What does spin 1/2 mean for a particle?

[Feeble Wonk]

Please help a poor stupid layman. When a particle has a spin of 1/2, what does that really mean? 1/2 of WHAT?

 

[facenian]

1/2 of $\hbar$ the quantum unit of angular momentum. So it happens that when try to meassure momentun of a fundamental particle you only obtein discrete values multiples of the fundamental unit. I don't know if anybody konws why

 

[edguy99]

Historically it comes from something like this at http://www.youtube.com/watch?v=cquvA_IpEsA

The mathematics of the gyroscope are the basis of quantum spin. It has only two directions of spin, left and right. Furthermore if we define magnetism with the right hand rule we get particles, with the left hand rule we get anti-particles, just like the real world.

Notice about half way through the video where the gyroscope starts to "precess", ie. rotate around an axis. It is important to note that there are two axis involved, first the axis of the gyroscope that most of the mass is rotating around. Second, the axis of gravitation, pointing straight up that the gyroscope is "precessing" around. The speed of the precessing is called the Larmor Frequency and is the basis of NMR imaging technology.

In an experiment called the http://web.mit.edu/8.13/www/JLExperiments/JLExp_18.pdf it can be shown that electrons go either up or down by fixed amounts in a magnetic field, not by a random amount that one would expect if the axis was fixed in a particular direction. The idea of precession, forces the "average" direction of the particle to align with the outside magnetic field and explains why the particle goes only up or down.

Some animation videos here model precession under a variety of magnetic field strengths.

Partly why the short hand term 1/2 is used, is that some go down 1/2, some go up 1/2 hence the difference between the two is one.

For spin 1/2 particles you have 2 states: 1/2, -1/2 (a difference of 1)
For spin 1 particles you have 3 states: 1, 0, -1 (always a difference of 1)
For spin 3/2 particles you have 4 states: 3/2, 1/2, -1/2, -3/2 (always a difference of 1)

 

[jewbinson]

It should be noted that since an electron is a fundamental particle, it has no internal structure, and so the spin of an electron does not have any relation to it's motion internally (i.e. the electron does not spin round like the Earth spins round on it's axis).

Spin is an intrinsic property of an electron.
You cannot see spin happening within the electron, but you can see it's effects on the electron (e.g. Stern-Gerlach experiment).