Understanding Atomic Particle 'Spin': Exploring Its Physical Meaning and Value

[cmb]

I've been looking hard (really, I have) for an explanation of what 'spin' is.

Is there any way to explain this in a physical-real way, or is it 'just a thing'?

Every description I have come across, and I mean dozens, say something like 'well, it's like angular momentum but it isn't really that it is something else. It's to do with the magnetic moment. It comes in integer or half integer values'.

OK, but what is it? Also, who decided to use half integer values? What is it a half of? Why not double up the number so 'spin' is always an integer?

Thanks. I really don't know how to access this information. Maybe it's just a characteristic with an unknown physical meaning? (That's OK, if it's the case, I just want to be clear.)

 

[PeroK]

OK, but what is it? Also, who decided to use half integer values? What is it a half of? Why not double up the number so 'spin' is always an integer?

In quantum mechanics, a measurement of angular momentum about a given axis must result in one of the following (quantised) values:

$0, \frac 1 2 \hbar, \hbar, \frac 3 2 \hbar, 2 \hbar \dots$

Someone at some stage decided it was a sensible idea to define the quantum number $m$, where the angular momentum is $m\hbar$ and $m$ takes the values:

$m = 0, \frac 1 2, 1, \frac 3 2, 2 \dots$

You could redefine this so that $m$ is an integer, but that doesn't change the measured values.

 

[sophiecentaur]

Is there any way to explain this in a physical-real way, or is it 'just a thing'?

It's a good idea to avoid insisting that things must be "real" before you are prepared to accept them. There is no reason to expect our world to make intuitive sense because our intuition is based on our experience and that is very limited.
The nearest I think you can get to what spin is must be based on the conservation laws, which seem to apply to quantum objects as well as classical objects.

A serious problem with particle spin is the axis! Why should it be in any particular direction? Clearly the only answer to that sort of problem is that the spin is only 'there' when the particle interacts with something which actually defines an axis. (My humble view of the thing!) This is similar to the notion of a photon, which need (/can) only exist when it interacts with something. People keep trying to nail what a photon 'looks like' and there just isn't a good answer to that question.

 

[Vanadium 50]

Is there any way to explain this in a physical-real way, or is it 'just a thing'?

`What's the difference? It's something you can measure in a lab, so does that make it "physical real"? Or "just a thing".

I suspect what your question boils down to is "can I understand this with less than X hours of study?"
Well, maybe.

 

[Dale]

dozens, say something like 'well, it's like angular momentum but it isn't really that it is something else

It is angular momentum, not just like angular momentum, it is in fact angular momentum. It has the units of angular momentum and everything.

What it is not is the angular momentum of a microscopic classical ball. There is no little rigid object spinning. It is more similar to the angular momentum of the electromagnetic field in Maxwell’s equations.

 

[cmb]

I suspect what your question boils down to is "can I understand this with less than X hours of study?"
Well, maybe.

Yes, exactly that. Less than X minutes, preferably. More than that and it's more information than I want.

I'd like to know if there is an explanation along the lines Feynman might have given for it to a six year old.

Maybe, in fact, as mentioned it is better to understand the ways of how to measure it, and work 'backwards' so to speak. Again, the 'popular' text is not very clear on this. When searching for that detail, most papers are either at that high level 'like angular momentum, but...' or descend into something very complicated very quickly and I can't make head nor tail how they'd actually measure anything.

I believe I understand how it is that some 'spinning' electromagnetic 'thing' would precess in a magnetic field, and you could measure an emission from that precession, viz NMR. I am happy with that, but are there more direct measurements of 'spin'?

I am also interested in how come spin cannot be changed (yet the axis can be changed, which presumably means the spin has changed a little bit during the transition?), why it cannot be increased indefinitely in multiples of that spin, whether if you spin an atom about an axis which is parallel to its spin axis does its spin artificially increase, and other stuff. I can't even picture if those questions are sensible to ask because I have no physical image of it beyond a little ball spinning on its axis.

Also, how come excited isotopes can have different spin to their de-excited states, if the spin is a composition of the spins of their fundamental particles (which don't change during a de-excitation)?

 

[cmb]

It is angular momentum, not just like angular momentum, it is in fact angular momentum. It has the units of angular momentum and everything.

What it is not is the angular momentum of a microscopic classical ball. There is no little rigid object spinning. It is more similar to the angular momentum of the electromagnetic field in Maxwell’s equations.

OK, so, in a conventional spinning thing with angular momentum, if you turn it upside down, reversing the axis, then there is a transfer of the change of that angular moment to something else. Is this the same for nuclear spin?

 

[Dale]

OK, so, in a conventional spinning thing with angular momentum, if you turn it upside down, reversing the axis, then there is a transfer of the change of that angular moment to something else. Is this the same for nuclear spin?

How do you turn a field upside down?

 

[cmb]

How do you turn a field upside down?

I don't understand your question.

If I have an object in my hand with all the spins of the atoms lined up (by whatever means you make them line up ... that was one of my questions) and then you turn the object over, how is angular momentum conserved?

If it was a spinning top in my hand, then as I invert it there would be a mechanical torque reaction that'd nudge me, and the planet, over a little bit. Is there such a mechanical torque from atomic spin as you turn an object over? Do all the spins stay lined up and the atoms don't turn over?

Really, I don't have even a starting footing to form an idea how to conceptualise this.

 

[Dale]

If I have an object in my hand with all the spins of the atoms lined up

I am not sure that is possible.

However, it doesn’t change my question to you. How do you turn a field upside down?

This is not me avoiding your question, this is me getting you to think more deeply about your own question. If you are interested in quantum spin then you need to ask about quantum objects which are fields. Macroscopic objects or tops are a distraction.

So how do you turn a field upside down? Or equivalently, how do you recognize that field B is field A turned upside down?

 

[cmb]

You turn the field generator upside down.

If I have a permanent magnet in my hand, I turn it upside down, the field is inverted. That being said, I would not presume there is necessarily a field there at all, unless there is another magnetic thing between which there is a field. So as I turn the magnet upside down, I would feel the magnet tugging on the magnetic thing, and impart some mechanical force there to turn the field over. If there was no magnetic thing there at all, maybe there was no field?

If I have an atom with spin, I turn it upside down.

That's the only answer I feel I can understand right now.

 

[Dale]

You turn the field generator upside down.

That is a good approach. How about if the field generator is a charged ball?

 

[Nugatory]

If I have an object in my hand with all the spins of the atoms lined up (by whatever means you make them line up ... that was one of my questions) and then you turn the object over, how is angular momentum conserved?

Your body is exerting a force on the object, applying a torque which turns the object and changes its angular momentum... but by Newton’s third law there is an equal and opposite force acting you, and the resulting torque is changing your angular momentum as well. The two changes cancel so the total angular momentum of the system consisting of the ball and the your body (and the entire earth, if your feet are solidly planted on the ground) does not change.

 

[Mister T]

I'd like to know if there is an explanation along the lines Feynman might have given for it to a six year old.

If you try to explain the angular momentum and the magnetic moment of something like an electron by modelling the electron as a spinning sphere it doesn't work. The electron has an angular momentum and a magnetic moment "as if" it were spinning and that is the reason it's called spin.

 

[A. Neumaier]

an explanation of what 'spin' is.

I'd like to know if there is an explanation along the lines Feynman might have given for it to a six year old.

Just like the total mechanical energy is the sum of several parts (kinetic and potential energy), so the total angular momentum is the sum of several parts: the orbital angular momentum and the intrinsic angular momentum. The intrinsic angular momentum of a particle (called its spin) is the part that it cannot get rid of by changing its motion. (It is due to the representation theoretic properties of the group SO(3) of 3-dimensional rotations.) Thus it is a property independent of its state of motion, which makes it useful for classifying particles. For example, electrons have spin 1/2 while the Higgs particle has spin 0.

Viewed in more detail, the wave function of a spin $k/2$ particle (used to characterize its detailed quantum state) has $k+1$ components. This explains why the spin must be one of the numbers 0, 1/2, 1, 3/2, 2,... It also explains why directions matter when the spin is positive, since then these components form a vector of dimension $>1$.

I have no physical image of it beyond a little ball spinning on its axis.

A classical ball spinning on its axis has zero spin (intrinsic angular momentum) since one can stop it spinning and is then left with a total angular momentum of zero.

how come excited isotopes can have different spin to their de-excited states, if the spin is a composition of the spins of their fundamental particles (which don't change during a de-excitation)?

Because under composition, the spins don't satisfy the rules of ordinary arithmetic but those of the representation theory of SO(3). The dimensions $k+1$ multiply because the wave function of the composition is represented in a tensor product, and then decompose additively into a sum of dimensions of irreducible representations of different spin.

 

[A. Neumaier]

If I have a permanent magnet in my hand, I turn it upside down, [...] If I have an atom with spin, I turn it upside down.

Unlike the former you cannot do the latter. Atoms cannot be handled like little balls.