Spin Explained for the "Wikipedia Physicist" - No QM Needed!

[haael]

What you call "standard spin" is the number j from when we write the eigenvalue of the operator $$J^2=J_x^2+J_y^2+J_z^2$$ as j(j+1). This number is the same in all inertial frames, and that makes it appropriate to use it as one of the labels that identify a particle species. That stuff about "spinors" and "vectors" refers to how the components of the quantum field changes from one inertial frame to another.

Those numbers are eigenvalues of $$J_z$$ . The eigenvalues are always -j, -j+1,..., j-1, j. (Photons have j=1, electrons j=1/2). These numbers have very little to do with directions in space.

Thanks, guys, that's what I wanted to know. So spin states basically carry less information than the whole spin tensor. That's why there are fewer spin states than tensor components.

 

[conway]

Thanks, guys, that's what I wanted to know. So spin states basically carry less information than the whole spin tensor. That's why there are fewer spin states than tensor components.

Actually, I think I was going to show, using the case of atomic orbitals, how to reconstruct the tensor picture from the spin states before I got sidetracked. Just as the three p states (1, 0, and -1) can be transformed to convey the vector information, the five d states (2, 1, 0, -1, and -2) can be transformed to convey what I would consider the tensor information. Just as the vector p-states, taken in superposition with the ground state, give you static displacements from the origin, the "tensor" d states allow you to make arbitrary small deformations of the s state into a general ellipsoid. That's the same thing the stress tensor does in a solid.

I can follow up on this if anyone is interested.

 

[Nick R]

Quick question - is it productive to ever think about spin as something other than a thing that describes the "intrinsic magnetic field" of a particle?

 

[conway]

Quick question - is it productive to ever think about spin as something other than a thing that describes the "intrinsic magnetic field" of a particle?

Well, I think so. The atomic orbitals have integer-valued spin numbers that don't come from the intrinsic magnetic field, they come from the motion of the electron wave around the atom. Those are the states I was proposing to analyze in my last post.

 

[Fredrik]

Quick question - is it productive to ever think about spin as something other than a thing that describes the "intrinsic magnetic field" of a particle?

Yes, especially when the particle is uncharged.

The spin operators are defined as the generators of the SU(2) subgroup of an irreducible representation of the universal covering group of the symmetry group of spacetime (which can be either the Galilei group or the Poincaré group), and unfortunately there's no easy way to really understand what that means.

A good start is to realize that the spin component operators are (by definition) the ones that appear in the first order terms when you Taylor expand a rotation operator around the identity:

$$U(\theta)=1-i\sum_k\theta_kJ_k+\mathcal O(\theta^2)$$

(The sign depends on how you define the parameters, and I don't remember if + or - is preferred). And the operator whose eigenvalue can be interpreted as one of the labels that identifies the particle species, is defined by

$$J^2=\sum_k J_k^2$$

 

[passingthru]

As others have said, spin is intrinsic angular momentum, and is assigned discreet values (unlike continuous values for orbits or rotation). The electron, eg, has two discreet (key word) values: 1/2 and -1/2 spin.

Please understand that the guy who coined the intrinsic angular momentum of a particle as "spin" is a complete imbicile. The term is misleading.

For the electron, "spin" is synonymous with "charge." You have a positive charge (same as +1/2 spin) and a negative charge (same as -1/2 spin).

That 'imbicilie' was P.A.M. Dirac. Name-calling is very stupid.

 

[Char. Limit]

That 'imbicilie' was P.A.M. Dirac. Name-calling is very stupid.

You must admit, however, that "spin" is as good a way to describe that particular property of a particle as "color" is to describe quarks.

And that's really not good.

 

[jtbell]

Quick question - is it productive to ever think about spin as something other than a thing that describes the "intrinsic magnetic field" of a particle?

It contributes to the total macroscopic angular momentum of a system. See for example the Einstein - de Haas effect.

 

[haael]

Actually, I think I was going to show, using the case of atomic orbitals, how to reconstruct the tensor picture from the spin states before I got sidetracked. (...)

I can follow up on this if anyone is interested.

I am interested.

 

[conway]

Okay. Did it make sense to you when I talked about how you can move the s cloud in any direction from the origin by adding in a small component of p_x, p_x, and p_z?

 

[SpectraCat]

Well, I think so. The atomic orbitals have integer-valued spin numbers that don't come from the intrinsic magnetic field, they come from the motion of the electron wave around the atom. Those are the states I was proposing to analyze in my last post.

Just a quibble .. it will be less confusing if you stick with the convention and refer to "orbital angular momentum" by that name, rather than by saying that atomic orbitals have "spin". In the context of atomic physics, "spin" is reserved for the intrinsic angular momentum.

 

[conway]

Ok .. I admit that I got confused by the similarity of this case with our other argument, and assumed that you were talking about non-degenerate s- and p-states. You are correct for the case of degenerate s- and p- states in the first-order Stark effect; there will be a net polarization of the charge density in the field direction.

I will go back and amend post #64 to clarify this point.

This is not the first time you have gone back and changed your posts after seeing my response.

When I post on Physicsforums, I take the risk of exposing myself to ridicule if my ideas are stupid. It is a risk I am willing to take. Apparently you are not.

The PhysicsForums archives are a permanent record of what was said in these discussions. By going back and altering that record to your benefit, you not only make yourself look smarter than you actually are, you make me look worse because I am seen to be responding inappropriately to things you apparently never said.

I have benefited a great deal from these discussions we’ve had over the last few weeks, and I will no doubt miss having these arguments with you. But I am not willing to continue on an unlevel playing field with an opponent who does not respect or even understand the basic principles of fair play. I will therefore not be responding to your posts in the future.

 

[SpectraCat]

This is not the first time you have gone back and changed your posts after seeing my response.

When I post on Physicsforums, I take the risk of exposing myself to ridicule if my ideas are stupid. It is a risk I am willing to take. Apparently you are not.

The PhysicsForums archives are a permanent record of what was said in these discussions. By going back and altering that record to your benefit, you not only make yourself look smarter than you actually are, you make me look worse because I am seen to be responding inappropriately to things you apparently never said.

That is something I have never done ... as far as I am aware it is expressly against the rules of PF, and is a bannable offense.

I have benefited a great deal from these discussions we’ve had over the last few weeks, and I will no doubt miss having these arguments with you. But I am not willing to continue on an unlevel playing field with an opponent who does not respect or even understand the basic principles of fair play. I will therefore not be responding to your posts in the future.

Conway .. get real. I *amended* my post .. that means I added clarifications to it .. and in the case of post 64 I removed one incorrect statement that I admitted was wrong in the context of your remarks. What more could you possibly want? If you go back and look at what I wrote, you see that I noted that post had been edited, and I said what I had changed. In fact, I am pretty sure you quoted the statement in question in another post, which means it is still in the public record. Go post a big all-caps announcement that you were right and I was wrong if you like.

This is not a game, so the "level playing field" analogy is nonsense. It is also not about you and me, or any other individual .. and you take this stuff WAY too personally. As I have said about 50 times in my posts to you, what I am concerned with is getting everything correct so that future readers can follow what we have done.

I could frankly care less what you or anyone else thinks about how smart or dumb I am ... I also am not afraid to make mistakes and own up to them. I try very hard not to make incorrect statements when I post, but when I do make mistakes, I try to make sure that they do not lead to the confusion of other readers. You need to lighten up and get that Everest size chip off your shoulder.

 

[Frame Dragger]

You know, I came to this site to LEARN, from people who were in various fields of research, teaching, etc. I'm constantly amazed by the number of people who come here thinking it will be their launching point for their new theories! Not only is that counter to the purpose of this site, but it's contrary to the scientific method.

Conway, I don't know why you haven't been banned... presumably because Cat is too kind to report you, but cut the crap. You haven't benefited one iota from these "discussions", because they are always semi-related ramblings from you, which SpectraCat, CollinsMark and others challenge. You sidestep, and continue with some other aspect of your "theory", all the while admitting total ignorance of the physics into which you're treading (QED, general QFTs, etc).

You're deluded, or you have a very focused agenda, but don't play this sob-story crap about editing posts, and level playing fields. Would you like to know why you percieve the field between you and Cat to be so uneven?... HE knows what the hell he's talking about, and when he doesn't he admits it and doesn't speculate.

You're yet to even post a proof of your non-theory which everyone has been telling you is frankly silly to begin with. Obviously a lot of your self-esteem is wound into this theory of yours, or the notion of your level of comprehension. My advice is that instead of NOT responding to the one person who has unfailingly engaged you (Cat), would be that you 'go home' and do the research required to level the field.

You COULD have come here to learn, then see if your theory matches existing evidence, right? Instead, you do... this. The sad thing, is that you're acting this way on a site full of people who see right through you. I grant that must not be what you're used to, but my advice is to find your level, and try to rise from that point. If you're a fabulous genius, then you should do so rapidly, and begin to form theories based on KNOWLEDGE, not complete horsegarbage.

 

[conway]

Conway, I don't know why you haven't been banned... presumably because Cat is too kind to report you, but cut the crap. You haven't benefited one iota from these "discussions", because they are always semi-related ramblings from you...

You know, I might have let it pass or taken it up with SpectraCat in a private communication, but I looked at his alterations (sorry: amendments! Spectracat never "alters" his posts.) and I’m pretty sure he was taking advantage of them to re-argue the points I had made after his original post. I can’t exactly prove it...because he’s amnded his postings. I don’t expect you to understand how wrong this is but Spectracat ought to. And he has certainly amended posts in the past to make some particular arguments look less foolish (or at least less incorrect) than they turned out to be.

You profess wonderment that the moderators haved not yet banned me from the forum. I am also sensitive to this possibility, and that is one reason why it is important to me to have an accurate record of what was said by whom and when. In light of the type of invective that has been thrown back and forth in this discussion (in fact mostly forth and very little back), including your own most recent missive, I want the record of who said what to be clear and accurate.

Spectracat's excuse for amending his posts seems to be so that future visitors will not be confused by wrong science. In his mind, this gives him license to repeatedly tell me I don't know what I'm talking about, and then when it turns out he was wrong, he's entitled to go back and fix his mistakes. For the sake of "future readers".

It’s true that I am not popular in this discussion group and people frequently criticize me for the my tone and attitude, but after carefully reviewing my correspondence and comparing it to that of others, FrameDragger, I’m pretty sure I have nothing to apologize for.

 

[haael]

Okay. Did it make sense to you when I talked about how you can move the s cloud in any direction from the origin by adding in a small component of p_x, p_x, and p_z?

Yeah, go on.

 

[vanesch]

Could you guys please stop having sterile fights here ? That doesn't help anybody, and honestly, I don't think "future generations" will care anything about who was able to put up the best image of himself during a silly fight on an internet forum

The fight about angular wavefunctions and their appearance and their different possible superpositions and so on is actually off-topic here, because the thread is about *intrinsic* spin. Intrinsic spin hasn't much to do with angular wavefunctions except for the fact that they are related to representations of the rotation group.

So let us focus back on the original discussion about intrinsic spin and let us forget about the souvenir future generations might get of us ...

 

[Frame Dragger]

Could you guys please stop having sterile fights here ? That doesn't help anybody, and honestly, I don't think "future generations" will care anything about who was able to put up the best image of himself during a silly fight on an internet forum

Pfft, are you serious? I'm fairly sure that whoever leaves the best impression on the internet wins total wisdom and a tasteful gift-bag from Sears.

EDIT: *looks at post #89*

Okay, looking at the history of the thread, I see that vanesch is right. It was an old thread from last year that got revived last week, and haael's question about the relation between the z-axis representation of spin versus the vector/tensor representation was off topic. I'll start a new thread to continue that discussion.

Hint: The staff member wasn't offering you a choice, and s/he probably didn't need your added input to realize that things in the thread would ultimately trend their way. That's what being an admin MEANS.

Still, thanks for obfuscating Vanesch's clarity.

 

[conway]

The fight about angular wavefunctions and their appearance and their different possible superpositions and so on is actually off-topic here, because the thread is about *intrinsic* spin. Intrinsic spin hasn't much to do with angular wavefunctions except for the fact that they are related to representations of the rotation group.

So let us focus back on the original discussion about intrinsic spin and let us forget about the souvenir future generations might get of us ...

Okay, looking at the history of the thread, I see that vanesch is right. It was an old thread from last year that got revived last week, and haael's question about the relation between the z-axis representation of spin versus the vector/tensor representation was off topic. I'll start a new thread to continue that discussion.

 

[conway]

Pfft, are you serious? I'm fairly sure that whoever leaves the best impression on the internet wins total wisdom and a tasteful gift-bag from Sears.

EDIT: *looks at post #89*


Hint: The staff member wasn't offering you a choice, and s/he probably didn't need your added input to realize that things in the thread would ultimately trend their way. That's what being an admin MEANS.

Still, thanks for obfuscating Vanesch's clarity.

The moderator asked us to stop our little catfight (no pun intended, SpectraCat) and I have respected that. I'm not sure he was offering you a choice either, so maybe you should consider doing the same.

 

[tayyaba aftab]

what is chirality of spin state?

 

[Char. Limit]

Well, chirality usually refers to "handedness" of something, or perhaps a better term, nonsymmetry. So it probably has the same sort of meaning here.

 

[es.no]

what exactly is Earth spin?
is there a quantum effect on the Earth spin?what is exactly causes the Earth spin?

You can think of spin as the intrinsic angular momentum of a particle (rather than say, orbital angular momentum).

E.g. If the Earth is moving around the sun, and rotating, the orbit is the regular angular momentum, while the rotation is the "spin" angular momentum.

This is JUST a tool to help you make the concept a bit more concrete. DON'T take it literally. Particles, as far as we know are point particles and therefore can't really spin like the Earth does. Also, if you take an upper limit for the size of the electron, and try to find out how fast it must "spin" then a "point" at the electron's equator would need to be moving faster than the speed of light. This is no good! So don't think of this analogy in the literal sense.

 

[DrChinese]

what exactly is Earth spin?
is there a quantum effect on the Earth spin?what is exactly causes the Earth spin?

Welcome to PhysicsForums, es.no!

Earth does not spin because of quantum effects. It is considered to spin due to classical effects. When free matter in space coalesces to form a celestial object such as a star or planet, total momentum is conserved. Therefore the object takes on the net momentum of its constituents. Usually, there is a net spin component in addition to other components. That is what we observe.

 

[sah-sah]

hello

my question isn't correlate with Earth spin'''''

can you explain to me:
1- In spectroscopy of atoms, such sodium, is specified that in absence of magnetic field,
Apiece of energy levels split to two component except S level.

Why S level isn’t split?

 

[SpectraCat]

hello

my question isn't correlate with Earth spin'''''

can you explain to me:
1- In spectroscopy of atoms, such sodium, is specified that in absence of magnetic field,
Apiece of energy levels split to two component except S level.

Why S level isn’t split?

A better question is why are the other energy levels split? Recall that the S-term correlates with L=0, whereas the other terms have non-zero L. Do you remember the formula for the degeneracy of a particular l-level? Do you know what the particular form of the interaction of the magnetic field with the atomic states is? If you can answer those last two questions, then you should be able to understand why the S-state is unsplit.

 

[sah-sah]

thank you.
you are right

actually,i don't know what the particular form of the interaction of the magnetic field with the atomic states is.

can you tell me?

A better question is why are the other energy levels split? Recall that the S-term correlates with L=0, whereas the other terms have non-zero L. Do you remember the formula for the degeneracy of a particular l-level? Do you know what the particular form of the interaction of the magnetic field with the atomic states is? If you can answer those last two questions, then you should be able to understand why the S-state is unsplit.