# What is spin for neutral particles

1. Dec 3, 2009

### ArielGenesis

I understand that an electron spin is intrinsic. We call it spin because electron has a magnetic moment, which would be naturally produced if the electron is physically spinning. All we know is that for whatever reason, electron has a magnetic moment.

My question is, how do we know if neutral elementary particle have spin?

2. Dec 3, 2009

### DrChinese

The magnetic moment is not the electron spin. Particles have spin independent of charge. An example would be the photon. As a general rule, particle spin is not assumed to be directly associated with physical spinning motion. A particle is not a ball which spins or turns in a direction. Probably the term "spin" should not be used, as that has classical connotations.

3. Dec 3, 2009

### Fredrik

Staff Emeritus
Particles have spin because they're defined as the physical systems that can be described by irreducible representations of the restricted Poincaré group, and spin is one of the numbers that label a particular irreducible representation. So asking why electrons have spin is kind of like asking why Champagne is made in France. It's just much more difficult to see that the answer is contained in the question. To really understand this, you'd have to go through the relativistic version of the argument I posted here, plus the actual construction of the representations. Chapter 2 of Weinberg's QFT book is a pretty good place to read about those things.

4. Dec 4, 2009

### DrDu

Last but not least, also neutral particles, like the neutron, not only have spin, but also an associated magnetic moment.

5. Dec 4, 2009

### ArielGenesis

does neutron have magnetic moment due to non neutral quark?

Umm... thx fredrik, I checked ur link but... I dont really understand it. So, for all purpose and intention, spin is just a vector that all elementary particle has, and it obey angular momentum commutator relation?

And it arise from some fact that I don't have to know about until I go to grad school?

6. Dec 4, 2009

### Fredrik

Staff Emeritus
Yes that's right. You should know that that fact is the assumption of rotational invariance of space, but you won't have to know the details for at least a few years.

7. Dec 4, 2009

### xepma

Spin is well-defined in non-relativistic systems as well, so it's not entirely correct to state that it arises from the principles of relativity. At best, you can say that it is compatible with relativity (although you need to invoke on infinite dimensional representations). But spin is definitely not limited to relativistic systems alone.

8. Dec 4, 2009

### Fredrik

Staff Emeritus
I didn't say that it does. You might want to click that link.

I think of "electrons" (and particles in general) as being defined relativistically, but I suppose we could define particles in non-relativistic QM as well, as systems represented by irreducible representations of the Galilei group.