# Elementary particle spin question

1. Jun 23, 2010

### mcjosep

Ok, when it comes to particle spin i know that all protons spin the same, all neutrons spin the same and so on. However i am confused as to whether or not these particles are actually spinning or if this is just a word that means something else like different colors of quarks even though they are not actually different colors.

If they are spinning what does a 1/2 spin mean in terms of velocity of spin?

2. Jun 24, 2010

### tom.stoer

Spin in general has nothing to do with orbital angular momentum. An electron with spin does not spin, there is nothing moving around in circles.

=> there is no velocity attributed to spin.

Your comparison with color in QCD is a good approach. Color is just an SU(3) degree of freedom. Spin is an SU(2) tegree of freedom. This SU(2) comes from the symmetry group of spacetime which is SO(3,1) ~ SU(2)*SU(2). SO(3,1) is just the Lorentz symmetry. By coincidence in four dimensions it happens to be locally isomorphic to SU(2)*SU(2) and this SU(2) allowes for integer and half integer representations.

So spin has something to do with spacetime, but there is nothing moving around in spacetime.

3. Jun 24, 2010

### blechman

spin is a very funny thing. It BEHAVES like angular momentum: it can be converted into angular momentum! (that is, a spin-1 particle can decay into two spin-0 particles with 1 unit of orbital ("ordinary") angular momentum between them, thus conserving total angular momentum). It also couples to magnetic fields the way ordinary angular momentum does (a charged particle moving in a circle has a magnetic dipole moment; so does a quantum particle at "rest" but with spin!). So in all ways, spin is an "angular momentum"!!

But it is not like anything classical - it's not that the particle is "spinning" - it just has this extra quantum-mechanical "sense of direction".

It takes some getting used to. It's nutz!

4. Jun 25, 2010

### kaksmet

One of the reasons you cannot see it as something that is really spinning, is that elementary particles which are thought to be point like have spin. but since they dont have any spatial extension it is impossible for them to rotate in the classical sense.

5. Jun 25, 2010

### tom.stoer

and they are not pointlike in the classical sense, either ...

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