Can anyone explain the physical meaning of spin in QM?

[LennoxLewis]

Can anyone explain the physical meaning of "spin" in QM?

I'm a physics master student and I've completed several quantum mechanics (or related) courses and i have no problem working with Pauli spin matrices, angular momentum L, spin momentum S and total momentum J for nuclear or atomic physics... i know that whether spin is an integer or half-integer determines the particle obeying Fermi-Dirac or Bose-Einstein statistics. I know that it's a fixed, inherently true characteristic of a particle, just like rest mass is. But I've never understood what spin REALLY means, in quantum mechanics.

Can anyone explain, perhaps with an analogy?

 

[jtbell]

What do you mean by "really means?"

Really.

This may or may not be what you're looking for, but intrinsic QM angular momentum does contribute to an object's macroscopic angular momentum, which can be demonstrated experimentally. See the Einstein - de Haas effect.

 

[tim_lou]

Spin comes from internal symmetry of a wave function. More explicitly, Lorentz invariance allows the existence of spin. (it doesn't say it must exist though).

Spin is no more different than a 4 vector. Under Lorentz transformation, a 4 vector transforms like
v'^\mu=\Lambda^\mu_\nu v^\nu

You can generalize this idea to allow spinors (so that they transform under Lorentz transformation):
\chi' = U(\Lambda)\chi
Of course, U is not the usual elements of the Lorentz group, but a representation of it. If you look at how wave functions transform under rotations, you get orbital spins. Similarly, looking at how spinors transform under rotations (part of Lorentz group) gives you intrinsic spins.

I tend to think of spinor as a vector, except that it doesn't point in any direction in space time but some abstract vector space. Like usual vectors, when you rotate the coordinate systems, spinor gets rotated in their abstract vector space.

 

[LennoxLewis]

Thanks for the answers, but they're way too deep and mathematical. Again, I've seen the derivations, presence in the wave function, etc. What I'm looking for is a physical explanation of what spin is.

I'm an assistant in a certain course and a student asked me how he can imagine spin in QM and i didn't really know how to explain it because i don't know myself. I know that it's not the same as spin in "a spinning toll", but somehow related still. I told him that it is an inherent quantity "baked in" to particles, but i couldn't really give a satisfying answer on the physical meaning of spin.

 

[Hurkyl]

Thanks for the answers, but they're way too deep and mathematical. Again, I've seen the derivations, presence in the wave function, etc. What I'm looking for is a physical explanation of what spin is.

Spin is the property of a physical system that behaves in the way described by the deep and mathematical answers. Really, that's all there is too it.

How did you come to understand what mass is? By learning the mathematics and seeing how it applied to real situations.

How did you come to understand what work is? By learning the mathematics and seeing how it applied to real situations.

How did you come to understand what gravitational potential energy is? By learning the mathematics and seeing how it applied to real situations.

How will you come to understand what spin is? By learning the mathematics and seeing how it applies to real situations.

 

[tiny-tim]

Thanks for the answers, but they're way too deep and mathematical. Again, I've seen the derivations, presence in the wave function, etc. What I'm looking for is a physical explanation of what spin is.

I don't see the problem …

physcially, QM spin is spin …

to be more precise, the QM spins of eg an electron are angular momentum …

as jtbell says, the http://en.wikipedia.org/wiki/Einstein-de_Haas_effect" shows that QM angular momentum contributes to macroscopic angular momentum …

and a spin-up electron in a magnetic field really does have the opposite angular momentum to a spin-down particle.

"Ordinary spin-ness" is a physical property …

in what respect do you think it doesn't describe QM spin?​

 

[malawi_glenn]

Do we HAVE to imagine spin?

I think you should, as Hurkyl suggested, let go of the thought that physics and math are distinct. Math is the language and formalism of physics, physics can be thought as math applied to nature - laws, converation theorems etc are derived mathematically from symmetry principles etc.

 

[mn4j]

One may ask the question in reverse. Why should the spin of an electron not mean the same thing conceptually, as the spin of a classical particle. Or in other words, why should the angular momentum of a photon or quantum particle not mean the same thing as the angular momentum of a classical particle?

 

[LennoxLewis]

One may ask the question in reverse. Why should the spin of an electron not mean the same thing conceptually, as the spin of a classical particle. Or in other words, why should the angular momentum of a photon or quantum particle not mean the same thing as the angular momentum of a classical particle?

Because outside of polarity, the QM spin of a particle doesn't change.

 

[strangerep]

What I'm looking for is a physical explanation of what spin is.
[...] I told him that it is an inherent quantity "baked in" to particles,
but i couldn't really give a satisfying answer on the physical meaning of spin.

Forget about QM for a moment and concentrate on the distinction between "intrinsic" angular
momentum and "orbital" angular momentum in a classical context. Better still, grab a copy of
Misner, Thorne & Wheeler's "Gravitation" text and look at Box 5.6, parts D and E on pp158-159.

Intrinsic angular momentum is the angular momentum about any event on the particle's
center-of-mass world line. (This is the sense in which it is "baked in" to the particle.)

Orbital angular momentum is an additional part of total angular momentum which arises
when you consider angular momentum about some other event that is not on the particle's
world line.

So (loosely speaking) the intrinsic angular momentum is the angular momentum of the
particle that you continue to measure no matter how close to the particle's world line
you get.

HTH.

 

[newbee]

LennoxLewis

Your question is analogous to ask the following QM question: What is the "physical meaning" of a particular Hamiltonian? The answer is: That scalar field which makes Schrodinger's equation hold. Where by "hold" I mean "agree with experiment".

 

[granpa]

isnt spin the source of the electrons intrinsic magnetic field in the same way that charge is the source of its electric field?

 

[Edgardo]

It may help if you talk about the experiments involving quantum spin, like the Stern Gerlach experiment. In an older thread here I compared the spin to a tiny bar magnet, see post #7.

 

[granpa]

https://www.physicsforums.com/showpost.php?p=564350&postcount=7

Hello Ariel Genesis,

maybe to give you an intuitive feeling for spin, I recommend reading about the Stern-Gerlach experiment
http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html#c5

In that experiment, a particle with spin 1/2 is shot through a inhomogeneous
magnetic field. What happens? You will notice that a force acts on that particle because the spin interacts with the magnetic field.

You can think of the spin as a tiny little bar magnet, that only has two orientations (for spin s=1/2 like free electrons) in a homogeneous magnetic field along z-direction.
http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html

You see the red arrows? They represent the spin of the electron, but we are interested in the projection to the z-axis.
You have two choices: projection to the upper part of z-axis, so you get +\frac{1}{2}\hbar. In this case you talk about spin-up.

In the other case, where you project to the negative z-axis, you get
+\frac{1}{2}\hbar as projection, and we talk about spin-down.

So when you hear someone talking about spin-up or spin-down, it is just the orientation of the spin (or projection).There is an effect, called nuclear magnetic resonance, where you can flip the spin orientation.
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmr.html
In the left picture they use the analogy to the bar magnet.

so basically the particles spin axis always points either toward or away from the externally applied magnetic field. (just so we are clear, there is no classical explanation for this). whereas the axis of a spinning massive object will always point in the same direction or will precess around an axis due to conservation of angular momentum. therefore spin is not due to the actual spin of the massive particle but is simply intrinsic.

anyone know the equation for how fast an electron would have to be spinning to produce its intrinsic magnetic field as a function of its radius r (or rather the radius of its charge cloud)?

 

[0xDEADBEEF]

The electron behaves as if it is spinning, but since it has no witdth that wouldn't make sense, but the electron doesn't care about that. Furthermore when you check how it is spinning you must always specify an axis, and when you measure, it turns out that the electron always spins around exactly that axis either clockwise or anti clockwise.

But you seem to have another concept of reality than me. What it really is, is the manifestation of the little group of the Poincaré symmetry. The physical pictures that many experimentalists resort to, are just sketches with crayons of the beauty of mathematics.

 

[granpa]

the electron may not have any width but its charge cloud does but that is another thread.

Furthermore when you check how it is spinning you must always specify an axis

you mean you must apply an external magnetic field. right?

 

[tiny-tim]

so basically the particles spin axis always points either toward or away from the externally applied magnetic field. (just so we are clear, there is no classical explanation for this). whereas the axis of a spinning massive object will always point in the same direction or will precess around an axis due to conservation of angular momentum. therefore spin is not due to the actual spin of the massive particle but is simply intrinsic.

But surely it's not intrinsic, because it's affected by the external magnetic field?

It's a bit like polarised light …

polarised light has an "real" plane of polarisation (in the sense that the direction of the plane genuinely exists in ordinary space), but when you put it through a filter, it has to choose either "up" or "down" …

put it through another non-parallel filter, and again it suffers re-orientation, and chooses a new "up" or "down" …

doesn't the spin of an electron in a magnetic field behave the same way: it genuinely has a spatial direction, and a spatial angular momentum, and a magnetic field simply changes that genuine direction?

(and the classical analogue would be that a spinning object in, say, a strong wind, would naturally precess its spin until it was aligned either into or against the wind)

 

[granpa]

oh. I guess they do precess. isn't that how mri works?

classically though the spinning electron should try to align with (never against) the externally applied magnetic field. there is no classical explanation for the electrons spin spontaneously aligning against the external magnetic field.

spin is measured in terms of Magnetic_dipole_moment.
http://en.wikipedia.org/wiki/Magnetic_dipole_moment
http://en.wikipedia.org/wiki/Spin_(physics)#Magnetic_moments

the magnetic moment of the electron is:

any electron's magnetic moment is measured to be −9.284764×10^-24 J/T.
T=kg/C*s
J=kgm^2/s^2

where mu_B, is the Bohr Magneton,

and g_s = 2 in Dirac mechanics

the magnetic moment produced by an electric charge moving along a circular path is

if I understand these equations then, just as a spinning mass has angular momentum, a spinning charge has magnetic moment. the angular momentum of a rigid sphere is 2/5 * wmr^2
w=v/r

the charge of the electron is -1.602 × 10^-19 coulombs

tentatively I calculate that if the electrons radius is taken as one angstrom then it must spin at 1% of the speed of light to produce its magnetic moment. and velocity is inversely proportional to the radius. but until someone checks my calculation though I wouldn't put much weight on that.

 

[LennoxLewis]

The electron behaves as if it is spinning, but since it has no witdth that wouldn't make sense

It has no width? Okay, the electron isn't really defined at a fixed position, but rather a probability distribution. However, isn't there a lower limit on the size of it?

It may help if you talk about the experiments involving quantum spin, like the Stern Gerlach experiment. In an older thread here I compared the spin to a tiny bar magnet, see post #7.

Thanks! That post helped a lot. I actually remember that from an atomic physics course i took years ago, but I've forgotten so much...

 

[jtbell]

It has no width? Okay, the electron isn't really defined at a fixed position, but rather a probability distribution. However, isn't there a lower limit on the size of it?

There's an upper limit on the size of the electron. No experiment (as far as I know) has observed a finite electron size, so the precision of our experimental techniques sets an upper limit only. That is, the electron might actually have a finite size, but if it does, it must be smaller than our current techniques can observe.

 

[Naty1]

Wasn't it Feynman who said something like "Nobody understands quantum mechanics"??

The physical meaning of spin is not obvious, any more than is the physical meaning of electric charge or time or mass or energy or gravity...we become accustomed to some physical characteristics more than others likely because of our intuition and senses...and math. As others have posted, we look at the math, make some inferences, draw some conclusions...but ultimately may never know everything...if only because of quantum uncertainty...

Whenever I hear "quantum spin" I think to myself "I don't even understand how rotational inertia can keep a gyroscope steady." How'd the first person get THAT idea?? Of course I accept it, but the fact that a spinning mass is SO different from a stationary one is just incredible...almost beyond belief!

You might consider reading about Bell's Theorem and EPR experiment which offers some quantum insights on spin. But you'll not get a precise answer, either. Spin is somewhat obscured by quantum uncertainty. Spin entanglement has it's own set of puzzles.

Brian Greene has a decent discussion regarding spin in FABRIC OF THE COSMOS beginning page 104...Here are a few excerpts:

particles...can spin only clockwise or anticlockwise at one never changing rate...a particles spin axis can change but its rate of spin cannot slow down or speed up...(Bell discovered) even if you can't determine the spin of a particle about more than one axis...if it has a definitie spin about all axis, then there are estable,observable consequences ...according to quantum theory (a particle) cannot have a definite spin... about more than one axis...Bell found something that escaped...all the other giants of...theoretical physics...the mere existence of certain things...even if beyond explicit measurement or determination...makes a difference that can be checked experimentally.

 

[PhilDSP]

It may be worth going back to the source of the idea of spin for an electron. If I remember correctly Dirac stated that "spin" is the characteristic that the angular momentum is not dependent on the radius.

From spinor analysis we know that an object that "spins" according to the Dirac equation, or any other place where spinors are employed, must rotate 720 degrees to return to its original angular position.

One possible explanation is that the space inside an electron is spinning also, assuming that an electron does have spatial distribution.

 

[0xDEADBEEF]

...
you mean you must apply an external magnetic field. right?

That's a good way to measure spin, and that's a way to fix the axis physically. I was still in the realm of mathematics though, mathematically we can never check where the spin points in three dimensions, any measurement we can possibly do will only yield up or down on a given axis.

 

[LennoxLewis]

There's an upper limit on the size of the electron. No experiment (as far as I know) has observed a finite electron size, so the precision of our experimental techniques sets an upper limit only. That is, the electron might actually have a finite size, but if it does, it must be smaller than our current techniques can observe.

Yes, i meant upper of course. But the electron most definitely has a mass, so that means it has a finite size.

 

[daschaich]

... But the electron most definitely has a mass, so that means it has a finite size.

I wouldn't be so quick to make that leap. While classically the thought of a singular mass distribution is "intuitively unphysical", classical intuition is not necessarily the most reliable guide to approaching quantum physics. In the Standard Model, for instance, the electron's mass arises from its interaction with the Higgs field, not from a finite size -- it is assumed to be a point particle. But that's getting a little far afield from the thread topic, so suffice it to say that an upper bound is all we have.

 

[granpa]

That's a good way to measure spin, and that's a way to fix the axis physically. I was still in the realm of mathematics though, mathematically we can never check where the spin points in three dimensions, any measurement we can possibly do will only yield up or down on a given axis.

or it can precess around that axis, giving off radio waves. right? isn't that how mri works?

 

[dlgoff]

or it can precess around that axis, giving off radio waves. right? isn't that how mri works?

NMR studies magnetic nuclei by aligning them with an applied constant magnetic field and perturbing this alignment using an alternating magnetic field, those fields being orthogonal.

http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance"

 

[granpa]

from the article above:

NMR resonant frequencies for a particular substance are directly proportional to the strength of the applied magnetic field, in accordance with the equation for the Larmor precession frequency.

The precessing nuclei can also fall out of alignment with each other (returning the net magnetization vector to a nonprecessing field) and stop producing a signal. This is called T2 relaxation.

from http://fas.sfu.ca/~stella/papers/blairthesis/main/node11.html

When a human body is placed in a large magnetic field, many of the free hydrogen nuclei align themselves with the direction of the magnetic field. The nuclei precess about the magnetic field direction like gyroscopes. This behavior is termed Larmor precession.

 

[ZapperZ]

or it can precess around that axis, giving off radio waves. right? isn't that how mri works?

Actually, this isn't quite right.

When an external magnetic field is applied and you have a steady state condition, i.e. each of the nuclear spins are now precessing about the direction of the magnetic field, I believe you do not get any RF being emitted. This is because the NET magnetization of the bulk is actually static in a particular direction. The net magnetization is the sum of the average projection of all the individual spins, which averages to be along the external field and static.

However, when the external field is turned off, or when a 90-degree field is applied, the net magnetization changes. This is where it will emit RF signal and can be detected by a pick-up coil.

Quantum mechanically, if you have a spin 1/2 nucleus (such as H), then in the applied field, the degeneracy of the 2 spin states is removed and you have 2 split state for spin + 1/2 and -1/2. At equilibrium, you have an average static number populating each state, depending on temperature and the strength of the external field. The energy gap between the two states corresponds to hf, where "f" is the Larmor frequency. It is only when the external field is turned off, or when another field causes a change in population, will there be a transition between the two states. In the case that the field is turned off, then the overpopulated higher energy states will decay, thus emitting RF signal.

Zz.

 

[granpa]

Actually, this isn't quite right.

When an external magnetic field is applied and you have a steady state condition, i.e. each of the nuclear spins are now precessing about the direction of the magnetic field, I believe you do not get any RF being emitted. This is because the NET magnetization of the bulk is actually static in a particular direction. The net magnetization is the sum of the average projection of all the individual spins, which averages to be along the external field and static.

my 2nd quote in post 28 talked about that.
furthermore you just seem to be nitpicking. this really has nothing to do with what I was saying. I was just pointing out that the particle really does (more or less) behave as if it were a spinning charge (whether it really is or not) and that the spin axis doesn't necessary have to point directly toward or directly against an externally applied magnetic field at all times. if so then it couldn't precess.

Quantum mechanically, if you have a spin 1/2 nucleus (such as H), then in the applied field, the degeneracy of the 2 spin states is removed and you have 2 split state for spin + 1/2 and -1/2.
Zz.

this basically just means that some of the particles align with the external field (as one would expect classically) and strangely some align against the external field. when it is said that the spin is always either up or down that doesn't mean that it always points directly up or direcly down relative to the externally applied magnetic field. if it did then it couldn't precess. rather it means that it either tries to align with the externally applied magnetic field (as one would expect classically) or (for some strange reason) it tries to align against the externally applied magnetic field.

so sometimes the particle does exactly what a spinning charge would do and sometimes it does exactly the opposite.