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Is the spin of an electron based on its direction of angular momentum? Is it based on the right hand rule of angular momentum? Does Spin up means that the electron is spinning anti-clockwise and spin down means that the electron is spinning clockwise according to the right hand rule?

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What do we mean when we say spin up of a particle or spin down of a particle?

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    $\begingroup$ Have a look at What is spin as it relates to subatomic particles? and its linked questions. Nothing is actually spinning. Electrons are not little billard balls. $\endgroup$ – ACuriousMind Mar 25 '16 at 16:52
  • $\begingroup$ Are you saying electrons do not spin or are you saying you think they don't spin? Many things in nature from raindrops to galaxies spin and spin is related to magnetic moment. Has it been proven that electrons do not spend? Thanks $\endgroup$ – Bill Alsept Mar 25 '16 at 18:58
  • $\begingroup$ Especially this answer of the question ACuriousMind linked stated that spin has really to do with rotation. More see here. $\endgroup$ – HolgerFiedler Mar 25 '16 at 21:08
  • $\begingroup$ @BillAlsept: though ACuriousMind would probably consider this a misleading description, an electron is an excitation in a quantum field not a little ball like some microscopic version of a pool ball. It has an angular momentum, but this cannot be simply interpreted as something spinning in the way a macroscopic object spins. $\endgroup$ – John Rennie Mar 26 '16 at 6:53
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    $\begingroup$ Yes, it has been established that electrons do not just rotate; there are allowed values for spin that are not allowed for regular angular momentum (in more mathematical terms, I think it can be described ilke this:fundamental particles with spin are associated with irreducible representations of the spin group which is locally the same as the rotation group and therefore not so simple to distinguish from it---hence the "rotational terminology"---but possesses certain irreducible representations that the rotation group does not possess. The two things are thus fundamentally different). $\endgroup$ – Danu Mar 26 '16 at 17:52