Quantum spin again.

[ppnl]

What is quantum spin?

Ok, I know this has been asked before. I have seen several physicists claim that it is a pure quantum concept and that it is just accident that it was named spin. An earlier discussion on this board confirmed my suspicion that this cannot be correct because it is a measure of angular momentum.

So let me change the question a little. How do we understand classical spin in terms of quantum spin?

For example if we took a large object like a baseball and alligned all the quantum spin of the constituant particles so they added would the ball have a large angular momentum? What could we say about its classical spin?

Or what if we gave it a huge classical spin. Would that have consequences for the spin direction of the average atomic particle? If so does that mean there is some maximum spin that the ball can hold because at some point all the atomic particles are alligned?

 

[epepke]

What is quantum spin?

Ok, I know this has been asked before. I have seen several physicists claim that it is a pure quantum concept and that it is just accident that it was named spin. An earlier discussion on this board confirmed my suspicion that this cannot be correct because it is a measure of angular momentum.

It is a quantum property. It is associated with angular momentum, which is what helped Ms. Wu to figure out parity asymmetry back in 1958 or 1957. Nobody knows what the hell it is. The damn things don't rotate.

For example if we took a large object like a baseball and alligned all the quantum spin of the constituant particles so they added would the ball have a large angular momentum? What could we say about its classical spin?

First off, you couldn't do that, because electrons with opposite spins share the same orbital, so half of the electrons would go somewhere else. Which you probably wouldn't notice anyway, because what would happen to the nuclei first, which wouldn't be much fun for anybody.

You could set the spin of some of the electrons, but only in some materials like iron, nickel, and for some reason I am completely unable to explain, liquid oxygen. So let's say it's not a baseball but a shot (as in "shot put"). What you'd get is a big, strong magnet.

Or what if we gave it a huge classical spin. Would that have consequences for the spin direction of the average atomic particle?

No, because the forces the particles feel are all in a line.

 

[scribble]

There's a lot I still don't know about QM either. If I can pile on with a question, why the hell are they called charm particles? Are they charming? How charming are they? Charming enough to give physicists hadrons?


(edit: making the funny out of a bad joke)

 

[Abdul Alhazred]

What is quantum spin?

It is angular momentum, just like classical spin or dynamic torque. What makes it 'quantum' is that it comes in discrete units.

Beyond that, I throw the question out to the real physicists. I am a mere engineer.

 

[wipeout]

There's a lot I still don't know about QM either. If I can pile on with a question, why the hell are they called charm particles? Are they charming? How charming are they? Charming enough to give physicists hadrons?


(edit: making the funny out of a bad joke)

Why "charm" is used as a name, I don't know.

Murray Gell-Mann dominated particle physics from about 1950 to 1970 so he got to name a lot of things. And he liked giving them quirky names.

"Quark" (actually pronounced by him as "qwork") being a literal case of that as it's based on the word "quirk" and not from the word "quark" in Joyce's Finnegans Wake as is widely claimed.

I don't know if "charm" is one of his. Quite possibly.

His "strangeness" for some "strange particles" was the one which started all the silly names off, though. Even he thinks it has got a bit out of hand, though, with selectrons and squarks turning up.

Murray Gell-Mann... so much to answer for.

It's not all his fault, though. Convention requires that "-ino" is added in some cases, as in photon and photino, graviton and gravitino.

W plus and W minus get an "-ino" as well.

Yeah, meet the "winos"...

 

[Cecil]

Spin is not angular momentum, nor are they associated, though the two behave similarly in many respects. Classical spin (your baseball) has nothing to do with QM spin. The two are not related in any respect. Spin is an intrinsic property of the particle, like charge or mass - it cannot be gained or lost like angular momentum can be. However, it can be described and analyzed using angular momentum equations.

Spin doesn't really have a macroscopic equivalent, so you can't really understand it - nobody does. The best we can do is to know that it exists and understand its implications. The simplest property of spin is that it's the of the number of times the particle looks identical to itself per 360 degree rotation. For example, the graviton (if it exists) likely has a spin of 2, so it looks the same after a rotation of 180 degrees. The electron has a spin of 1/2, so it has to be rotated 720 degrees before it looks the same (confusing, I know. )

Fermions are particles with half-integer spin (such as -1/2, 1/2, or 3/2). They make up matter (electrons, neutrons, protons) and must be distinguishable from each other in at least one quantum number. Essentially this means that two fermions cannot be "on top of" each other. This requirement is what keeps white dwarfs (electron pressure) and neutron stars (neutron pressure) from collapsing.

Bosons are particles with integer spin (1, 2, etc). They are the ones we think of as carrying forces (photons, meson, gluons), and they are allowed to be indistinguishable - that is, all their quantum numbers can be the same including position. This is how the Bose-Einstein condensate is produced, by "pushing" a large number of bosons all into the same quantum state, so they act like a single particle.

Spin also has implications for how particles behave in magnetic fields. I will go into this if you're curious.

Edited for clarification.

 

[QuarkChild]

Spin is not angular momentum, nor are they associated,

I feel a little uncertain challenging you on this one, since I'm not sure of your background...your profile describes you as an "armchair physicist." Has any of your armchair physics involved doing quantum mechanics problems? The reason I ask is that I seem to remember many times in my quantum mechanics classes adding orbital angular momentum to spin angular momemtum to determine a physically meaningful quantity. If they are truly not associated, I would not expect to find this calculation to be meaningful. So I was a little surprised to read your post.

Can you clarify your post? Perhaps you meant that the rotation of a macroscopic object is not associated with quantum mechanical spin?

Oh, and I disagree that spin cannot be gained or lost...you can stick particles with spin in a magnetic field and align them that way. Perhaps you meant that a spin-half particle will always be a spin-half particle, even if the direction of the spin flips?

Thanks.
QC

 

[Wrath of the Swarm]

Quite right, Quarkchild. The magnitude of the spin cannot be altered, although its sign can change depending on the spin's orientation.

I was always told that while quantum spin wasn't quite the same thing as normal rotation, it could be thought of and often treated in the same way. In a sense, it is 'spin'. For the particles themselves to rotate at the rates required, they'd have to go faster than light, but it's really their wave functions that rotate. The pattern of likely locations for the particle is what rotates.

Sort of.

What's really important is that we can write equations that give us meaningful answers. It would be nice to have a convenient metaphor to make it easier for us to imagine, but it's not necessary.

 

[Cecil]

I feel a little uncertain challenging you on this one, since I'm not sure of your background...your profile describes you as an "armchair physicist." Has any of your armchair physics involved doing quantum mechanics problems? The reason I ask is that I seem to remember many times in my quantum mechanics classes adding orbital angular momentum to spin angular momemtum to determine a physically meaningful quantity. If they are truly not associated, I would not expect to find this calculation to be meaningful. So I was a little surprised to read your post.

Well, if you've done quantum mechanics problems, you're more qualified than me.

Actually, I have no formal science education past Grade 12, but I've always been fascinated by QM, particle physics, string theory, relativity, and the like. I've done far more than my fair share of reading about these topics, though not in a mathematical context.

I was under the impression that while nobody really knew what spin was, we understood most of the implications of it. I did say it could be analyzed using the equations for angular momentum, though.

Can you clarify your post? Perhaps you meant that the rotation of a macroscopic object is not associated with quantum mechanical spin?

Yes.

Perhaps you meant that a spin-half particle will always be a spin-half particle, even if the direction of the spin flips?

Yes.

 

[ppnl]

Ok, my intuition was that classical spin must in some way be composed of quantum spin in the same way that classical momentum is composed of quantum momentum. If this is not so then there is no real connection between quantum and classical spin. They are two very different things that happen to be conserved in similar ways.


But is classical spin quantized?

Can an electron have a classical spin along with its quantum spin? My intuition would suggest not. But what about a proton? A lead atom? A baseball? At some point things start haveing classical spin.

Say you have a beam of polarized electrons and you flip their spin direction with a magnetic field. What changes in order to conserve spin? Do some of the electrons in the magnet change spin direction to conserve spin? Is there no torque exerted on the magnet?

It seems that a particle must have two different kinds of spin and dispite the fact they are both called spin they are really very different things. One of them should be renamed.

 

[Ziggurat]

I was under the impression that while nobody really knew what spin was, we understood most of the implications of it. I did say it could be analyzed using the equations for angular momentum, though.

Spin isn't just LIKE angular momentum, it really IS angular momentum. It's not merely that the equations of angular momentum also apply, it's literally angular momentum: it needs to be included as well whenever one talks about conservation of angular momentum. But yes, nobody has a really satisfactory explanation of how a point-like particle can have angular momentum, but it definitely does.

 

[Ziggurat]

Ok, my intuition was that classical spin must in some way be composed of quantum spin in the same way that classical momentum is composed of quantum momentum.

Classical mechanics has angular momentum, and quantum mechanics has a direct analogue to that in the orbital angular momentum of electrons around an atom, a quantity which is quantized. And in the macroscopic limit, orbital angular momentum becomes classical angular momentum. Spin is also angular momentum, but there really isn't a good classical analogoue: it just doesn't make sense classically to talk about a point-like particle (the electron, for example) having angular momentum. Even worse, the spin on many fundamental particles is never zero - that's VERY non-classical (orbital angular momentum can indeed be zero).

If this is not so then there is no real connection between quantum and classical spin. They are two very different things that happen to be conserved in similar ways.

Yes and no, and that's the agravating part. There's nothing quite like spin classically, but spin angular momentum isn't just conserved LIKE orbital angular momentum, it's conserved WITH orbital angular momentum: it's the sum of the two that needs to be conserved.

Say you have a beam of polarized electrons and you flip their spin direction with a magnetic field. What changes in order to conserve spin? Do some of the electrons in the magnet change spin direction to conserve spin? Is there no torque exerted on the magnet?

Spin is conserved in such cases with the help of spin-1 photons.

It seems that a particle must have two different kinds of spin and dispite the fact they are both called spin they are really very different things. One of them should be renamed.

Nope. Again, these two things (orbital and angular momentum) are conserved together, not independently.

 

[pgwenthold]

Nope. Again, these two things (orbital and angular momentum) are conserved together, not independently.

Assuming you refer to spin angular momentum here, then this is correct to within the Born-Oppenheimer approximation. However, for non-Born-Oppenheimer systems, I think you would have to include the rotational angular momentum as well. Heck, if you _really_ want to get picky, then you would have to throw in the macroscopic angular momentum as well (but that motion is generally far too slow on the molecular time scale to matter). Oh, don't forget the nuclear spin, as well.

In the end, all the angular momentum should be conserved. It is just that it is possible to separate different types at times because they don't couple very strongly. You are correct that spin angular momentum and orbital angular momentum do couple most strongly (hence the concept of "spin-orbit coupling;" the matrix elements are available in a CRC near you)

 

[ppnl]

OK, thanks zig but I'm still haveing a little problem here.

It does not bother me that a point like particle could have a quantum spin. You grow to expect such weirdness in QM.

Mass and energy are conserved together but not seperatly. You can convert between the two and show that in some sense they are aspects of the same thing.

The problem I'm haveing with quantum spin is I don't know if it is conserved absolutely in itself or if it can be converted to orbital momentum and even classical angular momentum. If you cannot convert each of these into the other then it would seem that they are different things. If you can convert between them then they can be seen as aspects of the same thing like matter and energy.

Ok, say some molecules absorbe a beam of palarized light. Is quantum spin conserved here or is it converted to orbital momentum? And can that be converted to classical spin?

In short I'm looking for a way to take a group of polarized particles and use it to cause an object to spin classically. If you cannot do this then it isn't clear what you mean when you say they are conserved together. It would seem they are conserved independently.

 

[ppnl]

Assuming you refer to spin angular momentum here, then this is correct to within the Born-Oppenheimer approximation. However, for non-Born-Oppenheimer systems, I think you would have to include the rotational angular momentum as well. Heck, if you _really_ want to get picky, then you would have to throw in the macroscopic angular momentum as well (but that motion is generally far too slow on the molecular time scale to matter). Oh, don't forget the nuclear spin, as well.

In the end, all the angular momentum should be conserved. It is just that it is possible to separate different types at times because they don't couple very strongly. You are correct that spin angular momentum and orbital angular momentum do couple most strongly (hence the concept of "spin-orbit coupling;" the matrix elements are available in a CRC near you)

OK, this seems to be what I'm getting at. The question is how do quantum spin and angular momentum couple. I'm trying to understand th relationship between the two.

 

[pgwenthold]

The problem I'm haveing with quantum spin is I don't know if it is conserved absolutely in itself or if it can be converted to orbital momentum

Sure it can. That is what spin-orbit coupling is all about. SOC is a mechanism for flipping the spin of an electron, so for example changing the spin from what we might call "up" (or (+1/2)h/2pi angular momentum) to "down" (or (-1/2)h/2pi). One of the requirements to do this is that there must be an orbital angular momentum change to compensate for the change in spin-angular momentum.

In principle, you could compensate for the spin flip with macroscopic rotation, too, but the angular momentum do not couple strongly. Think of it like the earth orbiting the sun. You could in principle apply a counter-torque that would stop the earth from rotating, but that would have little effect on the earth's revolution (although there is a small coupling - hence given enough time you can get the moon's rotation/revolution synchronized).

Electron spin angular momentum can couple fairly strongly with orbital angular momentum. It will couple with molecular rotational angular momentum only under extreme circumstances (for example, very, very high rotational states), and the coupling with anything else is basically too small to worry about.

 

[pgwenthold]

OK, this seems to be what I'm getting at. The question is how do quantum spin and angular momentum couple. I'm trying to understand th relationship between the two.

I don't know what you mean by "how do [they] couple"?

They are both angular momentum, and therefore are different forms of the same thing. It's no different from the relationship between, for example, potential energy and kinetic energy. You can provide mechanisms for converting between them, but it doesn't make sense to talk about "how they couple."

 

[epepke]

I think there's a semantic problem going on here. pgwenthold is saying that spin is angular momentum. I'm saying that it is associated with angular momentum. I'm not saying that spin is not angular momentum; I'm just using more conservative language.

Here's why. Almost everyone who knows what angular momentum is has learned that it can be calculated as the result of instantaneous measurements of relative linear momentum of a system of particles. None of this is true, nor even makes the slightest bit of sense, when talking about spin of what in the standard model are considered point particles. On the other hand, with respect to conservation laws, they work together, just as if they were the same thing.

So spin is both like and unlike classical angular momentum, in different ways.

To say that spin is angular momentum is essentially to define angular momentum in such a way that it describes only the properties that spin and classical angular momentum share. You can do that, but this is a popular audience, who probably have some familiarity with classical angular momentum.

The reason I stick to conservative language is because I think it's sometimes quite dangerous to use the word "is" when dealing with these kinds of models. Take the example of a neutron, which eventually decays into a proton and an electron, although it takes about ten minutes if it's just sitting there. One might be inclined (and every high-school student in a physics class seems to do it) to say that a neutron is a proton and an electron. Not only would this violate Heisenberg's Uncertainty Principle (an electron is too small to know that it's right next to a proton and not moving, which is why electrons are in orbitals in the first place), it would be highly misleading, as the best evidence is that the neutron is made up of an up quark and two down quarks, while a proton is made up of two up quarks and a down quark. So that electron wasn't just buzzing around waiting to be let out--it's what happens when one of the down quarks in the neutron becomes/is replaced by/whatever an up quark.

Incidentally, this is why you wait a while before going in after you switch the accelerator off. Thermal neutrons are not good for you, but hydrogen is no big deal.

 

[epepke]

I forgot. When a neutron decays, you also get an electron antineutrino. But nobody notices those.

 

[pgwenthold]

I think there's a semantic problem going on here. pgwenthold is saying that spin is angular momentum. I'm saying that it is associated with angular momentum. I'm not saying that spin is not angular momentum; I'm just using more conservative language.

But you don't need to. Spin angular momentum is angular momentum. We call it spin, but there is not a classical counterpart (which seems to be your bigger problem).

We know it is angular momentum because it can be converted to other forms of angular momentum, such as orbital or even rotational. What you are doing is like saying that potential energy is _associated_ with a form of energy. That would be silly. Potential energy is a form of energy.

Similarly, spin is a form of angular momentum. I can apply the spin angular momentum operator to the wave function and calculate an expectation value, if I want. Spin behaves exactly as angular momentum, and can be converted to angular momentum. That's angular momentum.

Now, whether it is easily considered in terms of classical terms is a different issue, but that is irrelevent to what it is.