Why is spin called spin? After all, nothing is spinning! To find out we need to go back about 100 years…
Tags: advent calendar 2012
It’s an interesting monologue but sorry, Aidan, I completely disagree with your statements that nothing is spinning and/or the word “spin” is caused by some historical inaccuracies or accident.
Spin is a perfectly valid description of the physical concept that doesn’t depend on the old Bohr atom in any way – although people started to observe things related to the spin before the modern quantum mechanics was really established in its current form.
But the electron *is* spinning. It’s rotating. The previous two sentences are mathematically equivalent to the fact that the angular momentum connected with the spin is nonzero. The angular momentum is what measures whether something is spinning. If it’s nonzero, it’s spinning.
A valid comment would be that the spin can’t be described or visualized by classical physics. But no other observable at the microscopic scale – and therefore controlled by quantum mechanics – can be properly described by classical physics, either. It doesn’t prevent us from using observables that become the usual classical observables in the classical limit. The angular momentum is one of them and despite the fact that the spin is tiny and quantized, it is a term in the angular momentum.
The quantization applies not only to the spin but to any other form of the angular momentum, too. It’s a true fact about Nature. For large objects, the spacing between allowed angular momenta (hbar or hbar/2) is so small relatively to the total angular momentum that the total angular momentum becomes approximately or effectively continuous. But strictly speaking, it’s still quantized. The spin or a spin-1/2 particle is just the smallest positive contribution to the angular momentum one may have.
When one thinks about Nature correctly in terms of quantum mechanics, it’s clear that the character of various concepts we know from classical physics will be altered, the predictions and behavior will be different. But they’re still the same quantity and the [quantum] spin *is* the [classical] spin subjected to the quantum formalism to treat observables.
It’s true exactly in the same sense as energy is energy and momentum is momentum. In quantum mechanics, momentum may be quantized in the compact space. The energy is quantized for bound states. It also violates the classical intuition of energy as some “continuous substance” that may be “gradually added”, and other things. One may also construct superpositions of different energy eigenstates, just like for the spin. But it’s still energy. It’s the quantity that is conserved because of the time translational symmetry, much like the angular momentum is the quantity that is conserved due to the rotational symmetry, and when these quantities become large and other conditions guarantee that the classical limit is appropriate, these quantities take on their exact and usual classical meaning!
So I think it’s misleading to pretend that the spin is something “entirely different” than the spin of the Earth etc. It’s the same thing, it’s just smaller, and what needs to be changed is the thinking about all of physics – all observables. The transition from classical physics (and/or classical rotating objects and other things) to quantum physics (and the spin of a particle) isn’t about adding a new observable analogous to other classical observables but different. Instead, it’s about keeping the same observables and changing the overall logic and “heart” of physics, how we think about statements, measurements, and predictions. It’s about the replacing of the classical framework, realism, and determinism by the probabilistic, positivist postulates of quantum mechanics based on the linear operators on the complex Hilbert space. But the observables are “the same”, just properly treated.
Hi Lubos, thanks for the comment! I don’t think you’ll be surprised to find that I disagree with your statements about whether the electron is spinning or not. It can’t be spinning in the classical sense since it is a point-like object. (I’d agree that a proton can said to be spinning, since it’s a composite particle, and it is, in principle, possible to measure the relative movement of two distinguishable quarks as one would in the classical sense.) The spin manifests as a form of angular momentum because it is the angular momentum required to balance the books, but that’s not same as saying that it’s spinning. In an analogous way there are no magnetic sources, even though it’s useful to speak of them (ie North and South poles). Magnetism is just a relativistic effect that’s required to balance the books and maintain invariance, but it can’t be treated in the same way that electrostatics is treated.
The comparison between spin and energy/momentum is not a fair one to make. They remain continuous in quantum mechanics (although in some circumstances they are, of course, quantized) and there is no “extra” momentum or energy that must be expressed in the same way as spin. The axioms of quantum mechanics make it very clear that energy and momentum are to be treated in the same way as they are classically (although subject to the uncertainty principle), that is they are continuous and the result of the spatial and temporal translational invariance. All quantum mechanics does is add the requirement that momentum is proportional to the gradient of the wavefunction, and quantum effects follow from there.
If you want your electron to physically spin then you need to find a way to show that a single point has enough structure to do so. Imagine you’re sitting next to the electron- how would you see if it’s spinning if you only have access to a single point in space? (Ask the same question of the proton and things get easier. Just watch the valence quarks move around each other!) It’s more precise to talk of the projection of some net angular momentum along an axis, and not imagine a point spinning in space. I think most physicists would agree that the electron is not actually spinning in the same sense that a gyroscope spins.
Hello again! I should also point out that certain atomic transitions are forbidden precisely because of spin being an act of balancing the books, and not an actual spinning of the electron. If the electron was actually spinning it should be possible to change its spin by radiating a photon, flipping its spin and jumping down to a lower energy orbital. (If this would violate some symmetry then it can exchange a virtual photon with the nucleus and everything is happy again.) Since an electron cannot do that, then it cannot just change the direction of its spin spontaneously, implying it is not spinning in the first place.
Apologies, Aidan, but pretty much every idea of yours about these matters is deeply wrong. I wrote a reply here:
Stop trolling, Lubos! We disagree on the interpretation of spin, but there’s no need for that kind of behaviour. I’ve taken you off my Christmas card list.
What sort of behaviour? Lubos’ post makes sense to me, is polite, and does not fall into the definition of trollish behaviour imo.
Lubos repeatedly misrepresents what I said (and what I didn’t say!) and then makes comments like ” Sorry, Aidan, but this is too much stupidity to be tolerated for an experimental particle physicist.” Pretty much the first thing people are taught about spin is that the electron is not actually spinning, and to assume that it is spinning will lead to nonsensical questions (for example, why can’t we excite higher angular momentum states?) and inconsistencies. Lubos wants to interpret it as a real spin in some model, which is fine, but it’s not correct to then impose that view on everyone else and say that anyone who disagrees is stupid. It’s not the first time we’ve crossed paths and it probably won’t be the last!
scientific facts and truths are nothing to agree or disagree about. Lumo just said what you are getting wrong and you should try to learn from it.
The only thing which could be considered as trolling is what you said about beyond the standard model physics in the comments at TRF …
You know whell that tausends of people, theoretical AND experimental (!) physicists, are still actively working at these things (righthly so!) and the searches for signs of it at the low energy scales accessiple at present by the LHC and many other experiments are far from over.
Your scornful comments at TRF about beyond the standard model physics are really inappropriate, dismiss the work of thousends of smart people, and undermine the natural scientific process.
Hi Dilation, thanks for the comment. If I gave the impression of scorning the work of theorists then that is not what I wanted to express, and I’m sorry for any offence caused. What I do object to ideas being presented as if they are fact, when they have no supporting evidence. I’ve already given my reasons for saying that the electron does not literally spin, citing the ortho- and para- forms of Helium as evidence, as well as lack of additional spin states (3/2, 5/2…) that are observed in other quantum systems that do literally spin. If someone wants to state that the electrons unambiguously do spin then they need to provide the evidence for this. I’m all in favor of people proposing models, searching for new physics and (of course) discovering new physics! But until we discover these phenomena we can’t appeal to such models for an accurate description of reality.
“Any resemblance between the Higgs field and gravity is purely coincidental!”. “If gravity only pulled on mass, then it wouldn’t pull on light, which consists of massless photons!”
During bigbang, the enormous temperature locked Gold stone bosons(h+, h-, h0) inside symmetry breaking(made mass)- but not Higgs boson(h), photons, neutrinos?
Higgs boson is locked, but also outside symmetry breaking for a while or simultaneously- thus behaving like photons awhile?- so it does affected by spacetime metric(or gravity)?
So the freedom of movement allowed or polarization of spin”1″ force carriers(bosons) and spin “1/2” matter particles(fermions) is(was) made by symmetry breaking or Higgs vev- thus making the mass. It may not by same Higgs field. The Higgs(h) associated with goldstone bosons are weak enough to be separated or intereacting with spacetime metric- not the energy in Higgs ripple which maintain electron-positron parity in creating electron mass.
So separating Higgs(h) from atoms will not affect its mass- but only the gravity.
I think these particles “really” are spinning, in some sense. For the electron, the amount of spin is always just hbar/2, so its hard to picture or take any classical limit. So it may be useful to think of a spin-1 photon instead. By Aidan’s reasoning it is not spinning either, which I also disagree with. Its spin is always hbar, but we can make it large. Because it is a boson we can prepare a macroscopic collection of photons all in the same state, each with the same spin. This is known as a “circularly polarized wave”. The E and B fields thst make up this wave are certainly spinning round and round, it is macroscopic and measurable, and it is all connected to each individual photon’s spin, nothing else. The electron is harder to picture because it is a fermion, but its still true that its spinning. Sorry Aidan, I think you need to relearn about spin.
Sad to hear I won’t get a Christmas postcard immediately after I learned that I should have gotten one. 😉
Hi Bob, thanks for the comment. I do love a good discussion in the comments, and you probably won’t be surprised to find we still disagree, although not by much. In any case let’s clear up the original point I made, because I feel that’s been lost in discussion. All I was saying was that the spin of the electron is not angular momentum in the L = r x p sense (ie the classical mechanics sense.) In my experience laypeople sometimes hear the analogy of a mini-solar system and the electron being compared to a planet, and then (understandably) think this implies that the electron has some structure, or even that there are other smaller particles orbiting it. After all, the angular momentum of the Earth due its spin about its axis is ordinary orbital angular momentum of the particles that are spinning around its axis. We can test this easily in principle (in practice its more tricky!) by setting up two stations far from each other on the surface of the Earth and measuring the relative motion of one to another. When we consider the electron we cannot do the same because r=0 (and hence any formulation of L = r x p is going to end in 0 for angular momentum, which is not what we see in experiment.)
If we take the spin in a literal sense then we can end up with different kind of problems, which I’ve already alluded to. Flip the spin in the middle of a transition to get an extra factor Delta J =1 and you can circumvent some selection rules in atomic transitions. That’s something we don’t see in experiment. (Although it got me thinking that in a collection of Helium atoms, for example, there must be an effective force due to the exchange of spin up and spin down electrons from neighboring atoms to go from a ortho- ortho- state to a para- para- state. Or is the other way around? I can’t remember off the top of my head.) Similarly if the electron really is spinning we should be able to add more angular momentum to it by sending in a photon or two. Such an electron would still be able to satisfy all the normal symmetries and spin statistics laws. But this state has never been seen. So then in what sense does the electron have angular momentum? In the sense that the Dirac equation tells it has intrinsic angular momentum, and that’s the only really complete and honest answer we can give without putting caveats in there.
After all the interpretations we use don’t actually matter. All that matters is that we agree on the outcome, and quantum mechanics has taught us time and time again to leave our intuition at the door and follow the mathematical framework. It’s been battle tested for about a century (depending on where you want to take the “start” of QM) and the consistent ideas have survived, even though they are so esoteric and obscure. Now if you want to picture gyroscopes or spinning tops on a sub-atomic scale in your head then I’m not going to stop you (when I picture helicity in my head I imagine arrows flipping to and fro in an effort to keep track of it all) because as long as we agree on the outcome it doesn’t really matter how we picture things. However we both know how to treat spin without getting into trouble so in that sense we’re “safe” when we use these analogies. But to someone new to the ideas it can just lead to more confusion, especially if they try to think about the spin of the electron as implying that the electron has some structure to it. All models that given the electron structure come up with contradictions that have not yet been resolved (Feynman gives a wonderful account of this in his lectures if you want some light reading!), and ever more stringent limits on the electron radius have only made things worse. Rather than confuse people by saying “The electron spins on its axis like the Earth does” I said “The electron has angular momentum in a similar way to the Earth, except you can’t see it in the same way. It’s not a property of its motion in the way the Earth has angular momentum.” because of all the substructure baggage that can be brought to the table.
I went further than this and made the stronger statement that the electron does not spin at all, and this seems to be what has ruffled feathers! This is, as far as I’m aware, the orthodox view of the situation. The story ends with the Dirac equation giving the electron intrinsic angular momentum that must be taken into account. It doesn’t say it’s physically spinning about an axis, or that we should expect a spectrum of spin states (even though this isn’t precluded by the Dirac equation, after all we have plenty of spin 3/2 and spin 5/2 particles.) If you disagree with this strong statement then I think we just have a semantic difference, and that’s really nothing to make a fuss about.
When it comes to the photon I don’t think it’s reasonable to sum of the angular momenta of a series of photons to get circularly polarized light and then claim that this is evidence of spinning. All that is happening there is that the spin statistics allow several photons in the same state, and we are smart enough to manipulate them to do that. When they get absorbed their intrinsic angular momentum must go somewhere and that is the sense in which it imparts angular momentum with circular polarization. You quite rightly draw attention to the E and B fields, because after all these are what carry the angular momentum from one place to another, but that’s not the same as saying an object spins as the photons propagate. (In any case, what does it mean to have an object traveling at light speed to also additional rotational motion? That kind of thought makes my head spin!)
So the “not really spinning” view is entirely consistent and leads to the kinds of predictions we need, and presumably your version of “they really are spinning” works too and is just as consistent. But for people who are new to the concepts I think it’s much better not to confuse them by making claims that the Dirac equation makes objects spin around. I think we can both agree that the Dirac equation does not go as far as to say that the electron has substructure, and that conclusion is one that the general public tends to be very fond of. People love the idea of things getting smaller and smaller forever for some reason. They also love the idea that anything massive has to have a finite width. I suppose our minds just aren’t evolved to cope with the alternatives very easily.
Thanks again for the comment, I hope to see you in here again!
1 point is a mathematical ideal
2 I can flip spin with an interaction . It is oriented in spacetime
3 because it is a simple quantum object adding momentum is equivalent to absorbing a photon and thus jumping to a higher level of energy and reverse true as well
4 Dirac 1955? Realized that point like idealization inconsistent with reality and coined term string to allow for a better analogy
5 Feynman qed
6 feynman also deals with tthe analogy to classic limit very well and he certainly was able to convince this old mind that if an additional degree of freedom is needed given that the absorbtion and release of photon take time and makes Consistent by treating the positron as moving backward in time. Analogies between QM and our experience are never sensible to us just more sensible than having no consistent picture . so you are also correct that the quantum world is not what we think of as spin in everyday experience. The math works best and the picture works best though for us mere mortal minds if we use the analogy. And even the planets spin is ultimately a quantized reality with a finite though huge number of eigenstates leading to our perceived reality.
7 Of course I learned and forgot most of this before you, by appearance, were an observable. So I leave it to you to and lubos to have it out. But until someone shows me better way to think if this he is right, you are wrong,
It’s a bit odd because you can have wavefunctions that have angular momentum but don’t actually “move around” other than advancing in phase. The state of a fermion (if you confined it in a suitable potential well) would be something like this. I tend towards Aidan’s view that it’s not “really spinning” because the wavefunction probability density isn’t moving around with time. But it does have real angular momentum that adds (I assume) in the normal ways with orbital angular momentum.