# I can't visualize spin I know that its not just a particle rotating

1. Jul 23, 2012

### Ezio3.1415

I can't visualize spin... I know that its not just a particle rotating about its axis... Then how do I think of it?

2. Jul 23, 2012

### Mark M

Unfortunately, you can't. It's a purely quantum phenomenon that doesn't have any classical analogue to use for visualization.

And as you say, it certainly isn't a particle rotating about an axis.

3. Jul 23, 2012

### Ezio3.1415

Re: Spin

Then we just think of it as a property of the particles...

4. Jul 23, 2012

### Whovian

Re: Spin

Correct.

5. Jul 23, 2012

### Mark M

Yes. Essentially, it refers to the number of times you must rotate a particle's wavefunction through the complex plane to bring it back to it's original value.

A misconception is that it refers to the number of times you must literally rotate a particle to bring it back to it's original state, but this is false. 'Rotation' in the above context refers to an operator on the wavefunction in Hilbert Space.

6. Jul 23, 2012

### Ezio3.1415

Re: Spin

Thanks... :)

7. Jul 23, 2012

### homeomorphic

Re: Spin

It might not have a classical analogue, but that doesn't mean that it can't be visualized mathematically, and this is particularly true for a spin 1/2 particle.

If you have a spin 1/2 particle, like the electron that is can be spin up or spin down, the Hilbert space is a 2-dimensional complex vector space. When you consider than multiplying by a constant give you the same physical state, you get a 1-dimensional complex projective space. This is the nothing but the Riemann sphere of complex analysis. Thus, the Riemann sphere can be associated to any system with a 2-d state space, which each point in the Riemann sphere corresponding to a physical state. And what's really interesting is that the geometry of the Riemann sphere is related to the probability of measuring spin up or spin down. For details, see The Road to Reality, by Roger Penrose, Chapter 22, I believe.

There seems to be some kind of similar picture for higher spin that he talks about, but I don't understand it yet.