# What all has intrinsic spin?

What does and does not have intrinsic spin?

Wikipedia Spin (Physics) https://en.wikipedia.org/wiki/Spin_(physics) says:

“In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.”

But it doesn’t say that only those items have intrinsic spin.

Is this list comprehensive? Or do other things have intrinsic spin? (as opposed to orbital angular momentum?) For example: molecules? Buckyballs?Ball Bearings? Schrodinger cats?

Wikipedia Spin (Physics) goes on to say:
“Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. Orbital angular momentum operator is the quantum-mechanical counterpart to the classical notion of angular momentum: it arises when a particle executes a rotating or twisting trajectory (such as when an electron orbits a nucleus). The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which particles are observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone.”

Of course every large item has lots of electrons among other things and so it has spin due to the constituent electrons. I mean does the large object have any intrinsic spin of its own, beyond that inherited from its constituents.

Arguing the other way is http://www.askamathematician.com/2011/10/q-what-is-spin-in-particle-physics-why-is-it-different-from-just-ordinary-rotation/
In its derivation that every three dimensional object is either a fermion or a boson, where it states:

“By the way, notice that at no point has mass been mentioned! This result applies to anything and everything. Particles, groups of particles, your mom, whatevs!”

Is everything either a fermion or a boson?
No matter how large? And thus perhaps possess its own intrinsic spin? Or does this only apply to total angular momentum and not intrinsic spin. I’m confused. Help!

• Well, there is the Einstein-de Haas effect. – Sebastian Riese Sep 1 '15 at 20:11
• @SebastianRiese A number of people have been throwing that link around a lot lately and trying to imply that it proves something that it doesn't. All that the Einstein-de Haas effect tells you is that spin is angular momentum. But we knew that. It doesn't address why spin can take on values that are forbidden by the quantization of $\mathbf{r}\times\mathbf{p}$, and that is why it doesn't prove that electrons are little whirling balls. – dmckee Sep 1 '15 at 20:29
• I did not want to overstress the relevance of this for the question. But it does say, that a ferromagnet (whose magnetic moment is not due to orbital angular momentum) carries a "macroscopic" amount of intrinsic angular momentum (due to the aligned angular momentum of the constituent electrons). I guessed this might at least be relevant for part of the question. – Sebastian Riese Sep 1 '15 at 20:33
• The Einstein-de Haas effect "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". Along with magnetic moment it's the hard scientific evidence that the electron is something going round and round. IMHO it's a straw-man non-sequitur to say the electron can't be spinning like a planet and therefore intrinsic spin is not a real rotation. – John Duffield Sep 1 '15 at 21:41

## 2 Answers

Things have intrinsic spin.

There's no "class of objects" that has spin and another class of objects that doesn't. Everything is a quantum object with a quantum state, and spin is a number that tells you how the state of the object transforms under rotations. It is different from "classical" angular momentum in that spin is not the operator associated to $\vec r \times \vec p$, which would be the usual angular momentum, but it is an angular momentum since it is a conserved charge of the rotation group. In most cases, though, the individual spins of the constituents of macroscopic objects will be completely uncorrelated, and sum to zero on average, so you don't notice it in large objects. A notable exception are permanent magnets, which derive their magnetic properties from the alignment of the individual electron spins.

Not everything is "a fermion" or "a boson". These are terms for elementary particle states for which one can write down creation and annihilation operators, and the property essentially derives from whether these commute or anticommute. Entire systems are not created in such a simple Fock creation/annihilation formalism, it doesn't really make sense to assign the terms "boson" or "fermion" to them because they are not associated to any bosonic or fermionic creation/annihilation operators.

Not even every particle is a fermion or boson, in two dimensions, the spin statistic theorem fails due to the different structure of the Lorentz group, and there are anyons with fractional spins and fractional statistics.

• "spin is a number that tells you how the state of the object transforms under rotations" might be the only satisfying definition of spin I've ever heard. – T3db0t Mar 18 '18 at 16:40
• @T3db0t Exactly! Among the books I have seen, only Landau puts it this clearly. :3 – Dvij Mankad Apr 18 at 21:57

What does and does not have intrinsic spin?

An electron's got intrinsic spin, and so has a proton. And a neutron, which will decay into an electron and a proton and an antineutrino. So anything made of matter has got it. Matter as we know it Jim.

Wikipedia Spin (Physics) https://en.wikipedia.org/wiki/Spin_(physics) says: "In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei."

Yep. But check out the Wikipedia Einstein-de Haas effect article: "the Einstein–de Haas effect demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics."

But it doesn’t say that only those items have intrinsic spin. Is this list comprehensive? Or do other things have intrinsic spin?

Anything made of matter ought to be fairly comprehensive. But you can take it a step further. Think about a cyclone. It has intrinsic spin on another level, and this spin is intrinsic because it makes it what it is. Take away the spin, and all you're left with is wind. And how would you do this? With an anticyclone.

(as opposed to orbital angular momentum?)

Orbital angular momentum is something like a cyclone swirling around an anticyclone. Don't worry about it.

For example: molecules? Buckyballs? Ball Bearings? Schrodinger cats?

Yep. Neutrinos are a bit of a complication, best save them for another day. Meanwhile think electrons and positrons. If you took away the spin, all you're left with is light. We call it annihilation.

Wikipedia Spin (Physics) goes on to say: "Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. Orbital angular momentum operator is the quantum-mechanical counterpart to the classical notion of angular momentum: it arises when a particle executes a rotating or twisting trajectory (such as when an electron orbits a nucleus). The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which particles are observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone".

Yep. Take a look at an old version of the Wikipedia Stern–Gerlach article. It contains a non-sequitur that says the electron can't be rotating like a planet, so it can't be rotating at all. That's wrong. Magnetic moment says its wrong. Of course it isn't rotating like a planet, it's a spin ½ particle. Duh!

Of course every large item has lots of electrons among other things and so it has spin due to the constituent electrons. I mean does the large object have any intrinsic spin of its own, beyond that inherited from its constituents.

Tornados have spin, so do whirlpools and cyclones. If they didn't they wouldn't be what they are. Other things spin too, like planets, but that spin doesn't make them what they are.

That article is the usual non-answer popscience that ends up with the non-sequitur: "they’d need to be spinning faster than the speed of light in order to produce the fields we see". Check out Goudsmit: "But don't you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates". But note that the electron isn't some billiard-ball thing that rotates. It's a 511keV electromagnetic wave in a Dirac's belt path. There's a major-axis rotation at c and a minor-axis rotation at half that rate, wherein the "and" acts like a multiplier. The end product looks like a standing wave. See atomic orbitals. Electrons exist as standing waves. Standing wave, standing field. See the Poynting vector for a static field: Public Domain image by Michael Lenz, see Wikipedia

And I quote: "While the circulating energy flow may seem nonsensical or paradoxical, it is necessary to maintain conservation of momentum."

In its derivation that every three dimensional object is either a fermion or a boson, where it states: "By the way, notice that at no point has mass been mentioned! This result applies to anything and everything. Particles, groups of particles, your mom, whatevs!”

If it's got this intrinsic spin, it's got mass. Think of photon momentum as resistance to change-in-motion for a wave moving linearly at c. What might you call resistance to change-in-motion for a wave moving in a closed path like that Poynting vector?

Is everything either a fermion or a boson? No matter how large? And thus perhaps possess its own intrinsic spin? Or does this only apply to total angular momentum and not intrinsic spin. I’m confused. Help!

No, everything is not either a fermion or a boson. Space isn't a fermion or a boson, nor is a black hole. As for your confusion, remember the wave nature of matter. Fermion and bosons re just two different wave configurations, that's all.

• This answer is completely wrong. The Einstein-de Haas effect demonstrates that both classical angular momentum and spin are angular momentum (e.g. in the sense of being the conserved charge of the rotation group). It does not demonstrate spin is classical angular momentum. An electron is not an electromagnetic wave in a Dirac belt, and I don't know where you got that ridiculously wrong idea. Atomic orbitals might be stationary solutions of the Schrödinger equations, but to describe them as "standing waves" is neither related to the question nor useful in most other contexts. – ACuriousMind Sep 1 '15 at 21:47
• The Einstein de-Haas effect "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". I didn't make that up, nor did I make up Dirac's belt or the Dirac spinor or spherical harmonics and standing waves. And if all the above is bona-fide physics, my answer isn't completely wrong, now is it? – John Duffield Sep 1 '15 at 22:20
• Spin anugular momentum takes on values that are forbidden to $\mathbf{r}\times\mathbf{p}$ angular momentum (i.e. the stuff involving extended matter actually whirling around). So it is "of the same nature" (i.e. angular momentum), but not generated by extended matter in rotational motion. So, yeah. Pretty much wrong. – dmckee Sep 2 '15 at 0:07
• @dmckee : of course it isn't generated by matter in rotational motion. The electron doesn't rotate like a planet. The Dirac equation is a wave equation, the wave nature of matter is not pretty much wrong, and that wave isn't propagating linearly at c now is it? – John Duffield Sep 2 '15 at 12:26