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I know that the Spin Quantum Number is NOT necessarily some kind of measure of the rotation of an electron. I guess they chose that name when they realized an electron has a magnetic field around it in the same fashion several other configurations have the same one. In this case, I guess they thought of some positive anti-clockwise flow of charges in a loop or, some positively charged fluid revolving anti-clockwise inside a sphere (like a planet or a star). Hence the association. A permanent magnet bar exhibit a similar magnetic field but I guess that configuration did not provide an attractive name for them.

I know the terms up-spin and down-spin are more important when two electrons are in the same orbital. And it does not matter which is up and which is down as long as their north magnetic poles point to opposite directions. So, I am not asking for an explanation for the definition of Spin Quantum Number.

Many websites and forums say "electrons do not spin". For instance this one says that if an electron were able to spin, that would break the principles of Relativistic Physics. For me it is like saying that a proton/neutron/quark/gluon/etc. cannot spin/rotate. I can accept that maybe when bound to some atomic orbital, an electron, for some reason, cannot rotate. Ultimately, I guess that at least free electrons must be able to spin/rotate. In short, can an electron rotate/spin? If, so, what conditions must be met so it can rotate/spin? Can it spin/rotate when free? If it cannot spin/rotate when bound, why cannot it spin/rotate when it is in some orbital?

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An electron can not rotate on its axis, because it is not a small ball. An electron is a point-like particle: it does not have radius and it does not have rotation degrees of freedom (like Euler angles). An electron has a non-zero angular momentum, but the reason, the mechanism for the angular momentum is not related to rotation, and it lies deep in quantum field theory.

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  • $\begingroup$ Now, I get it. Thanks for "pointing" that out! I asked the same thing in Quora and they said "it is a wave". I know that as a wave, rotation makes little sense. I wanted to stick to the particle-oriented analysis. No dimensions, no rotation! So elegant and simple" Thanks, again! $\endgroup$
    – gEoRgE
    Commented Sep 30, 2022 at 5:26
  • $\begingroup$ P. S.: Back in the day, Compton said that the electron had dimensions. (journals.aps.org/pr/abstract/10.1103/PhysRev.14.20) Today, the "size" is smaller the greater the energy used to probe it. So, I guess, that at some "point" (he-he) the energy used could be so high that it will become dimensionless. Some consider it to have the same size as the orbital as it can be anywhere. But, if dimensionless, some things get easier to understand and others pieces of info will fit. $\endgroup$
    – gEoRgE
    Commented Sep 30, 2022 at 6:01
  • $\begingroup$ But... how do they get "upside down" when sharing an orbital with another electron? Could their magnetic fields change direction without physical rotation? Hmmm, I guess so. There is no other way. They can translate for sure. That does not require them to have dimensions, right? $\endgroup$
    – gEoRgE
    Commented Sep 30, 2022 at 6:23
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    $\begingroup$ Since an electron has angular momentum, it is no spherically symmetrical anymore. Roughly speaking, an electron has an arrow pointing in some direction. Thanks to this, we can rotate an electron, for example, using a magnetic field. But this rotation is not an analogue of the classical spin, instead it is an analogue of the classical spin precession. The free electron spin does not precesses: its “arrow” keep points in same direction. In the end an electron has three spatial degrees of freedom and one internal degree (discrete, with two basic values ​​"spin up" and "spin down"). $\endgroup$
    – warlock
    Commented Sep 30, 2022 at 6:57

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