# How did gyromagnetic ratio come up before quantum mechanics, and who introduced it?

I am really curious about who was the first one to define the gyromagnetic ratio $\gamma$ of a body, i.e. the ratio of its magnetic dipole momento to its angular momentum. It is a very important concept in quantum mechanics, but I was wondering whether it first appeared in a classical context or in a quantum one, who defined it, and why.

We can see it appears in the formula for the Larmor precession: $$\omega=\gamma B\tag{1}$$ which tells us the frequency of precession of a body in the presence of a magnetic field $B$. Was Larmor the first person to highlight the importance of this ratio? was he the first one that used it in a formula? Was $(1)$ the first formula where $\gamma$ appeared? If he was indeed the first one, could you tell me what was the name of the paper in which he published the results?

At least implicitly, the ratio came up earlier in Maxwell's work on gyromagnetic effect. He noted that "electricity circulates with something like momentum or inertia" (even earlier Ampere conjectured that magnetism is caused by "molecular currents" in matter), and concluded that magnetization should cause slight rotation of the magnetized material. Maxwell's attempts to measure it were unsuccessful, but the mantle was picked up by none other than Einstein himself, who wanted to confirm Ampere's hypothesis. Together with de Haas he conducted a series of experiments in 1915-16 with theoretical predictions featuring the gyromagnetic ratio prominently. They denote it $\lambda$ and show that the theory predicts $\lambda=2e/m$, where $m,e$ are the mass and the charge of the electron. Of course, the formula would have been pointless earlier because the mass/charge ratio wasn't known. Their experiments confirmed the prediction, but... only due to a measurement error.
The truth is that the gyromagnetic effect in their experiments was due not to molecular currents, but to electron spin, and because it is $1/2$ the correct value is about half of their classical prediction. Curiously, Barnett who conducted similar experiments at the same time originally got values that differed from Einstein-de Haas ones by a factor of $2-2.3$, but after their publication "corrected" himself down to $1.1-1.4$, see Jeng's Selected History of Expectation Bias in Physics. However, the discrepancy soon came to light, and went under the name "gyromagnetic anomaly".
• "My answer will only be partial" i must admit, the answer was far more complete that I expected! Im very thankful for you taking time to write this, as I found it very clarifying. I will read each and every one of the links in this post. PS: as a clear representative of the bias in physics (and rather related to this post) was the case of Millikan's value of $e$, as explained by Faynman (en.wikipedia.org/wiki/…). Its worth reading. Dec 1, 2015 at 22:43