# What exactly is intrinsic angular momentum (spin)?

1. Jan 5, 2012

### gnardog777

I think I understand the gist of it. Is it a property that exhibits properties of angular momentum, without actually spinning, because it isn't made of anything else as far as we know, and has no inner structure?

2. Jan 5, 2012

### Staff: Mentor

I think you hit the nail right on the head. It is simply a property of particles, similar to how electric charge is a property.

3. Jan 5, 2012

### gnardog777

Thanks, dude. Unfortunately, I don't even completely understand what angular momentum is :( Sometimes I feel that I jump too far ahead into concepts that I can't completely understand, due to the fact that I lack the prerequisite knowledge required in order to fully understand the material, which is why I've been reading hyperphysics like crazy. Sorry if I'm ranting.

4. Jan 5, 2012

### Staff: Mentor

Angular momentum is associated with rotating objects, such as a top or a rotating planet. I don't know if it will help, but you can look here: http://en.wikipedia.org/wiki/Angular_momentum
Quantum mechanics kind of makes these things difficult to understand since they don't quite work like macroscopic objects do. You never see a basketball that can only spin at certain speeds or that needs to spin around twice to get around once for example.

5. Jan 5, 2012

### ytuab

Many books tend to avoid explaining "what the spin actually is", I think.

p.187 Deep down things: the breathtaking beauty of particle physics (Bruce A. Schumm)

-- So the question arises, what exactly is spin and this oddly construed spin space in which it lives ?
On the one hand, it's quite real, having associated with it the measurable physical quality of angular momentum.
Furthermore, the angular momentum associated with ordinary orbital angular momentum is the same physical quantity as spin
angular momentum ....

On the other hand, a particle with no spatial extent shouldn't possess angular momentum, and the axis about which it spins shouldn't have to be rotated through 720 degrees to return the particle to its original state.

We don't have really have a clue about the physical orgin of spin.
To describe spin as "intrinsic angular momentum" is like your best buddy describing how your car's differential works by explaining that it "employs a mechanical linkage"; the only useful information contained in the statemant is that its author probably knows next to nothing about how differential actually works.

The question of the origin of quantum-mechanicsl spin and the nature of spin-space is a conundrum that physicists have yet to solve. If you've understood, even vaguely, what you've read in this chapter, then your guess is truly as good as mine.

6. Jan 5, 2012

### gnardog777

Yeah, I understand that, I'm just trying to understand what's going on conceptually. You said that particles need to spin around twice to get around once. Would that apply to half-spin particles such as fermions? Also, since bosons have a whole-spin, would they only need to spin around once to get around once?

7. Jan 5, 2012

### Staff: Mentor

To my knowledge there is no way to understand it conceptually. It is purely a result of observations and math. The particle isn't spinning around on it's axis, yet it still possesses angular momentum! It doesn't make any sense!

8. Jan 5, 2012

### maverick_starstrider

To the OPs inability to conceptualize spin let me say this, classical mechanics is the laws of physics that govern the macroscopic universe we interact with in our day to day lives, it governs billiard balls and tops and gyroscopes, etc. In the atomic realm classical physics gave wrong answers and thus a new physics had to be developed called quantum mechanics. If one could apply classical intuition to all of quantum mechanics then quantum mechanics WOULD BE classical mechanics, which it's not. The fact that it exists at all tells you that our world of billiard balls and tops is INSUFFICIENT in this realm.

As to Drakkith spin is one of those things that the MORE abstract your understanding and thinking the more it makes sense. Many will say you prove the existence of spin by postulating the Dirac equation on the electron by considering all terms in the action (including spinors) that obey lorentz invariance and quantizing to find an extra degree of freedom. Well this is true, it can actually come straight from QM (not QFT). I'd recommend reading the 3rd chapter of Ballentine''s book on this. In a nutshell you have the result that the angular momentum generates angular motion and you can naively find the form of it which is akin to the classical case. However, you realize that you can obtain the same relations if you allow an extra term with no dependence on q or p (intrinsic), you get the same relations. In this way spin is something like a gauge, a redundancy of description of the angular momentum. You can also prove that such an intrinsic term CAN'T be added to the linear momentum.

9. Jan 6, 2012

### Staff: Mentor

Maverick I barely understood anything you said lol.

10. Jan 6, 2012

### maverick_starstrider

The general modern prescription for developing physical theory is to state the symmetries of a system and then write down every possible mathematical term (I'm fudging this a bit, it's a little more complicated) that obeys this symmetry then do what's called extremizing the action (and possibly quantizing). In other words, if something isn't STRICTLY FORBIDDEN by a symmetry you assume it's there (if you can't disprove it then you assume it's true). Thus if you look at the angular momentum in quantum mechanics there's nothing PREVENTING you from adding a term which does not depend on position or momentum thus, we add it. The result of this extra term is spin. However, to establish the connection between half-integer spins and fermion statistics (particles obeying Pauli exclusion) and whole integers and bosons one needs to move to quantum field theory.

11. Jan 6, 2012

### gnardog777

I understood the first paragraph, but you completely lost me on the second one. I can't wait until I go to college.

12. Jan 6, 2012

### maverick_starstrider

It was more for Drakkith's benefit.