# Quantum theory: what is ''spin''?

I’ve read a lot of pop-culture books on quantum mechanics, and they always wave their hands on discussing spin, or come up with analogies. I’m more curious than that, though, so would someone care to explain what exactly spin is?

Spin is what polticians use to indicate “superposition”, an statement that indicates both support and opposition to any given “issue” that is in fact both and neither at the same time. Intensive questioning under oath will destroy this superposition and render a lame but definite position, but will not reveal what the superposition was.

The term ‘spin’ is, I think, just a convention for describing the magnetic fields of electrons. I’d imagine that the analogies keep popping up because that’s where the term originated: in newtonian mechanics a ball with a charge can create a magnetic field by spinning, and the direction of the magnetic field depends on the direction the ball spins. This is neat, but unfortunately it doesn’t apply to electrons because they really aren’t big enough (they aren’t extended objects). Anyway, when referring to elecrons in orbitals the spin is always opposite for two electrons in the same orbital; if it were the same they would repel each other too much to remain together. At least, I think that’s a fair explaination. Try this webpage.

http://sfu.ca/chemcai/QUANTUM/Quantum_Primer.html

That webpage doesn’t work for me.

Sorry, my mistake.

http://www.sfu.ca/chemcai/QUANTUM/Quantum_Primer.html

An electron in an atom can have two types of angular momentum, orbital angular momentum and spin (intrinsic) angular momentum.

Orbital Angular momentum (in an atom) is not the same as an electron orbiting the nucleus. But this is a pretty good analogy and if in the limit Planck’s constant (h) goes to zero it can be increased without bound, and therefore OAM has a clearly defined classical counterpart.

However, this is not true of spin (intrinsic) angular momentum. The spin quantum number is a fixed quantity (s = ½) and so cannot be increased to infinity as h tends to zero. The property analogous to electron spin therefore disappears for classical objects, and spin most definitely cannot be thought of as an electron spinning on its axis. And it, therefore, is a strictly quantum mechanical construct

The reason classical properties can be derived from quantum properties when Planck’s constant h goes to zero is because the Heisenberg Uncertainty principle disappears and therefore so does quantum mechanics. Wouldn’t that be great news?

I’ve never really understood spin myself, and sort of accepted it as one of those properties that has no classical description.

In one of my popular science books, they try to explain spin as describing a sort of symmetry. Some particles look the same from all angles, so they have a spin of 0. Some look the same when rotated half-way around, so their spin is 1/2. Others only look the same when rotated all the way around, so they have spin 1. This analogy breaks down with particles of spin 2, since they apparently need to be rotated twice around to appear the same.

Hopefully someone who ‘gets’ this concept can pop in to tell us why that book’s explanation either makes sense or is totally inadequate.

OMG, I think I have found a new signature.
Returns to laughing on floor

The symmetry thing is somewhat true, but misleading: It’s not the particle itself that’s being rotated, but the state vector which describes the particle. Since the state vector doesn’t live in the same “space” as our familiar three plus one dimensions, the analogy is inherently flawed.

The magnetic explanation also doesn’t cut it, since the electron has a magnetic moment twice what would be expected classically of something of its angular momentum, and its spin is half of what you’d guess. In other words, the electron has (almost) the same magnetic moment that you’d expect of a classical charged ball with a classical angular momentum of hbar. Where does the factor of two come from?

Here’s the best I can explain it: Angular momentum is conserved, at all scales. We know that there’s such a thing as orbital angular momentum, and we can measure it. It’s similar to classical angular momentum, so we can wrap our brain around it pretty easily. It’s quantized in units of hbar: Any component of the orbital angular momentum can be equal to zero, hbar, 2*hbar, -hbar, etc., but not any values in between. Well, sometimes an atom (let’s say it’s a hydrogen atom, for simplicity) can change its orbital angular momentum, without a change in the AM of its environment. There must be some other sort of angular momentum in the atom, and we have reason to believe that it’s in the electron. For various mathematical reasons, we know that this angular momentum must also occur in discreet amounts, separated by hbar. It turns out, from experiment, that you can only swap out one hbar of AM from the electron this way, so there’s only two states, separated by one step. It also turns out that the angular momentum in one state seems to be the negative of that in the other. Combining these two, the only possibility is plus a half, and minus a half.

The consensus seems to be that spin is not easy to understand without the math. Know a good site/book for that?

Yeah, spin = a (fundamental?) property of subatomic particles, unless you plan to do grad or post-grad physics work.

The symmetry explanation is valid, but this detail is wrong. A spin 1/2 particle must be rotated 720 degrees to appear the same!

A way I’ve thought about it is this. Start with a circle. No matter how you rotate it, it looks the same. This is a spin 0 object. Next, put a small bump on the circle. You must rotate the circle 360 degrees for it to look the same. This is a spin 1 object.

If we put another small bump on the circle, directly opposite the first bump, we only need to rotate 180 degrees. This is a spin 2 object. We can continue this pattern, by evenly distributing small bumps on the circle.

For a spin 1/2 particle, somehow we have to rotate the object 720 degrees before it looks the same. AFAIK, there are no such classical objects. This ties in with what Ring has said about spin being a purely quantum construct.

And how do we know which particles have which spins? We look at the wavefunctions and determine which symmetry each has.

Any basic textbook on QM will cover the maths involved. It’s sufficiently standard that, for the beginner, the variations between such treatments are pretty irrelevant.

A macroscopic object with 1/2 spin?

A Moebius strip.

How do you figure? It’s still a three-dimensional object.

Am I correct in understanding, that for an electrically neutral particle, its antiparticle simply has the opposite spin?

If so, why does the meeting of a particle and its antiparticle release so much energy?

Not quite. There’s also baryon number, lepton number, strangeness number, isospin, etc. that are opposite, though many of these may be 0.

A particle and an anitparticle annihilate each other, and convert their mass to energy per e=mc[sup]2[/sup].

Indeed, that much I “understand” , but why does the meeting of such a pair of particles do that? More specifically, what is it about having opposite charge, spin, baryon number, lepton number, etc., (thanks Achernar) that permits/facilitates the annihilation?

That’s sort of like asking what causes atoms to bond into molecules. The answer is that there is a thermodynamical relationship between a particle and an antiparticle that favors, upon close interaction, a new state of photons of energy equal to the energy of the reactants. It happens that in most conditions you’re familiar with, the equilibrium in such reactions tends to favor the production of photons because the ambient energy of the universe or the lab or wherever usually is well below the rest-energy of the particles you are pairing up.

Think of it this way: if you react a neutral oxygen atom with another neutral oxygen atom at room temperature you will tend to get diatomic oxygen for the reason that the energy associated with these species at room temperature is less than the energy associated with breaking the oxygen-oxygen bond. However, if the temperature gets warm enough, you will tend to exist in equilbrium which means you’ll tend to see both the single- and double-atom species.

Basically all reactaions in all of chemistry and particle physics obey this simply law as long as the conditions are ripe for equilibrium and there are no quantum tunnelling effects. Of course, those last two are major, major caveats. In any case, the annihilation of a particle and its antiparticle is simply a basic law of fundamental physics. The properties of antiparticles come out of the thermodynamic conditions that are required for said interaction to be true. For example, we know that lepton number must balance, that chemical potentials must balance, and that charge must balance for any reaction you care to write down. Therefore the antiparticles have the very properties that allow for reactions that create photons.

There actually is a more complex answer to the question that involves Dirac’s development of quantum theory of electrons which required the existence of antimatter that had the properties outlined above. Dirac’s work made connection between Einstein’s special relativity and electrodynamics and led to the eventual discovery of the positron in 1933. For more, see this Scientific American article.