So, I know that spin is very important in quantum mechanics/elementary

[CyberShot]

So, I know that spin is very important in quantum mechanics/elementary particles. But just what is spin, PHYSICALLY?

Is it the way a particle rotates (spins)? The direction? The velocity at which it rotates? What does it mean for a particle to half 1/2 a spin and the other to have spin 1? Does it mean that the spin 1 has "twice" as much of this so-called spin as the spin 1/2 particle? Is the spin number a relative measure of whatever "spin" is?

Just to show you how frustrated I am trying to get a complete answer.

Wikipedia's view on spin:

"a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei"

OK, but that's not very descriptive at all. The fact that when I asked my physics TA what spin was, and he gave me an answer which was kind of non-informative and avoidant of the answer, just shows how extremely vague the term really is.

Can anyone give me a non-technical, physically relevant answer? Just what the heck is spin, anways?

 

[Matterwave]

It is an additional degree of freedom, intrinsic to a particle, which obeys the commutation relations of angular momentum.

A physical picture is very hard to come up with because particles are thought of as point particles, and so cannot really "spin" in any sense. One would intuitively think that point particles should really have just 6 degrees of freedom (3 position, and 3 momenta); however, it has an additional one, spin. It's another parameter that characterizes the state of a particle, but cannot be described in classical terms.

 

[jtbell]

The "Spin" of a particle is intrinsic angular momentum. It contributes to the total angular momentum of a system of particles, e.g in the Einstein - de Haas effect.

 

[Fredrik]

So, I know that spin is very important in quantum mechanics/elementary particles. But just what is spin, PHYSICALLY?

Is it the way a particle rotates (spins)? The direction? The velocity at which it rotates? What does it mean for a particle to half 1/2 a spin and the other to have spin 1? Does it mean that the spin 1 has "twice" as much of this so-called spin as the spin 1/2 particle? Is the spin number a relative measure of whatever "spin" is?

Just to show you how frustrated I am trying to get a complete answer.

Wikipedia's view on spin:

"a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei"

OK, but that's not very descriptive at all. The fact that when I asked my physics TA what spin was, and he gave me an answer which was kind of non-informative and avoidant of the answer, just shows how extremely vague the term really is.

Can anyone give me a non-technical, physically relevant answer? Just what the heck is spin, anways?

The term isn't vague at all. I'd say that the problem here is that you expect a sort of answer that simply doesn't exist in quantum mechanics (the theory that defines the term). What QM does tell you about spin is very mathematical, so you will either have to study the mathematics (theorems about symmetries in QM and about representations of Lie groups and Lie algebras), or accept that it's just one of the numbers that characterizes a particle species. A spin n particle (where n is some integer or half integer) isn't really doing anything to earn that label.

 

[CyberShot]

The term isn't vague at all. I'd say that the problem here is that you expect a sort of answer that simply doesn't exist in quantum mechanics (the theory that defines the term).

I'd say from the point of view of a physicalist, the words "a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei" are pretty vague. What exactly is this fundamental property?

What QM does tell you about spin is very mathematical, so you will either have to study the mathematics (theorems about symmetries in QM and about representations of Lie groups and Lie algebras), or accept that it's just one of the numbers that characterizes a particle species. A spin n particle (where n is some integer or half integer) isn't really doing anything to earn that label.

Yes, but then the theory doesn't paint a very accurate description of reality, now does it? Sure, it makes sense mathematically, as an idealization that only makes our computational tasks simpler, but does nature really care about our computational struggles or what the maths says? I'm sorry to be so very stubborn, but I can't simply accept things without the deeper meaning behind them being revealed. That's probably why Einstein so despised QM. Now where's the fun in that! =/

 

[jtbell]

What exactly is this fundamental property?

Angular momentum. It contributes to the total angular momentum of a system of particles (e.g. in a chunk of metal, the "spins" of the electrons contribute to the total macroscopic angular momentum of the chunk).

If you're looking for an answer in terms of what the electrons are "really doing" in a classical sense (e.g. little balls spinning around their axes), QM doesn't provide such an answer.

 

[alxm]

But [for a spin-1/2 particle] it doesn't transform like angular momentum does under a rotation...

 

[Fredrik]

Yes, but then the theory doesn't paint a very accurate description of reality, now does it?

It sure doesn't. But it makes unbelievably accurate predictions about results of experiments.

Sure, it makes sense mathematically, as an idealization that only makes our computational tasks simpler, but does nature really care about our computational struggles or what the maths says? I'm sorry to be so very stubborn, but I can't simply accept things without the deeper meaning behind them being revealed. That's probably why Einstein so despised QM. Now where's the fun in that! =/

Does nature care what you think is fun?

Yes, Einstein came to the conclusion that QM is really just a set of rules that tells you how to calculate probabilities of possible results of experiments, rather than a description of reality. (This is my interpretation of the Einstein quotes in Ballentine's QM book). And that's precisely what he meant when he said that QM doesn't seem to be a "complete theory" *. We would all prefer a more descriptive theory, but that's another thing that nature doesn't care about.

*) I use different terminology: A "theory" makes predictions about results of experiments, and an "interpretation" of a theory is an attempt to turn it into a "description of what actually happens", i.e. what Einstein would have called a "complete theory". Interpretations of this kind are strictly speaking not a part of science, since they don't give us any new predictions.

 

[JesseM]

I'd say from the point of view of a physicalist, the words "a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei" are pretty vague. What exactly is this fundamental property?

I'd say it's just defined practically in how it causes them to behave in certain experiments, for example when electrons pass through a Stern-Gerlach apparatus whose magnetic field is oriented at a particular angle, then the electrons are deflected in one of two directions and that defines whether they have the property "spin-up" or "spin-down" at that angle.

 

[edguy99]

So, I know that spin is very important in quantum mechanics/elementary particles. But just what is spin, PHYSICALLY?

Is it the way a particle rotates (spins)? The direction? The velocity at which it rotates? What does it mean for a particle to half 1/2 a spin and the other to have spin 1? Does it mean that the spin 1 has "twice" as much of this so-called spin as the spin 1/2 particle? Is the spin number a relative measure of whatever "spin" is?

Just to show you how frustrated I am trying to get a complete answer.

Wikipedia's view on spin:

"a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei"

OK, but that's not very descriptive at all. The fact that when I asked my physics TA what spin was, and he gave me an answer which was kind of non-informative and avoidant of the answer, just shows how extremely vague the term really is.

Can anyone give me a non-technical, physically relevant answer? Just what the heck is spin, anways?

I think a great example of spin is the http://en.wikipedia.org/wiki/Bloch_sphere" . It is commonly used to model a proton in modern NMR machines. Imagine this thing spinning very very fast.

 

[netheril96]

I'd say from the point of view of a physicalist, the words "a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei" are pretty vague. What exactly is this fundamental property?

Yes, but then the theory doesn't paint a very accurate description of reality, now does it? Sure, it makes sense mathematically, as an idealization that only makes our computational tasks simpler, but does nature really care about our computational struggles or what the maths says? I'm sorry to be so very stubborn, but I can't simply accept things without the deeper meaning behind them being revealed. That's probably why Einstein so despised QM. Now where's the fun in that! =/

So the theory can perfectly predict outcomes, and what do you need? What's the "deeper meaning" you are asking?

Put it this way, why don't you feel the same way about mass and charge as spin? They are mathematical quantities intrinsic to fundamental particles that may be required to do some calculations. Tell me the "deeper meaning" of charge and mass.

Besides, don't quote Einstein in QM discussions. A lot of his depictions of QM have been refuted by experiments.

 

[Matterwave]

Besides, don't quote Einstein in QM discussions. A lot of his depictions of QM have been refuted by experiments.

So, when you are discussing the Photoelectric effect, Bose-Einstein Condensation, and radiation in thermal equilibrium (Einstein A's and B's), you have someone else to quote in mind...?

Einstein may not have liked QM, and his general conception of the underlying reality may be wrong (local realism), but that doesn't preclude him from QM discussion!

 

[netheril96]

So, when you are discussing the Photoelectric effect, Bose-Einstein Condensation, and radiation in thermal equilibrium (Einstein A's and B's), you have someone else to quote in mind...?

Einstein may not have liked QM, and his general conception of the underlying reality may be wrong (local realism), but that doesn't preclude him from QM discussion!

OK, I correct what I said. Don't quote some of Einstein's words, like "God doesn't play dice" in QM discussion, or refer to Einstein's despisal of QM.

 

[alxm]

I think a great example of spin is the http://en.wikipedia.org/wiki/Bloch_sphere" . It is commonly used to model a proton in modern NMR machines. Imagine this thing spinning very very fast.

No, it's not. It's commonly used in introductory textbooks to illustrate spin precession*. It isn't used and can't be used for any real NMR purposes because you can't model coupled spins with a vector model.

Real NMR calculations are done in density matrix formalism.

*Edit: Also, the precession of the state vector in the Bloch sphere has little to do with the angular momentum or 'spinning' motion of the spin itself. It's a vector in Hilbert space, not real space.

 

[edguy99]

No, it's not. It's commonly used in introductory textbooks to illustrate spin precession*. It isn't used and can't be used for any real NMR purposes because you can't model coupled spins with a vector model.

Real NMR calculations are done in density matrix formalism.

*Edit: Also, the precession of the state vector in the Bloch sphere has little to do with the angular momentum or 'spinning' motion of the spin itself. It's a vector in Hilbert space, not real space.

I disagree. The larmor frequency is modeled on a spinning sphere whose axis points to a location on a bloch sphere which precesses around the vertical north of the bloch sphere. The Rabi cylcle is based on the flipping of an axis that is pointed in a particular direction on a bloch sphere and is used in demonstrating the coupling of spins. I will try and find more concrete examples I can provide links to.

 

[edguy99]

I found this video that gives a pretty neat starting point when considering spin:


If you stop the video at 1:30 you see slow precession, and at 1:48 you see fast precession. If there were less friction, this precession would linger for quite some time. If you imagine a bloch sphere with its center at the center of this device, the axis of the gyroscope would rotate around the 'north' axis of the bloch sphere. The average location of the gyroscope's north is rotating around the 'true north' of the bloch sphere (determined in this case by Earth's gravity) and is the larmor frequency. This is how protons (one type of spin 1/2 particle) appear to react in a magnetic field.

 

[alxm]

I disagree.

Yes, but you simply don't know what you're talking about at all. The Bloch sphere can model any two quantum states. it has nothing to do specifically with spin, and the Rabi frequency applies to any transition caused by light. Read the wikipedia page you linked to yourself.

Instead of looking at youtube, try a textbook. Just because the vector representation of two spin states precesses in a transition has absolutely nothing to do specifically with the 'rotation' or intrinsic angular momentum that is spin. When the system is in its ground spin state that vector is not precessing but the electron (or whatever) still has just as much 'spin' as it ever had.

Repeating your misconceptions doesn't make them true.

 

[edguy99]

Yes, but you simply don't know what you're talking about at all. The Bloch sphere can model any two quantum states. it has nothing to do specifically with spin, and the Rabi frequency applies to any transition caused by light. Read the wikipedia page you linked to yourself.

Instead of looking at youtube, try a textbook. Just because the vector representation of two spin states precesses in a transition has absolutely nothing to do specifically with the 'rotation' or intrinsic angular momentum that is spin. When the system is in its ground spin state that vector is not precessing but the electron (or whatever) still has just as much 'spin' as it ever had.

Repeating your misconceptions doesn't make them true.

I agree the Bloch spere can model any two quantum state and much more. When modeling such things as http://en.wikipedia.org/wiki/Larmor_precession" (that is at the heart of understanding of NMR) the axis of a spinning sphere (as is done on the linked page) is shown to be precessing around the axis of measurement. Finally in response the OP, this type of gyroscope is an example of a classical spin 1/2 particle and some may find helpful in understanding spin.

 

[ytuab]

OK, I correct what I said. Don't quote some of Einstein's words, like "God doesn't play dice" in QM discussion, or refer to Einstein's despisal of QM.

I think most people loves EPR paradox or something than another important thing.
For example, relativistic QED (including the Lamb shift and g-factor) is based on the "local" Relativity.
which means QM (QED) is protected by Einstein's Relativity.
In other words, Einstein's Relativity is protected by the QM (relativistic QED) which Einstein hates.

This thread is about spin. This spin is gotten from relativistic Dirac equation.

(So denying one theory means the necessity of a little modification on another theory.)

I agree the Bloch spere can model any two quantum state and much more. When modeling such things as http://en.wikipedia.org/wiki/Larmor_precession" (that is at the heart of understanding of NMR) the axis of a spinning sphere (as is done on the linked page) is shown to be precessing around the axis of measurement. Finally in response the OP, this type of gyroscope is an example of a classical spin 1/2 particle and some may find helpful in understanding spin.

O.K. the spin doesn't mean the real rotation.
So the precession doesn't mean the real rotation, either ?
(How the point particle like electron precess correctly?)
If so, the frequency of the precession is valid ?

 

[strangerep]

This spin is gotten from relativistic Dirac equation.

Actually, you can get spin (half-integer) just by studying the unitary irreducible
representations of SO(3) -- which can be done in the nonrelativistic (Galilean) case.

 

[dextercioby]

Actually, you can get spin (half-integer) just by studying the unitary irreducible
representations of SO(3) -- which can be done in the nonrelativistic (Galilean) case.

Sorry to be picky on this, but the half-integer spin is not from the irreds of SO(3), but from the irreds of SU(2). ;)

 

[ytuab]

Actually, you can get spin (half-integer) just by studying the unitary irreducible
representations of SO(3) -- which can be done in the nonrelativistic (Galilean) case.

You probably say about spin itself.
But spin-related things need Relativity even in QM.

For example, when we consider the external magnetic field (B) in nonrelativistic Schrodinger equation,

H = \frac{p^2}{2m} = \frac{(\sigma p)^2}{2m} \to H=\frac{(\sigma(p-eA))^2}{2m} + e\varphi

Here we pick up one part such as

(-\frac{-e}{2m})(\sigma_i p_i \sigma_j A_j + \sigma_j A_j \sigma_i p_i) = \mu_B \sigma\cdot B = g_e \mu_B S\cdot B

So the interaction between external magnetic field (B) and electron spin appears even in nonrelativistic Schrodinger equation.

But the spin-orbital (=internal magnetic field) interaction needs Relativity.
Actually Thomas precession factor uses "complicated" Relativity.
And if we don't use this Thomas precession, we need to use relativistic Dirac equation to explain the spin-orbital interaction (=fine structure).

And the antisymmetric property of spin 1/2 particle needs Dirac equation, doesn't it ?

The important point is that we don't know about what spin itself actually is.
(for example, electron must spin faster than light to get 1/2 angular momentum, and it returns by 2 rotation.)
This strange property can not be changed even if we use Relativity.

So we can't take anything else but Pauli matrices to explain spin itself.
(We can't move from Pauli matrices to more concrete things, because we don't know anything about spin itself.)
This is why nonrelativistic Pauli matrices is always valid even in \gamma matrices of relativistc Dirac equation.

 

[edguy99]

... O.K. the spin doesn't mean the real rotation.
So the precession doesn't mean the real rotation, either ?
(How the point particle like electron precess correctly?)
If so, the frequency of the precession is valid ?

I am not sure I understand the question, what do you mean by spin vs real rotation? The gyroscope example illustrates 2 important properties of spin. You start with a spinning object (perhaps a sphere, a ball, a disk, a torus, or whatever ...) and define 'north' as the direction of the objects axis of spin, perpendicular to the direction of spin (particles right, antiparticles left). When this type of object is subjected to an external field (gravity in the gyroscope case), it will start to precess around the true 'north' of the external field. Wrt a magnetic field, this precession of the particles 'north' around the external fields 'north' makes the particles 'average value of north' the same as the external field. The causes all the spinning, precessing particles to go either up or down at about the same rate regardless of the original axis orientation giving a spin 1/2 particle 2 states, up or down.

I suspect, this is the kind of spin Rabi and Larmor had in mind when they worked on this and I think is fair to say, is the source of the wording used today. To quote Rabi: "As a beginning graduate student back in 1923, I ... hoped with ingenuity and inventiveness I could find ways to fit the atomic phenomena into some kind of a mechanical system... My hope to [do that] died when I read about the Stern-Gerlach experiment... This convinced me once and for all that an ingenious classical mechanism was out and that we had to face the fact that the quantum phenomena required a completely new orientation."

http://www.upscale.utoronto.ca/PVB/Harrison/SternGerlach/Flash/SG3Magnets.html" , gives a better example of what spin in the classical sense means.

 

[yoda jedi]

So, I know that spin is very important in quantum mechanics/elementary particles. But just what is spin, PHYSICALLY?

Is it the way a particle rotates (spins)? The direction? The velocity at which it rotates? What does it mean for a particle to half 1/2 a spin and the other to have spin 1? Does it mean that the spin 1 has "twice" as much of this so-called spin as the spin 1/2 particle? Is the spin number a relative measure of whatever "spin" is?

Just to show you how frustrated I am trying to get a complete answer.

Wikipedia's view on spin:

"a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei"

OK, but that's not very descriptive at all. The fact that when I asked my physics TA what spin was, and he gave me an answer which was kind of non-informative and avoidant of the answer, just shows how extremely vague the term really is.

Can anyone give me a non-technical, physically relevant answer? Just what the heck is spin, anways?

what is spin ?

http://jayryablon.files.wordpress.com/2008/04/ohanian-what-is-spin.pdf

 

[DrChinese]

... gives a better example of what spin in the classical sense means.

Why would we want to show someone about a classical model? I would think that in almost any application, the quantum model would be more appropriate. Same comment for yoda's link, which is based on a classical model as well.

 

[ytuab]

Sorry . edquy99.
The "precession" of spin is widely-used, and very important.
But do you think the precession is very difficult to imagine ?

For example, you quote the Stern-Gerlach experiment, in which the direction of the spin is quantized in the external magnetic field (= z direction). (up and down).
But if you consider the spin precession, is it really so?

According to QM, total spin angular momentum is \sqrt{s^2} = \sqrt{s(s+1)} = \sqrt{\frac{1}{2}(\frac{1}{2}+1)}.
So when the spin is up (z = +1/2), the spin component in other directions (= x or y) is
\sqrt{\frac{1}{2}(\frac{1}{2}+1) - (\frac{1}{2})^2} = 0.7 > \frac{1}{2}
This means that in spite of the external magnetic force (=z), the spin points toward other direction, and this component is bigger than z direction (0.7 > 1/2).
So what on Earth is the influence of the external magnetic force ?
Because spin almost points to the directions other than z (0.7 > 1/2).
So I wonder why you can accept it easily.

And the frequency means \omega/2\pi.
If the angular frequency exists in spin precession, why the orbital motion of the electron doesn't have the angular frequency ?
As you say, larmor frequency is the heart of understanding NMR.
If so, are there some reasonable explanations about this ?

 

[strangerep]

The important point is that we don't know about what spin itself actually is.

I don't know why people keep saying that.

Spin (aka intrinsic angular momentum) has a classical meaning.
See Misner, Thorne & Wheeler, p158 (Box 5.6 part D).

 

[strangerep]

Sorry to be picky on this, but the half-integer spin is not from the irreds of SO(3), but from the irreds of SU(2). ;)

OK, two can play at that game...

Sorry to be a really nit-picky, but it's the "unirreps", not the "irreds".

A little more seriously, we only need find the unirreps of the Lie algebra to
get half-integral spin.

 

[dextercioby]

I've never seen <unirreps>. I assume the <un> comes from <unitary> which is indeed true for Lie groups (and especially compact ones), but not algebras. Lie algebras are represented on subdomains of Hilbert spaces in terms of essentially self-adjoint linear operators, not by unitary ones, so <[...]find the unirreps of the Lie algebra> is an inaccurate statement.

 

[Q-reeus]

But [for a spin-1/2 particle] it doesn't transform like angular momentum does under a rotation...

This has me intrigued. Say we have a bar magnet with uniform magnetization along the z axis and a corresponding collective electron spin angular momentum +H_z. Rotating the magnet about an axis y normal to z will give the expected EM induction effects of a collection of tiny classical magnetic dipoles. Yet the mechanical precessional torque would differ from that expected of a collection of classical spinning 'balls'?

 

[edguy99]

Sorry . edquy99.
The "precession" of spin is widely-used, and very important.
But do you think the precession is very difficult to imagine ?

For example, you quote the Stern-Gerlach experiment, in which the direction of the spin is quantized in the external magnetic field (= z direction). (up and down).
But if you consider the spin precession, is it really so?

According to QM, total spin angular momentum is \sqrt{s^2} = \sqrt{s(s+1)} = \sqrt{\frac{1}{2}(\frac{1}{2}+1)}.
So when the spin is up (z = +1/2), the spin component in other directions (= x or y) is
\sqrt{\frac{1}{2}(\frac{1}{2}+1) - (\frac{1}{2})^2} = 0.7 &gt; \frac{1}{2}
This means that in spite of the external magnetic force (=z), the spin points toward other direction, and this component is bigger than z direction (0.7 > 1/2).
So what on Earth is the influence of the external magnetic force ?
Because spin almost points to the directions other than z (0.7 > 1/2).
So I wonder why you can accept it easily.

And the frequency means \omega/2\pi.
If the angular frequency exists in spin precession, why the orbital motion of the electron doesn't have the angular frequency ?
As you say, larmor frequency is the heart of understanding NMR.
If so, are there some reasonable explanations about this ?

I do think spin projection is difficult to imagine and there are some additional videos http://www.animatedphysics.com/videos/larmorfrequency.htm" that I find helpful.

I am not sure I have a reasonable explanation or understanding of your question, but I do have an opinion regarding the spin projection along the x and y direction. The case you are discussing is somewhat similar to what is shown http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html" . If that red arrow was offset 1/2 up, 1/2 to the right and 1/2 towards yourself, you would be using
\sqrt{\frac{1}{2}(\frac{1}{2}+1) - (\frac{1}{2})^2 - (\frac{1}{2})^2} = 0.5 = \frac{1}{2}
I think the symplified version of your question is why is 1/2h measured for straight up rather then sqrt(3)/2 which appears to be the 'real' angular momentum when pointed up?

 

[KOSS]

Getting back to the original question... and in plain English?

What is spin?

I think a few respondents have implicitly answered it. Maybe I can attempt a reduction in simple English. Well, I'll have a go...

Spin is a way of labeling elementary particles that describes their symmetry properties under rotation and spacetime exchange. Sounds fairly abstract, but I think that's a real enough description that most well-read physics students can cope with.

It ain't about a spinning motion, it's not about quantized angular momentum, those classical concepts only come into play because of analogies. The mathematics of the underlying symmetries that the Hamiltonians (for interacting particles) obey gives the correspondence to the classical concepts of angular momentum in the correspondence principle limit.

 

[vanhees71]

In an abstract way, spin is defined by the behavior of the single-particle state vectors for a particle at rest (i.e., for massive particles).

Massless particles are a bit more special. Here a more costumary quantity instead of spin is helicity.

All this is closely related to the representation theory of the Poincare group for relativistic particles or the Galilei group for nonrelativistic ones (in the latter case of course only for massive particles since there's no nonrelativistic limit for massless particles).

 

[CyberShot]

In an abstract way, spin is defined by the behavior of the single-particle state vectors for a particle at rest (i.e., for massive particles).

Massless particles are a bit more special. Here a more costumary quantity instead of spin is helicity.

All this is closely related to the representation theory of the Poincare group for relativistic particles or the Galilei group for nonrelativistic ones (in the latter case of course only for massive particles since there's no nonrelativistic limit for massless particles).

As Einstein once said, you don't truly understand something in physics unless you can explain it to a third grader.

Now, assume I know nothing about physics. Please explain it to me in layman and concrete terms, preferably even a single sentence. :-)

 

[Fredrik]

As Einstein once said, you don't truly understand something in physics unless you can explain it to a third grader.

Now, assume I know nothing about physics. Please explain it to me in layman and concrete terms, preferably even a single sentence. :-)

I can explain it to a third grader, but it would take about ten years.

If I had to try to do it in less time than that, I would just say that each species of particle is identified by a short list of numbers, and that "spin" is one of those numbers. I might add that the fact that spin belongs on that list is a consequence of the rotational invariance of space, but I guess they would have stopped listening before the sentence is over.

 

[CyberShot]

I can explain it to a third grader, but it would take about ten years.

If I had to try to do it in less time than that, I would just say that each species of particle is identified by a short list of numbers, and that "spin" is one of those numbers. I might add that the fact that spin belongs on that list is a consequence of the rotational invariance of space, but I guess they would have stopped listening before the sentence is over.

Don't you think you're being vague here? It's not just you, however, as I see that "definition" given everywhere. You haven't defined spin, you've said what characterizes it. Am I being extremely stubborn here, or is there just no simple, physical meaning of spin?

 

[strangerep]

[...] is there just no simple, physical meaning of spin?

I've posted a reference to it a few times. See, e.g., this post:

https://www.physicsforums.com/showthread.php?p=2024618

Quick summary:

- Spin is a classical concept, also known as "intrinsic angular momentum",
which is a distinct notion from orbital angular momentum.
You'll have to look up the MTW reference I gave for the details since
I don't have time to type it in here, sorry.

- The passage from classical to quantum causes total angular momentum
to come only in discrete amounts.

- The classification of elementary particles involves these discrete
angular momentum quantum numbers.

 

[KOSS]

First, referring to the posts on pages & 2 of this thread - collectively they provide a satisfactory definition of spin. Though some kind PF mentor could probably do us all a favour and summarize.

Second. just modify your third grader version: instead of "a consequence of the rotational invariance of space" you need to say instead that "because spin is a way of accounting for the symmetry properties of particles when rotated or exchanged."

Third, why fret if the definition is only a characterization? That is all you can expect from any definition of any physical quantity! Do you suppose you know what mass or charge are in any simpler terms than the above definition of spin? If you do, please tell me! It'd be a breakthrough in meta-physics.

 

[chafelix]

If you have a problem with spin, try some more exotic notion such as charm.
It was Feynman who said that if we cannot explain something in simple terms, it means we do not understand it well. And yes, Feynman also said "nobody understands quantum mechanics" and this is normal, because our experience is with larger scales. Spin is certainely not something that spins around-that would mean speeds much larger than the speed of light. It's an internal degree of freedom. What does that mean? Take a car for example. It means that as long as we are limited to small energies, a car is a body that behaves as one particle: All of its parts move in unison. All we need to specify is position and momentum(classically speaking). But if you want to look inside, there are other degrees of freedom, such as belts moving, passengers, engines and so on. Their motion does not affect the car motion to a first approximation, but for some experiments it might. You can understand spin this way. Nonrelativistically and non-methematically, there is no deeper explanation

 

[Goldstone1]

You probably say about spin itself.
But spin-related things need Relativity even in QM.

For example, when we consider the external magnetic field (B) in nonrelativistic Schrodinger equation,

H = \frac{p^2}{2m} = \frac{(\sigma p)^2}{2m} \to H=\frac{(\sigma(p-eA))^2}{2m} + e\varphi

Here we pick up one part such as

(-\frac{-e}{2m})(\sigma_i p_i \sigma_j A_j + \sigma_j A_j \sigma_i p_i) = \mu_B \sigma\cdot B = g_e \mu_B S\cdot B

So the interaction between external magnetic field (B) and electron spin appears even in nonrelativistic Schrodinger equation.

But the spin-orbital (=internal magnetic field) interaction needs Relativity.
Actually Thomas precession factor uses "complicated" Relativity.
And if we don't use this Thomas precession, we need to use relativistic Dirac equation to explain the spin-orbital interaction (=fine structure).

And the antisymmetric property of spin 1/2 particle needs Dirac equation, doesn't it ?

The important point is that we don't know about what spin itself actually is.
(for example, electron must spin faster than light to get 1/2 angular momentum, and it returns by 2 rotation.)
This strange property can not be changed even if we use Relativity.

So we can't take anything else but Pauli matrices to explain spin itself.
(We can't move from Pauli matrices to more concrete things, because we don't know anything about spin itself.)
This is why nonrelativistic Pauli matrices is always valid even in \gamma matrices of relativistc Dirac equation.

Nice post.

 

[Goldstone1]

In an abstract way, spin is defined by the behavior of the single-particle state vectors for a particle at rest (i.e., for massive particles).

Massless particles are a bit more special. Here a more costumary quantity instead of spin is helicity.

All this is closely related to the representation theory of the Poincare group for relativistic particles or the Galilei group for nonrelativistic ones (in the latter case of course only for massive particles since there's no nonrelativistic limit for massless particles).

Massive particles are restrained to spin? Photons are certainly not massive but contain an angular momentum. Spin is an intrinsic property of all fields, the Klein-Gorden equation describes particles with zero spin - these psuedoscalar fields have never been observed.

 

[Cruikshank]

To OP: I have the very same question. Let me try to summarize what I've learned so far:
1.Classical spinning objects (tops, the earth, etc) tend to keep spinning. So there is this classical stuff we call "spin" and more formally "angular momentum" which has units of energy*time, or kg m^2/s, and it is conserved in the universe.
2.Now for electrons orbiting a nucleus, we have these weird "smeared out clouds" of probability representing them, such that the electron can "orbit" the nucleus without "accelerating", (as a classical object would, a=v^2/r). The math plays out such that the electron would "trip over its own wave" unless it sticks to specific orbitals. It turns out that these orbitals have 0,1,2,3...units of angular momentum, measured in multiples of hbar, Planck's constant over 2pi. So *orbital* angular momentum is quantized, and it really does map over to classical as the same "stuff" because if you do some experiment with a magnetic field and yank all the electrons around into new orbits, the whole object ends up rotating the other way. So classical spin can get tied up in electron orbits, and pulled back out, roughly. So orbital angular momentum counts when you add angular momentum up to conserve it.
3.Now for the weird part: particle "spin."
As near as I can tell, particles have a property with quantized values that are integer multiples of hbar/2, not hbar. This property follows the same math relationships as orbital angular momentum in QM. There are apparently ways to add orbital (L) and "intrinsic" (S) spins to get totals (J). I think--not sure--that you can do the same sort of magnet trick and use particle spins to make a classical object move by conservation of angular momentum.
4.So, it almost sounds as if there's no big(ger) mystery here; we could posit that these alleged point particles have some sort of radius and are like spinning balls, and that prospect is probably why it got named "spin" in the first place. BUT--the intrinsic spin comes in values half the size of what ought to be possible when you try to wrap an electron wave around a sphere. I read in a book somewhere that "it is as if the electron has to turn around twice to get back where it started."
5.What I would love is a geometrical depiction of that. Where I personally got stuck was in the details of the proof that the wave wrapping in 3D Euclidean space had to be integer and not half integer multiples of hbar.
6.Like you, I want a picture, a model, something to hang my intuition on and make it easier to *see* answers to QM problems instead of blindly calculating and hoping I got it right. That's what models are for; most of the physics community seems to be having a "sour grapes" reaction to our collective inability to make that model for QM, and some even get annoyed with those of us who stubbornly refuse to give up.
7.Luck to us both. Luck to us all.

 

[Q-reeus]

Cruickshank - you have raised some very interesting issues. Touches on what I posed in #30 but got zero response to. So will ask it anew. A bar magnet contains a collection of tightly oriented electron spins S, + orbital angular momentum L. In ferrites for instance the two contributions are roughly equal. Let's assume the orbital part L behaves macroscopically in a classical manner re a rotation of the bar magnet. What is the situation though for the spin part S. In QM there is this 1/2 integer spin -> 'rotation through 4pi' thing to restore everything. But is this reflected in the macroscopic behavour of the bar magnet as gyroscope? If not, why not?

 

[strangerep]

As near as I can tell, particles have a property with quantized values that are integer multiples of hbar/2, not hbar. This property follows the same math relationships as orbital angular momentum in QM.

Actually, it's more like the other way around. One derives half-integral quantized spin from the general su(2) Lie algebra. But when the generators of this algebra are restricted to be of the form q x p (i.e., orbital angular momentum), this causes a consequential restriction of quantized angular momentum to integer values. Details can be found in Ballentine.

"it is as if the electron has to turn around twice to get back where it started."
5.What I would love is a geometrical depiction of that.

Have you tried "Dirac scissors", a.k.a the "belt trick" ?

 

[Cruikshank]

Thank you for the suggestions. I must own 30 QM textbooks and 10 on group theory, and I'm not sure any of those things are even mentioned. Every answer I've gotten that sounds knowledgeable seems to include a lot of group theory terminology I've never heard of, even though I have a Master's in Math and took Abstract Algebra. I've gotten two textbooks on spinors and after reading a chapter of each could not find any content and gave up. It was as if the book was just spouting random trivia, not describing an entity or having a point. Frustrating.

 

[syberraith]

As Einstein once said, you don't truly understand something in physics unless you can explain it to a third grader.

Now, assume I know nothing about physics. Please explain it to me in layman and concrete terms, preferably even a single sentence. :-)

I'm just learning about this myself and I lack knowledge to explain it in mathematical form. Although I think I can provide the general concept.

It's called spin because it has some of characteristics of a rotating mass like a gyroscope. Spin tend to point in one direction like a gyroscope standing up by itself until some thing causes it to change its alignment. With particles they keep spinning because there's a lack of any friction to slow them down like a gyroscope.

I know with neutrons and electrons and presumably protons too, spin is related to magnetism. That is a magnetic field can change the orientation of the spin.

Also the spin of particles seem to have particular magnitude when they interact with other particles.

So there you have it, at least with an electron spin has some of the character of a magnet gyroscope. that is it has an axis and magnitude of rotation and is subject to magnetic fields.

 

[strangerep]

Thank you for the suggestions. I must own 30 QM textbooks and 10 on group theory, and I'm not sure any of those things are even mentioned. Every answer I've gotten that sounds knowledgeable seems to include a lot of group theory terminology I've never heard of, even though I have a Master's in Math and took Abstract Algebra. I've gotten two textbooks on spinors and after reading a chapter of each could not find any content and gave up. It was as if the book was just spouting random trivia, not describing an entity or having a point. Frustrating.

In Misner, Thorne & Wheeler, "Gravitation", there a diagram showing a point connected by flexible strings to a sphere at infinity. They use this diagram to try and illustrate how spinors are related to a kind of orientation entanglement.

But more helpful (perhaps) is Penrose & Rindler's "Spinors & Spacetime" which delves into such geometric pictures in vast detail. That's where I first read about the Dirac scissors thing and was so astonished that I immediately took off my belt and tried it then and there (fortunately in the privacy of my own home :-)

 

[Q-reeus]

Seems I have an invisible presence on this thread. What was posed in #30 and #43 was a genuine query. Has no-one here an answer, or is it 'too dumb' a question? Bad manners to ignore - if someone here can explain, please provide the explanation!

 

[Cruikshank]

Q-reeus: As far as I know, you can make macroscopic rotation out of particle spins as well as their orbital angular momentum. But someone more knowledgeable about experimentation could be more definitive.

 

[Cruikshank]

Strangerep: thank you very much for the text references. I was thinking it was time for another assault on MTW anyway...and I'll look up the other as well.