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

1. Jan 6, 2009

### 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?

2. Jan 6, 2009

### Staff: Mentor

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

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.

3. Jan 6, 2009

### tim_lou

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

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.

Last edited: Jan 6, 2009
4. Jan 6, 2009

### LennoxLewis

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

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.

5. Jan 6, 2009

### Hurkyl

Staff Emeritus
Re: Can anyone explain the physical meaning of "spin" in QM?

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.

6. Jan 6, 2009

### tiny-tim

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 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?​

7. Jan 6, 2009

### malawi_glenn

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

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.

8. Jan 6, 2009

### mn4j

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

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?

9. Jan 6, 2009

### LennoxLewis

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

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

10. Jan 6, 2009

### strangerep

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

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.

11. Jan 6, 2009

### newbee

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

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".

12. Jan 7, 2009

### granpa

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

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

13. Jan 7, 2009

### Edgardo

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

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.

Last edited: Jan 7, 2009
14. Jan 7, 2009

### granpa

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

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

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)?

Last edited: Jan 7, 2009
15. Jan 7, 2009

### 0xDEADBEEF

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

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.

Last edited: Jan 7, 2009
16. Jan 7, 2009

### granpa

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

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

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

17. Jan 7, 2009

### tiny-tim

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)

18. Jan 7, 2009

### granpa

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

oh. I guess they do precess. isnt 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 wouldnt put much weight on that.

Last edited: Jan 7, 2009
19. Jan 7, 2009

### LennoxLewis

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

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?

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... :grumpy:

20. Jan 7, 2009

### Staff: Mentor

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

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.

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