Deviations from 2

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measure for measure Deviations from 2 Alberto Moscatelli surveys a series of experiments on the electron g-factor that marked the departure from the Dirac equation and contributed to the development of quantum electrodynamics.

ometimes a new experimental that “Aesthetic objections In December 1947, Kusch technique, improving the precision could be raised against such and Foley corroborated Sof certain measurements, can a view”2. their previous conclusion, unveil unexpected deviations from an Nevertheless, using results obtained with

2 5 accepted theory. Such was the case with experimental techniques sodium in the S1/2 state . the molecular-beam magnetic-resonance had by then evolved enough The fact that the discrepancy method developed by Isidor Rabi in the to probe directly the fine was observed with another 1930s. Rabi showed how to induce and and hyperfine structure of atom implied that if some detect transitions between states with atoms. In another seminal perturbation was in fact in different nuclear- or spin-magnetic moments 1947 experiment3, Lamb operation, it would have to using radio and microwave frequencies, in and Retherford reported be of the same magnitude, 2 2 principle enabling the direct measurement of that the S1/2 and the P1/2 which made it an unlikely magnetic moments. levels in the hydrogen proposition. In a footnote, From the Dirac equation, established in atom are not degenerate, they pointed to a parallel AIP EMILIO SEGRÈ VISUAL ARCHIVES, ARCHIVES, VISUAL AIP EMILIO SEGRÈ COLLECTION TODAY PHYSICS 1928, it followed that electrons possess an conflicting with the Dirac development in the theory intrinsic angular momentum (spin), and description of hydrogen’s fine structure. of the electron: a personal communication

that the proportionality between the spin Investigations about the existence of with Julian Schwinger indicated that gL is magnetic moment and angular momentum is an anomalous magnetic moment were necessarily 1, whereas gS may not be exactly 2. given by geµB/ħ, with µB the Bohr magneton, carried out by Kusch and Foley. Their Finally, the conclusive paper containing ħ the reduced Planck constant and ge — the approach was to choose atoms with only more accurate measurements using three electron g-factor — exactly equal to −2. one electron in the outer shell, so that the atoms (gallium, sodium and indium) There was no experimental ground to doubt Russell–Saunders relationship linking the appeared in August 1948 with the confident the validity of the equation. In fact, the g-factors of the angular and spin magnetic title “The magnetic moment of the electron”,

assumption that an electron’s spin magnetic moments (gL and gS = −ge, respectively) to reporting a value of gS = 2(1.00119±0.00005) moment was equal to the Bohr magneton that of the total angular momentum (gJ) (ref. 6). Meanwhile, Schwinger had calculated was used by Rabi and his students to calibrate was valid to a high degree of precision. the deviation from 2 based on concepts from their setup for the determination of magnetic An important issue at the time was the quantum electrodynamics. moments of various nuclei. accurate determination of the magnetic field, From that moment on the goal of Then, in May 1947, Nafe, Nelson and Rabi the uncertainty being much higher than measuring the g-factor of the electron reported measurements of the hyperfine required for such a measurement. The trick was not so much to ascertain whether or splitting of both hydrogen and deuterium. was to determine the ratio of the transition not it deviates from 2, but to improve the Because the hyperfine theory for these two frequencies associated with a change in the precision for testing the theory of quantum atoms was considered to be complete, the total electronic angular momentum of two electrodynamics. In 1955, Polykarp Kusch experimental values should have matched atoms in two different spectroscopic states (pictured) shared the Nobel Prize in the theoretical ones. But Nafe et al. observed in the same magnetic field. This would yield Physics for “his precision determination

a discrepancy of about 0.25% — well above gS without needing the actual value of the of the magnetic moment of the electron”. the error associated with the calculated field. In November 1947, using this approach The current accepted value of the electron 2 2 values, prompting the authors to comment, for gallium in the P1/2 and P3/2 states, they g-factor is −2.00231930436182(52) (ref. 7). “Clearly this interesting deviation is worthy obtained gS = 2.00229 ± 0.00008, assuming 1 of further study” . gL = 1 (ref. 4). The authors acknowledged, ALBERTO MOSCATELLI is a senior editor In September of the same year, however, the alternative possibility that at Nature Nanotechnology.

Breit advanced the hypothesis that this gL < 1 and gS exactly equals 2. Moreover, discrepancy would not be at odds with the gallium was not an ideal atom, because of References assumption that the electron may possess an the presence of quadrupolar interactions 1. Nafe, J. E., Nelson, E. B. & Rabi, I. I. Phys. Rev. 71, 914–915 (1947). 2. Breit, G. Phys. Rev. 72, 984 (1947). intrinsic magnetic moment — that is, a small possibly perturbing the magnetic energy 3. Lamb, W. E. Jr & Retherford, R. C. Phys. Rev. 72, 241–243 (1947). contribution to the Bohr magneton. There levels; theory predicted these perturbations 4. Kusch, P. & Foley, H. M. Phys. Rev. 72, 1256–1257 (1947). is a clear sense of tentativeness in Breit’s to be small, but the interpretation of 5. Foley, H. M. & Kusch, P. Phys. Rev. 73, 412 (1948). 6. Kusch, P. & Foley, H. M. Phys. Rev. 74, 250–263 (1948). communication: quite respectful of the the results could be debatable, calling 7. Fundamental Physical Constants: Electron g Factor (NIST, 2014); Dirac description of the electron, he admits for caution. http://go.nature.com/2ogBXkn