## 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?
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 Mentor 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.
 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.

## 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.

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 Quote by 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.
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.

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 Quote by 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 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?
 Blog Entries: 9 Recognitions: Homework Help Science Advisor 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.
 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?

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

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 Quote by LennoxLewis 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.
 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".
 isnt spin the source of the electrons intrinsic magnetic field in the same way that charge is the source of its electric field?
 Blog Entries: 2 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.

http://www.physicsforums.com/showpos...50&postcount=7

 Quote by Edgardo 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...clear/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)?
 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 Poincar้ symmetry. The physical pictures that many experimentalists resort to, are just sketches with crayons of the beauty of mathematics.

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?

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 Quote by granpa 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)

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