What exactly is electron spin?

[akhmeteli]

the speed of the electron in ground state of the bohr model of hydrogen is ac

I think you'll agree that there are better theories than the Bohr model. For example, for the Dirac equation, eigenvalues of velocity projections are +-c (see, e.g., Dirac's book "Principles...", the chapter where he discusses Zitterbewegung.)

 

[jobsism]

Thanks a lot, guys! :D I'm quite the beginner in QM. So,I still don't completely understand all of it, but I think I'm on the way...

 

[alxm]

Spin is a type of angular momentum, where angular momentum is defined in the modern way as the "generator of rotations" (see Noether's theorem).[1][2] This modern definition of angular momentum is not the same as the historical classical mechanics definition, L = r × p. (The historical definition, which does not include spin, is more specifically called "orbital angular momentum".)

Good quotes; I feel this is seldom emphasized enough. The problem when describing spin as 'intrinsic angular momentum' is that it gives the impression that it can be described as classical (or orbital) angular momentum - as if the electron is 'spinning on its own axis', even though it's not. The oft-cited rationale that it can't be doing that "because it'd spin faster than the speed of light" easily furthers that misconception. -What if you're working non-relativistically? That's usually the case when describing electrons in atoms/molecules. If that's the case, there's no reason to care about exceeding the speed of light. Can't you model electron spin that way anyway?

But you can't model electron spin as if it were spinning on its axis; it's not SO(3). Spinors aren't vectors. Or in layman's terms: A rotating object doesn't reverse its direction if you rotate it 360 degrees - and an electron does. That fact is much more critical to electron behavior than the actual "rotation" itself (spin-orbit coupling being a relatively small effect in many cases). Since without it, you have no Pauli principle!