# On Rotation

Does spin for particles actually refer to spin as in rotation? Or does it mean something else.

Do all elementary particles rotate?

Without a magnetic field can you have rotation or does the rotation create the magnetic field?

ShayanJ
Gold Member
Does spin for particles actually refer to spin as in rotation? Or does it mean something else.
It means something else. But no one knows what's that yet.
Do all elementary particles rotate?
If by rotate, you mean they have spin, no, some of them have spin zero.
But you shouldn't use rotate as having the same meaning of having spin. This is very very wrong.
Without a magnetic field can you have rotation or does the rotation create the magnetic field?
Spin is an intrinsic property of particles, like their mass and charge. Now a charged particle with non-zero spin, will have a non-zero magnetic moment.(Not that neutral particles can't have magnetic moment.)

It means something else. But no one knows what's that yet.

If by rotate, you mean they have spin, no, some of them have spin zero.
But you shouldn't use rotate as having the same meaning of having spin. This is very very wrong.

Spin is an intrinsic property of particles, like their mass and charge. Now a charged particle with non-zero spin, will have a non-zero magnetic moment.(Not that neutral particles can't have magnetic moment.)
So what is spin, rotation across an axis?
Could an isolated particle just spin on its own? As in just spin aroud at one point like a dreidel?

I'm new to quantum mechanics.

ShayanJ
Gold Member
So what is spin, rotation across an axis?
Could an isolated particle just spin on its own? As in just spin aroud at one point like a dradle?
As I said, as far as I know, no one knows what is spin.
But to tell you why the rotation model is wrong.
If we assume the particles are actually points, then they can't rotate around an axis passing through them. The reason is simple. When an object rotates around an axis through itself, only the points not located on the axis move. But for a point particle, there is no point not located on the axis and so there can be no rotation.
But if we assume particles have spatial extension, then it is inconsistent to model spin as rotation around an axis passing through them. Because the upper bounds we have on the size of particles, tell us that they should rotate faster than light to produce the observed effects which can't be correct.

bhobba
Mentor
As I said, as far as I know, no one knows what is spin.
Hmmmm. Its the quantum version of angular momentum and comes from rotational symmetry exactly as the classical case - see page 82 Ballentine - QM - A Modern Development.

Although not amenable to a simple analysis its fully accounted for in QFT.

But to tell you why the rotation model is wrong.
It's not the same as classical angular momentum - that's true - but it is the quantum analogue of it.

If we assume the particles are actually points, then they can't rotate around an axis passing through them.
Hmmmm. And if charged what happens to its electric field?

Thanks
Bill

dextercioby
Homework Helper
One definitely knows what spin is: a form of angular momentum, a direct consequence of any reasonable postulation of Quantum Mechanics. The exact nature of spin has been clarified since 1939 by Wigner and later by Bargmann 1954 and Levy-Leblond (several papers in the 1960s).

vanhees71 and bhobba
ShayanJ
Gold Member
Hmmmm. Its the quantum version of angular momentum and comes from rotational symmetry exactly as the classical case - see page 82 Ballentine - QM - A Modern Development.

Although not amenable to a simple analysis its fully accounted for in QFT.
One definitely knows what spin is: a form of angular momentum, a direct consequence of any reasonable postulation of Quantum Mechanics. The exact nature of spin has been clarified since 1939 by Wigner and later by Bargmann 1954 and Levy-Leblond (several papers in the 1960s).
OK. But why particles have this form of angular momentum? What is "rotating"? That's a question that I think no one has given an answer to yet!
It seems to me that this is OP's question!

It's not the same as classical angular momentum - that's true - but it is the quantum analogue of it.
Yeah, but I meant spin is not the result of particle rotating around an axis through itself.

Hmmmm. And if charged what happens to its electric field?
Well, yes. That's one problem with point particles but I didn't say particles are point-like. I said if we assume they are point like. And as far as I know, we treat particles as point like in QFT and use renormalization to avoid the mentioned problem. But I guess I need to understand renormalization group to be able to talk about it more than this which I don't right now.
But actually, now that I think, I don't understand what you're trying to say. Could you explain?

bhobba
Mentor
OK. But why particles have this form of angular momentum?
As I said there is a deep theorem in QFT that explains it.

What is "rotating"? That's a question that I think no one has given an answer to yet!
Nothing is rotating in a classical sense. But mathematically, as Dextercioby said, it was sorted out ages ago by Wigner to have exactly the same basis as classical mechanics - symmetry.

Yeah, but I meant spin is not the result of particle rotating around an axis through itself.
Sure - that part is true.

we treat particles as point like in QFT and use renormalization to avoid the mentioned problem.
I am no expert on renormalisation but I don't think the modern Wilsonian view looks at renormalisation that way. Without a cut-off you get things like the Ladau pole and we know long before that the electroweak theory takes over anyway.

Thanks
Bill

ShayanJ
Gold Member
As I said there is a deep theorem in QFT that explains it.
Nothing is rotating in a classical sense. But mathematically, as Dextercioby said, it was sorted out ages ago by Wigner to have exactly the same basis as classical mechanics - symmetry.
I think you're talking about irreducible representations of the Lorentz group here, right?
So spin appears only because irreducible representations of Lorentz group can be classified according to it?
That's a very abstract way of looking at it!(But its good enough of course)
But to say spin is the analogous of classical angular momentum, I think we should find something to rotate, otherwise such an analogy has no reason!

I am no expert on renormalisation but I don't think the modern Wilsonian view looks at renormalisation that way. Without a cut-off you get things like the Ladau pole and we know long before that the electroweak theory takes over anyway.
Yeah, I wasn't careful in that. But as I said, I don't know much about renormalization group so I can't talk in a way which is consistent with it.

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ShayanJ
Gold Member
I am thinking of the spin-statistics theorem:
http://en.wikipedia.org/wiki/Spin–statistics_theorem

Thanks
Bill
I knew about that but I didn't think it can be used in this way. This theorem relates the spin of a field to the statistics it obeys. It assumes spin from the beginning. I don't think it can shed light on the nature of spin.

dextercioby
Homework Helper
The nature of spin is known already. Asking what spin is is basically asking why the harmonic oscillator's hamiltonian has a discrete spectrum or why [p.q]=-ih1 holds. BTW, do you know why the sky appears blue to the human eye during the sunny day and black during the moony night? :)

vanhees71
bhobba
Mentor
I knew about that but I didn't think it can be used in this way. This theorem relates the spin of a field to the statistics it obeys. It assumes spin from the beginning. I don't think it can shed light on the nature of spin.
It shows fields must commute or anti-commute with each other. It also shows those that commute must have integral spins and those that anti-commute have half integral spin.

Thanks
Bill

bhobba is correct.In quantum mechanics, spin refers to an elementary particle's angular momentum(it is an intrinsic property).one could even say it is a vector quantity,because it has magnitude and has direction(although this direction is different from a normal vector). Eg- Bosons have integer spin, while fermions have half-integer spin.As a side note, it's SI unit is joule-second, which is also the SI unit of angular momentum in classical mechanics.

ShayanJ
Gold Member
The nature of spin is known already. Asking what spin is basically asking why the harmonic oscillator's hamiltonian has a discrete spectrum or why [p.q]=-ih1 holds.
Yeah, I accept. I'm reasonable enough to understand that I shouldn't oppose PF's SAs in physics issues. I'm just trying to decipher what are you referring to. As I say, I don't understand the relevance of spin-statistics theorem here. As this isn't my thread, I don't ask for clarification. But some references will do I think.
It shows fields must commute or anti-commute with each other. It also shows those that commute must have integral spins and those that anti-commute have half integral spin.
Oh...I thought the theorem only says fields that commute have integral spin and fields that anti-commute have half integral spin. I didn't know it says the first part too. But again, it seems to me its just relating commuting and anti-commuting to spin. I don't see how it can shed light on nature of spin. I was better with the irreducible representations of the Lorentz group. I really think they're relevant here. Am I wrong?

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bhobba
Mentor
Oh...I thought the theorem only says fields that commute have integral spin and fields that anti-commute have half integral spin. I didn't know it says the first part too. But again, it seems to me its just relating commuting and anti-commuting to spin. I don't see how it can shed light on nature of spin. I was better with the irreducible representations of the Lorentz group. I really think they're relevant here. Am I wrong?
It explains why some particles are integer, and others half integer - but the commutation relations implied from symmetry considerations says it must be integer or half integer eg see page 171 Ballentine.

Thanks
Bill

vanhees71
Gold Member
Spin is indeed a pretty abstract subject, but it's fully understood within both nonrelativistic quantum mechanics and relativistic quantum field theory. In both cases it arises from the fact that for an inertial observer at any instant of time space is Euclidean and thus obeys rotational symmetry (around any fixed point). Thus a quantum theoretical description of a single particle must allow to define rotations, and the fundamental laws of nature do not depend on the orientation of the inertial reference frame.

Now you can analyse the representations of the rotation symmetry group within quantum theory. This is a pretty mathematical and abstract subject but at the same time belongs to the most beautiful ideas in theoretical physics ever. The analysis first tells you that not the classical rotation group is the fundamental way to describe rotations in quantum theory but its covering group, the SU(2). Then the mathematics of SU(2) tells you how the irreducible unitary representations on Hilbert space look like, and the spin defines to which representation the subspace of Hilbert space of a single particle with vanishing momentum belongs (I assume massive particles here, for massless particles it's a bit more complicated). Thus it tells you how the state of a single particle at rest transforms under rotations.

That's very abstract, as I said, and it's also a bit incomplete since a concept is only physically well-defined, if we can say how to observe and even measure it somehow. Fortunately, as is well known already from classical physics, angular momentum of charged systems implies the existence of a magnetic moment, and this magnetic moment can be measured by bringing the system (or in our case a single quantum particle) into an inhomogeneous magnetic field. One of the fundamental experiments done in the history of quantum physics is the Stern-Gerlach experiment, which explcitly shows the existence of the magnetic moment of the electron (more precisely of silver atoms, but it's total spin is due to the one valence electron in the atom's outermost shell) explictly, and it turns out to be indeed a spin 1/2 particle. This is something that is not in any way observable within classical physics and thus is, as stressed above, very hard to visualize intuitively. The idea of a point-like magnetic dipole, however, is, and on an operational level one can invisage spin as such.

In addition, the spin occurs in the angular-momentum bilance of reactions, and this shows that it is indeed a kind of angular momentum in the literal sense. So, spin is very well understood in both a very abstract level and well established by observation.

As bhobba said, the best book to learn about the non-relativistic foundation of quantum theory in symmetry principles is Ballentine's book Quantum Mechanics. For the same subject in relativistic QT, see Weinberg, The Quantum Theory of Fields 1.

dextercioby and ShayanJ