Physical Interpretation of Spin

[tannerbk]

We are starting to learn about spin in my introductory quantum mechanics course, and I was wondering if anyone could provide a physical interpretation of an electron's spin. I understand its a form of angular momentum which has nothing to do with the motion of the electron in space, but since an electron is a structureless, point particle, is there a good way to think about an electron's spin?

 

[Matterwave]

There appears to be no good "picture" of the electron spin. You can think in your mind like it's the electron spinning around, but that picture is met by many difficulties which you correctly point out.

All that can be really said is that the spin is an additional degree of freedom intrinsic to particles, and that it acts like an angular momentum because it gives rise to coupling to the magnetic field of these particles (in a fashion similar to what would be the case if the particles were spinning) in e.g. the Stern-Gerlach experiment.

 

[jtbell]

Also, the intrinsic angular momentum ("spin") of the particles that make up an object, contributes to the object's total macroscopic angular momentum. The best-known experimental demonstration of this is the Einstein-de Haas effect. If you know the Feynman Lectures on Physics, it's in there somewhere. (I don't have my copy handy so I can't give an exact reference.)

 

[tannerbk]

Thanks for the responses. I was wondering if there was any significance to the fact that particles that make up ordinary matter all have spin 1/2. I understand mathematically why this is, but is there a deeper reason for this specific quantization?

 

[The_Duck]

Thanks for the responses. I was wondering if there was any significance to the fact that particles that make up ordinary matter all have spin 1/2. I understand mathematically why this is, but is there a deeper reason for this specific quantization?

Simplifying somewhat, in the framework of quantum field theory we find that

-fundamental spin 0 particles are naturally very heavy (so that they would be unstable to decay to other, lighter particles);
-fundamental spin 1 particles must be massless; and
-it's not clear how to write down a consistent theory of fundamental particles with spin > 1 (though someone more knowledgeable may correct me on this).

That leaves spin 1/2 particles, which have no particular reason to be heavy and no particular reason to be massless. So it's natural to expect spin 1/2 particles to be the lightest stable massive particles in nature.

 

[tom.stoer]

it's not clear how to write down a consistent theory of fundamental particles with spin > 1 (though someone more knowledgeable may correct me on this).

Even so it's not absolutely clear whether certain SUGRAs are renormalizable I would say that SUGRA is a consistent theory with spin 2 (graviton) and spin 3/2 (gravitino). What you are saying applies to spin > 2.