Spin Magnetic Moment: Does an Electron Really Spin?

[Prashasti]

Does an electron really spin about its own axis? If not, what does spin magnetic moment imply? My physics teacher said "Besides the orbital moment, an electron has an intrinsic magnetic moment, it is called the spin magnetic moment, But I hasten to add that it is not as though the electron is spinning."

But, in my chemistry textbook, there's an illustration of an electron apparently "spinning" about its own axis. Moreover, the direction of spinning has also been shown.

 

[Nugatory]

It's a historical accident that we use the word "spin" to describe the quantum mechanical property that leads to an electron having a magnetic moment. What's going on actually has nothing to do with rotation about an axis; it's not clear that an electron even has an axis to rotate around.

However, there are many situations where an electron behaves enough like a little rotating ball that we can use that as a model. It's not quite right, but it avoids some very hairy quantum mechanical complications, and it's no more "wrong" than pretending that the Earth is a perfect sphere (it's actually a bit misshapen) when you're thinking about latitude and longitude.

That's what your chemistry textbook is doing.

 

[Prashasti]

So, it is an assumption, right?
Thanks.

 

[M Quack]

The spin of the electron is a relativistic effect that drops out of the Dirac equation. It is a very strange quantum mechanical beast that has nothing to do with the electron rotating like a prima ballerina. For example if you rotate the spin by 360 degrees you turn it upside down.

This picture is not an assumption, it is more like a crutch that allows people to come to grips with spin and relate it to something they know from the macroscopic world.

Spin has been observed in countless experiments. Electrons, neutrons and protons all have spin. There are thousands of experimental results that cannot be explained without taking spin into account.

 

[Khashishi]

If the electron was actually spinning on its axis, how would we ever know? For a composite object, we look at parts of the object while they revolve around the center of the object. For an object with no parts, what does it mean to spin? The question is not, does an electron spin, but, what exactly does it mean to spin?

If I define spin from basic experience, it is that it continuously evolves into rotated copies of its former self. For an object with perfect rotational symmetry, this condition is trivially satisfied. So I think it's fine to say it is really spinning, as long as you define your terms.

 

[Khashishi]

Neutrons and protons have parts, so something more complicated is happening for them. I think the neutron spin must be equal to the total of the spin of the constituent quarks and the orbital angular momentum of the quarks. I think the orbital angular momentum of the quarks is 0 in the ground state, but someone with more particle physics expertise should chime in.

 

[M Quack]

Quarks have spin 1/2, just like the electron. So the effective spin of the proton and the neutron (both also 1/2) are not simply the sum of the 3 quarks' spins

 

[Khashishi]

Of course when adding angular momenta, they needn't point in the same direction. Is there a 3/2 spin excited state for a proton?

Edit: a Delta+ particle is an excited proton, with spins aligned, I think. Is that right?