I'm writing a physics article with significant historical content, and I'm struggling to find something. Forgetting about the anomalous magnetic dipole moment for a minute, the electron's g factor is approximately 2. This is twice the "classical" value.

Who predicted and/or discovered or measured this g factor of 2?

I'm currently look at H Stanley Allen's 1921 paper The Angular Momentum and Some Related Properties of the Ring Electron. It dates from 1921. He gives the magnetic moment as 9.232 x 10ˉ²¹ EMU, ½(e/m)(h/2π)


2 Answers 2


From Crane, H. R. "The g factor of the electron." Scientific American 218.1 (1968): 72-85.

Samuel A. Goudsmit and George E. Uhlenbeck proposed

... in 1925 that the electron itself had an angular momentum and a magnetic moment. ... That the electron should have in addition an intrinsic magnetic moment was part and parcel of the idea that it was spinning. ... Thus at the time of the discovery of electron spin the g factor of the electron could be expressed as the number of "natural units" of magnetic moment (...) divided by the number of "natural units" of angular momentum (...). When defined in this way, the g factor for the orbital motion of the electron in its lowest energy state in hydrogen is 1, whereas the g factor of the free electron is 2. (The g factor as a term designating a ratio of magnetic moment to angular momentum in these special units had been introduced a few years earlier for the case of the atom by the German physicist Alfred Lande.) ... In the case of the g factor of the electron, a strong reinforcement for the belief in the exactness of the value 2 came in the late 1920's from the new formulation of quantum mechanics by P. A. M. Dirac.

Also helpful is Tomonaga, S. The story of spin. University of Chicago Press, 1997

From Enz, Charles P. No time to be brief: A scientific biography of Wolfgang Pauli. Oxford University Press on Demand, 2010. Chp. 5 The Hamburg years: The curious history of spin.

"But who should now be considered the discoverer of the electron's spin, Pauli, Kronig, or Uhlenbech and Goudsmit?" [p.116]. "That in the history of modern physics the idea of spin has stirred up so much controversy is a strange fact." [p.119].

From Pais, Abraham. Inward bound: of matter and forces in the physical world. Oxford: Clarendon Press, 1986.

"Following a hint by Ehrenfest, George [Uhlenbeck] found in an old article by [M.] Abraham [1903] that an electron considered as a rigid sphere with surface charge only does have g = 2." [p.277]. Similar proposals to Abraham were made by Fitzgerald [1900], Compton [1921] and Kennard [1922]. Pauli made a proposal of spin which influenced Goudsmit and Uhlenbeck in 1924. [p.279]. Pais quotes Dirac on the Dirac equation, "It was found that this equation gave the particle a spin of half a quantum. And also gave it a magnetic moment. It gave just the properties that one needed for an electron. That was really an unexpected bonus for me, completely unexpected." [p.286].

From Pippard, Brian. "Magnetic Moments." Rev. of Inward Bound: Of Matter and Forces in the Physical World, by Abraham Pais. London Review of Books 8.15 (1986): 17-18. 16 Nov. 2019 https://www.lrb.co.uk/v08/n15/brian-pippard/magnetic-moments.

Why should anyone wish to know the magnetic moment of the electron to ten-figure accuracy? The answer is worth giving in some detail as an exemplary account of the research process. We must return to the early days of quantum mechanics and the task Dirac set himself in 1927 to make it consistent with relativity theory, as it was not when first formulated. In one of the masterpieces of physics he showed that the restrictions imposed by relativity, as well as others which he regarded as essential, allowed only one formulation. Applied to the electron, its solutions described, without any extra assumptions, a number of properties which the electron had been found experimentally to possess, but which had not been explained hitherto. Among them was the magnetic moment whose magnitude is conventionally expressed by a number g; in Dirac’s theory g turns out to be exactly 2, and the spectroscopists at the time were satisfied that this agreed with their extremely precise measurements. There was, however, an exceedingly curious consequence of the theory: that it permitted electrons to have negative as well as positive energy, something that is inconceivable in classical mechanics.

Did anyone mention the possibility of antimatter before 1928?

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    $\begingroup$ Thanks for that Michael. $\endgroup$ Commented Nov 18, 2019 at 8:02

According to this Nature Physics article, it appears to have been Paul Dirac:

From his theory of relativistic quantum mechanics, Paul Dirac predicted that the g-factor of elementary spin-1/2 particles, such as the electron, is exactly 2.

Further corrections to this value come from QED.


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