What makes spin different from classical angular momentum and magnetic moment?

[zrek]

Dear members,

I'd like to collect those properties of "spin" that makes it different to a normal (classical) angular momentum or magnetic moment.
Please help me, correct, reword my sentences one by one. I'd like to create a short but still understandable and correct list.

1. Spin quantum numbers may take half-integer values (There are particles with half-integer spin)
2. Although the direction of its spin can be changed, an elementary particle cannot be made to spin faster or slower.
3. The spin of a charged particle is associated with a magnetic dipole moment in a way that can not be explained classicaly.
4. The particles with half-integer spin (fermions obey the Pauli exclusion principle) behaving differently from the particles with integer spin (bozons may "bunch" together even if in identical states) and that difference is not possible to explain classical way.
5. Particles with half-integer spin can be created only in pairs.
6. It is possible that fermions (particles with half-integer spin) can bound together to form a Cooper pair and behave like bosons.
7. The spin (as vector) projection can be mesured only in one direction of the possible 3
8. A magnetic field is always sets the mesurable direction of the spin.
9. If we measure the spin projection in one direction, then in another direction, then the second measurement invalidates the result of the first.
10. In case of photon the spin represents it polarisation. The spin of a charged particle is connected to its magnetic moment.
11. The quantum entanglement of two particles can be detected only by analyzing their spins. (The spin is the only property of a particle that is effected by the entaglement)


(The 1st one is most uncomplete. Unfortunately I have no idea how to explain it in a short way why is that property is unusual in the classical world.)

Please correct me if one of the statements above are misleading or invalid.
Do you have a better, shorter, clearer explanation of the above properties?
Is there an additional property that is worth to mention?

Thank you for your help!

 

[edguy99]

I'll make a couple of comments:

1/ Assuming a right hand rule for a spinning object, the spin will point either up or down. Calling it a spin 1/2 particle is only a convention to allow you to say that a particle is in a spin 1/2 state (up) or a spin -1/2 state (down). Spin 1/2 particles have two states, either up or down and mathematically you can change one to the other by adding 1, and can be represented classically. Assuming the left hand rule gets you the spin 1/2 antiparticles.
2/ The speed of the spin does not matter in the sense that a particle in an up state will still be in an up state if it spins faster. The speed of the spin does not determine if it is up or down, only the direction does that.
3/ I am not sure I would agree with that.
4 and others/ When thinking about 1/2 integer spin particles or integer spin particles, it helps sometimes to have a visual representation.

For example, a spin 1 particle can be represented as two spin 1/2 particles "stuck" together. If both are up, the particle will go up in a magnetic field. If one is up and one is down, it will not react to a magnetic field. If both are down, the particle will go down in an magnetic field. A spin 1 particle has 3 possible states, 1, 0 or -1.

A spin 3/2 particle can be represented as three spin 1/2 particles "stuck" together. If all three are spinning up, it goes up a lot in a magnetic field. If two are up and one down, it goes up a bit. If two are down and one up, it goes down a bit. If all three are down, it goes down a lot. A spin 3/2 particle has 4 possible states, 3/2, 1/2, -1/2 or -3/2.

An important difference between an integer spin particle and a 1/2 integer spin particle is that a 1/2 integer spin particle does not have a 0 state. It always reacts to a magnetic field.

Hope this is somewhat helpful.

 

[ChrisVer]

7 is true for both spin and angular momenta...