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I was taught that the 'spin' of an elementary particle was its inherent, unalterable magnetic moment due to its physical spin, or angular momentum, that may or may not actually exist.

Therefore, if the quantum spin of a particle is not directly observable (because it probably doesn't exist, as such), but is measurable as its magnetic moment due to its seeming physical spin, how can its gyromagnetic ratio, or $g$-factor, be anything other than one?

What am I missing here?

Michael Seifert
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Kurt Hikes
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    The Landé $g$ factor of the electron is approximately $2$ because the spin of the electron is $1/2$. The spin of a particle is different from its spin magnetic moment, but the latter is derived from the first: $\vec{\mu}_s = -\frac{e}{2m}g\vec{S}$. Spin is not due to a rotation of the electron but it is an angular momentum, more precisely the intrinsic angular momentum of the electron. – Jeanbaptiste Roux Apr 13 '21 at 11:31
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    its magnetic moment due to its seeming physical spin... Start your reading at Wikipedia's page on Spin but I've never seen or heard a really clear explanation and I tend to fall back on the math to explain where it comes from. Dirac's equation was an eye-opener for me in this regard. That Wikipedia page has a nice graphic showing how a point in space can spin without screwing up everything. – StephenG - Help Ukraine Apr 13 '21 at 11:43

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