as a simulator setting can illustrate its consequence; it cannot independently measure that value.

Read the evidence: P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstractX. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801

Sources and reading notes

The 1948 Kusch–Foley author abstract supplies the atomic comparisons and quoted result; its full PDF requires authorization. The 1947 value is not substituted with the later number. Dirac’s paper and the 2023 single-electron measurement supply distinct theory and method comparisons; no original resonances are refitted.

  1. P. A. M. Dirac (1928), The Quantum Theory of the Electron, Proc. R. Soc. A 117, 610–624 — UC San Diego scan
  2. P. Kusch and H. M. Foley (1948), The Magnetic Moment of the Electron, Phys. Rev. 74, 250 — author abstract
  3. X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801
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