# Quantum Spin - If It’s Not Spinning, What Is It Doing?

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I read about quantum spin a while ago. If it’s not spinning, what is it doing?

It's evolving according to the Schrodinger equation.

I read about quantum spin a while ago. If it’s not spinning, what is it doing?
Nothing.
The word “spin” is used for historical reasons, but that property of quantum particles has nothing to the normal meaning of the word. It would have been better if we called it “intrinsic angular momentum” from the beginning, but it’s too late now - physicists used the word “spin” a century ago and it has stuck.

vanhees71, Hamiltonian, pinball1970 and 1 other person
An off-topic digression has been removed. If any of the participants in the digression want it continued, let me know.

dextercioby
I read about quantum spin a while ago. If it’s not spinning, what is it doing?
It has angular momentum. Is there any reason that it needs to be doing something with it?

vanhees71
As an analogy (which probably has some flaws) you can try to exchange the following concepts:
spinning <-> movement
angular momentum <-> energy

Then, it is true that when a particle is spinning, it has some angular momentum. Similarly, when a particle moves with some velocity is has some energy associated with that movement.
Now, this doesn't mean that any energy that the particle has is due to its movement, nor all the angular momentum is due to the spinning of the particle.
There is an intrinsic energy that the particle has only because it exists, is not due to any movement, we call it mass.
Similarly, there is an intrinsic angular momentum that the particle has only because it exists, not due to any spinning or anything else. We call it spin.

vanhees71, phinds, A. Neumaier and 2 others
Leonard Susskind: "spin is an abstract mathematical quantity [intrinsic to particles] that transforms like angular momentum under rotation transformations."

vanhees71, Hamiltonian and PeroK
Angular momentum without "spinning" isn't unique to QM. In classical electrodynamics, an electromagnetic field can have angular momentum.

vanhees71 and dextercioby
The analogy given by @Gaussian97 points to spin and (invariant) mass being somewhat analogous.

But one could ask why choose energy and not (linear) momentum as comparison. After all, if there exists an intrinsic angular momentum for a massive particle without an angular movement, couldn't there also be an intrinsic linear momentum for a massive particle without linear movement?

Well, if we talk about the 3-momentum of classical mechanics, the answer is of course no. No linear movement means using the rest frame of the particle as reference for the description and there, the 3-momentum is zero. But even in this frame, the magnitude of the 4-momentum of relativity is equal to the invariant mass of the particle. So in this sense, mass plays the role of an intrinsic linear momentum which strengthens the analogy between spin and mass.

I think it's still a quite shaky analogy but there is a rigorous way in which spin and mass are analogous: both play similar roles in the application of representation theory to spacetime symmetries in QM. It's usually done within the relativistic context but does already work in non-relativistic QM.

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docnet and sysprog
Angular momentum without "spinning" isn't unique to QM. In classical electrodynamics, an electromagnetic field can have angular momentum.

One doesn't even need electrodynamics. Point particle moving uniformly along line can have non-zero angular momentum.

vanhees71 and Dale
Angular momentum without "spinning" isn't unique to QM. In classical electrodynamics, an electromagnetic field can have angular momentum.

There is even no necessity of fields, you can attach an intrinsic angular momentum to a classical point particle.

this question has been raised as well as answered many times before
Indeed it has, so this thread is closed