# What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does spin mean if not an actual spinning motion?

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Was there something in particular you didn't understand in the wikipedia article? en.wikipedia.org/wiki/Spin_%28physics%29 –  j.c. Nov 2 '10 at 19:11
If a little historical perspective would help, I recommend this series by Nature on the effect that studying "spin" has had on the world of particle physics (and vice-versa). –  Herb Nov 2 '10 at 19:18
@j.c.: Does it matter if there was or wasn't? I was under the impression that we answered questions regardless of whether or not they have been answered in other sites, unless you're just asking to see if there's a specific property of spin the asker wants explained in detail. –  Mana Nov 2 '10 at 19:43
@Mana, I agree, which is why I didn't vote to close. I tend to think my time answering questions is best spent if I'm writing the answer at a level the questioner might understand. –  j.c. Nov 3 '10 at 14:24
I don't like the subatomic tag here. Is particle-physics more appropriate? –  Nick Nov 3 '10 at 16:34

Spin is a technical term specifically referring to intrinsic angular momentum of particles. It means a very specific thing in quantum/particle physics. (Physicists often borrow loosely related everyday words and give them a very precise physical/mathematical definition.)

Since truly fundamental particles (e.g. electrons) are point entities, i.e. have no true size in space, it does not make sense to consider them 'spinning' in the common sense, yet they still possess their own angular momenta. Note however, that like many quantum states (fundamental variables of systems in quantum mechanics,) spin is quantised; i.e. it can only take one of a set of discrete values. Specifically, the allowed values of the spin quantum number s are non-negative multiples of 1/2. The actual spin momentum (denoted S) is a multiple of Planck's constant, and is given by $S = \sqrt{s (s + 1)}$.

When it comes to composite particles (e.g. nuclei, atoms), spin is actually fairly easy to deal with. Like normal (orbital) angular momentum, it adds up linearly. Hence a proton, made of three constituent quarks, has overall spin 1/2.

If you're curious as to how this (initially rather strange) concept of spin was discovered, I suggest reading about the Stern-Gerlach experiment of the 1920s. It was later put into the theoretical framework of quantum mechanics by Schrodinger and Pauli.

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I don't think electron are fundamental particles in the standard model. Also to my knowledge they are not point like. –  Albert Nov 2 '10 at 19:53
@Albert: They most certainly are! There are fringe theories which consider them composite particles, but the standard model of particle physics and most extensions of the theory consider them fundamental point particles. –  Noldorin Nov 2 '10 at 19:54
The only sense in that they are not point-like is that there position may be indefinite/fuzzy due to the Heisenberg principle. They are still however considered "point particles" since their position eigenstates are functions of a single position vector. –  Noldorin Nov 2 '10 at 19:55
I think the flaw in your thinking comes from considering angular momentum as a consequence or property of spinning. Angular momentum really is the fundamental quantity here. It is a direct consequence of the rotational symmetry of the universe (see Noether's theorem). Realise, the maths is the basis of the physics here; nothing gives a more precise pictures. –  Noldorin Nov 4 '10 at 17:29
Note that experimentally one can only say that election have no structure down to [length scale] and/or up to [energy scale]. Which makes them point-like for the purposes of all the experiments we've been able to do. I believe the limiting length scale is currently around $10^{-18}$ meters, which is pretty small. –  dmckee Nov 30 '10 at 4:06

Imagine going to the rest frame of a massive particle. In this frame, there is rotational symmetry, which means that the Lie algebra of rotations acts on the wave function. So the wave function is a vector in a representation of Lie(SO(3)) = Lie(SU(2)). "Spin" is the label of precisely which representation this is. Note that while SO(3) and SU(2) share a Lie algebra, they are different as groups, and it is a fact of life ("the connection between spin and statistics") that some particles -- fermions, with half-integral spin -- transform under representations of SU(2) while others -- bosons, with integral spin -- transform under SO(3).

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An accurate answer, but if the poster doesn't understand the actual concept of spin (not to mention group theory), this is all but useless. –  Noldorin Nov 2 '10 at 19:32
I agree. This comment speaks to my confusion (see my Physics Meta question) over how this Physics site is conceived. Namely, what is the level (high school, undergrad, grad) of the intended audience? –  Eric Zaslow Nov 2 '10 at 22:05
Yeah, it's a point worth discussing. I think all three of those levels you point out should be acceptable. (You are clearly aiming at lower graduate level plus in this case.) Personally I would not like to see this site dominated by too many basic high school questions nor by many research-level ones. –  Noldorin Nov 3 '10 at 13:22