I have always found the concept of spin a little weird. I had read somewhere that for the charge or size of electrons, their magnetic field is very high. In order to produce such fields, they must be spinning faster than the speed of light which is not possible. So where do the electrons get their high magnetic field from?
An answer without too much math would be preferred.
So I quote this source http://scienceblogs.com/principles/2010/07/26/electron-spin-for-toddlers/ :-
If we want to say that the magnetic moment of the electron is due to the motion of a spinning ball of charge, then we can easily calculate what the spin rate should be, given what we know about the size of an electron. If you use the maximum size you could possibly associate with the electron, the “classical electron radius”, and calculate how fast a sphere of that size would need to be spinning to produce the observed magnetic moment, you find that a point on the surface would need to be moving at a speed several times the speed of light in vacuum, which is impossible. That’s also a gross overestimate of the size of an electron– as far as well can tell, the electron has no physical size. It’s a point particle, and thus doesn’t have a surface that can be physically rotating.
OK, then, maybe the magnetic moment is just one of those things, you know? Maybe the “spin” angular momentum isn't really angular momentum at all. This is also false– spin angular momentum is real angular momentum. We know this because you can drive transitions from one spin state to another using polarized light, and we know from careful experiments done in 1936 that the angular momentum carried by light is real angular momentum. The angular momentum of a polarized photon can be used to make physical objects rotate, and it can also be used to make electron spins change states; this at least strongly suggests that spin angular momentum is real angular momentum comparable to that of spinning basketballs and all the rest.
So I do not understand what all this is suppose to mean. It first says maybe it is not spinning at all and then says that it is real angular momentum. Please clarify this for me. Or is this topic yet to be researched upon?
EDIT after answers
I think I have nearly got the answer but it was not what I was expecting (I am not talking about the quality of the answers). In the end I just want to ask as the electron actually does not spin but has angular momentum. I have pretty much understood that actual spinning is not the reason for its angular momentum. So is it safe to say that the actual reason behind the angular momentum is unknown?
Best Answer
First, the electron isn't actually spinning. Physical objects made up of collections of electrons and protons (and neutrons) can have angular momentum because they rotate; the electron does not get its angular momentum for the same reason.
Second, the magnetic moment of an object with angular momentum L is proportional to
$$ \mu \propto \frac{qL}{M} $$
The angular momentum of an electron due to its spin is a fixed constant, proportional to $\hbar$. Since the electron has a very small mass, its magnetic moment is very large.