# What is spin up and spin down?

1. Nov 16, 2006

### davidong3000

I tried to find this on google but could not find any solid answers. What is spin up and spin down? I know its something only applying to spin 1/2 particles. Does spin up mean a right hand rule spin with the magnetic north pole of the particle parallel in the direction of the thumb? Or does it mean that when u look at a particle in a certain direction it appears to be rotating anti clockwise along that direction?

2. Nov 16, 2006

### Jheriko

As far as I know we have limitations on how we can measure spin due to the Heisenberg uncertainty. In practice this means it is only possible to measure the magnitude of the spin vector and the magnitude of one component. If I remember correctly this axis is usually labelled $$S_z$$ and since the z-axis is usually tied to up and down directions I would guess that $$S_z$$ < 0 is spin down and $$S_z$$ > 0 is spin up.

3. Nov 16, 2006

### davidong3000

I have seen that link and was reading it long time before u sent this message :(

I still dont get it... when they talk about measuring the particle from z direction is z direction any agreed upon angle? And when the particle is up does this mean the north pole of the particle is facing toward the viewer or instrument along that angle?

some 1 please help, there seems to be zero proper definition of spin up or down on the internet...

Dave

4. Nov 16, 2006

Staff Emeritus
The observer picks a line, any line, and orients his apparatus along it (in Stern-Gerlach, for example, this would be the orientation of the magnetic field). This then divides the incoming particle stream into three, one of the outer ones of which is labeled spin up and the other spin down, while the middle stream is regarded as having spin component zero along that line. The important point here is that spins along different lines do not commute, and are subject to an uncertainty relation in consequence.

5. Nov 16, 2006

### Jheriko

AFAIK the z is just an arbitrary label for a direction.

Also after looking in Wikipedia more thoroughly myself there is a little bit defining spin up and spin down. It also reminds me that I neglected to mention the importance of spin-1/2, afaik the spin up and spin down labels only apply to these particles, presumably because other spins have more eigenstates (I am not sure, I am a quantum noob myself).

http://en.wikipedia.org/wiki/Spin-1/2

6. Nov 16, 2006

### davidong3000

Found It!

Check this out

http://www.ncsu.edu/felder-public/kenny/papers/bell.html#FOOTNOTE_9

and scroll down to "Appendix II. What's Being Measured"

According to this link, what ever angle u choose to look at a particle it's magnetic south pole with either point directly toward or away from you. If toward : spin up, if away : spin down.

Last edited: Nov 16, 2006
7. Nov 17, 2006

### dextercioby

There's no such thing as "magnetic north pole of the particle"...Nor "south pole", nor any pole. These terms apply only to macroscopic spherical objects which have an internal structure as to give them magnetic properties: planet Earth is a good example (it's a revolution ellipsoid really, but nvm).

Besides, particles in quantum mechanics are point particles...

Daniel.

8. Nov 17, 2006

### Los Bobos

^ And in addition with this one has to remember that spin is not rotation (quite evident for point like objects). The particles just happen to have a property, whose observables are the generators of SU(2).

9. Nov 17, 2006

### Gza

As a physicist, it's not easy to accept the fact that "particles JUST HAPPEN to have a property, whose observables are the generators of SU(2)." In the case of spin 1/2 particles such as the electron, the concept of their spin really comes out of the dirac equation, and the fact that in completing the square of the Klein-Gordon equation, in order to factorize it, and allow space and time to be on the same footing, in the form of them both having a first derivative, one must resort to the use of 4X4 matrices and 4 component spinors. These 4-d spinors can be decomposed into 2-d spinors which form the familiar spin up and spin down particles we all know about. Bringing group theory into this before tackling what I talked about makes very little sense, unless you're a pure mathematician.

10. Nov 17, 2006

### davidong3000

Then this literature below must be wrong then?

http://www.ncsu.edu/felder-public/kenny/papers/bell.html#FOOTNOTE_9
Apendix II
" If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole. The direction of the spin can be identified as the direction of the south pole of the magnet."

Dave

11. Nov 17, 2006

### dextercioby

Mind you that spin comes into play in QM not necessarily in connection with the Dirac equation, which is a relativistic one, but in connection with the representation theory of the Galilei group, which is the symmetry group of nonrelativistic classical mechanics. The only reason that equations invariant under the Galilei group are not used in a QM description of the electron and other spin 1/2 particles is the appearence of the Special Theory of Relativity which forbids using the Galilei group as the fundamental symmetry group of flat spacetime, but rather the Poincare' group.

So the concept of spin really comes out of nonrelativistic physics.

Daniel.

12. Nov 17, 2006

### dextercioby

The exact formulation "If you're not familiar with quantum mechanics, then the simplest way to think about spin is to note that electrons, like many other particles, are small magnets with a measurable north and south pole." has the advantage of using the expression "simplest way to think about spin". However, as the author implies, this view is incorrect(oversimplified, if you prefer) and a full understanding of the concept of spin cannot be done without group theory.

Daniel.

13. Nov 17, 2006

### Gza

I bolded the most important part of your quote. He obviously presupposes a laymans perspective in his description of spin, so in a sense he's only right to a certain degree. If you aren't familiar with the intracacies of the dynamics of spin in quantum mechanics, I guess it's okay to think about the magnetic field generated by a "spinning" electron (cringe,) since thats the only way to connect with the concept of spin in a classical sense(electrons really don't have any extended structure, so speaking about their "spinning", along with the magnetic field generated by this "spinning" makes little sense at the scale described by quantum mechanics). In fact, you can use this classical picture of spin to generate a hamiltonian(basically a quantum mechanical operator that represents the total energy of a system) that describes the interaction of a spin 1/2 particle with a magnetic field in a quantum mechanical context (but please don't take your author's picture of spin too literally).

14. Nov 17, 2006

### Gza

Very interesting viewpoint dex; thank you.

15. Nov 17, 2006

### Los Bobos

You completely misundestood my point. I tried to say, that the reason why we called it spin is that this internal property happens to have almost the same group structure as the 3-D rotations.

16. Nov 17, 2006

### lightarrow

Yes. I just would like to express my personal opinion that this image of a "spinning particle" or of a "little magnet" has made more damage than benefit.

17. Nov 17, 2006

### davidong3000

I know that the electron is a point particle and does not have a rotating physical volume, thats not what im debating here. But surely it has a north magnetic and south magnetic pole? Otherwise how do natural magnets have north and south magnetic poles too? What's their source?

Dave

18. Nov 17, 2006

### Gza

If I remember correctly, natural magnets aren't fully understood, but to a close enough degree, you can think of the north and south poles of magnetized material as arising from the charged electron being in "orbit" around the nucleus, of an atom in the material, thus giving rise to a north or south pole as a consequence of the charge being seen as a "current" generating the field. (once again, don't take this classical picture as the end-all of what happens sub-atomically)

19. Nov 17, 2006

### sicjeff

interesting. I always thought that this was basically an interesting property describing the sign of the wavefunction. I guess I learn something new each day.

20. Nov 17, 2006

### davidong3000

Actualy most of the internet literature indicate that although the electron's orbit does generate part of the magnetic field, a majority of the magnetic field is generated from the electron's spin not it's orbit.

http://en.wikipedia.org/wiki/Magnetism
"This can arise either from movement of electrons in an electric current, resulting in "electromagnetism", or from the quantum-mechanical spin and orbital motion of electrons, resulting in what are known as "permanent magnets". Electron spin is the dominant effect within atoms. The so-called 'orbital motion' of electrons around the nucleus is a secondary effect that slightly modifies the magnetic field created by spin."

Dave