# Difference between "Spin" and "Angular Momentum"?

• avito009
In summary: I think that's what you're saying.Yes, the spin of an electron is related to the electrical center of the nucleus.
avito009
I am hesitant to write this post. I am a bit overwhelmed that many members have questions of a higher level. They may be reading scientific journals. My question is very basic. I might be called stupid.

Coming to the question. Is angular momentum same as spin of an electron?. But I read that spin means not that the electrons actually spin.

Spin is one of the identities of a particle, just like rest mass. One can't say two different particles as having equal spin angular momentum quantum numbers, if the spins are different then so are the particles.
Orbital angular momentum is a kinetical quantity of a moving body, it can always be related to the change of spatial degree of freedom.

EDIT: I didn't pay a close attention to your question, I thought you wrote orbital angular momentum. So, spin is an angular momentum, just orbital angular momentum is.

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Spin is the angular momentum of a particle in the frame where the particle is at rest. If the particle is moving, then there are additional contributions to it's angular momentum, namely the orbital angular momentum.

bhobba
If something is actually spinning like for example a top or Earth then it has angular momentum. Anything that spins has angular momentum.

But in case of Electron: “Spin” is the quantum version of angular momentum. Unlike regular angular momentum, spin has nothing to do with actual spinning. I also read that spin is the intrinsic form of angular momentum. How?

avito009 said:
Unlike regular angular momentum, spin has nothing to do with actual spinning.
That's not true in general. For a compound particle, like an atom or a nucleus, the spin, i.e. angular momentum in the rest frame of its center of mass or energy, has contributions from the relative motion of the particles making up the compound particle around each other.
An electron is not a point particle but a quantum field. This makes it harder to say what is actually spinning.

bhobba
avito009 said:
Unlike regular angular momentum, spin has nothing to do with actual spinning. I also read that spin is the intrinsic form of angular momentum. How?

It is quantised angular momentum. If that has anything to do with classical angular momentum is pure semantics of no relevance. What's going on is in the math, and the math is simply the math of classical angular momentum in quantum language.

If you want the technical detail here it is:
http://www.thphys.may.ie/Notes/MP463/MP463_Ch1.pdf

Thanks
Bill

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The Earth spins in its own axis. So this spinning can be called "Spin Angular Momentum". Time taken is 24 hours. The Earth also orbits the Sun and this is called orbital angular momentum of the Earth. Time taken is 365 days. Am I right Drakkith?

avito009 said:
The Earth spins in its own axis. So this spinning can be called "Spin Angular Momentum". Time taken is 24 hours. The Earth also orbits the Sun and this is called orbital angular momentum of the Earth. Time taken is 365 days. Am I right Drakkith?

Yes. And when you take the mathematics describing that and express it in quantum language you get quantum spin. But if that makes it the same as the classical situation is another issue.

In both cases it's linked to invariants related to rotational symmetry:
http://www.physics.usu.edu/torre/6010_Fall_2010/Lectures/04.pdf

Thanks
Bill

bhobba said:
It is quantised angular momentum. If that has anything to do with classical angular momentum is pure semantics of no relevance.

The intrinsic angular momentum ("spin") does contribute to an object's macroscopic angular momentum. See the paragraph preceding this diagram in the Feynman lectures:

http://www.feynmanlectures.caltech.edu/II_37.html#Ch37-F3

bhobba
jtbell said:
The intrinsic angular momentum ("spin") does contribute to an object's macroscopic angular momentum. See the paragraph preceding this diagram in the Feynman lectures:

Good point. Looks like a nice example of Ehrenfest's Theorem.

To the OP - there is an interesting theorem linking classical and quantum properties:
http://www.physics.drexel.edu/~bob/Manuscripts/Ehrenfest.pdf

Thanks
Bill

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avito009 said:
The Earth also orbits the Sun and this is called orbital angular momentum of the Earth.
...and together with the spin of the sun and earth, it makes up the spin of the system sun-earth.
Likewise your (as you are part of the Earth and move around its center once a day) angular momentum contributes to the spin of the earth.

bhobba
Spin is an intrinsic angular momentum of a particle. The name is misleading because the particles aren't actually "spinning" in a classical sense. Really, you should think of it as a property of matter like charge. Electrons have an intrinsic charge, mass, etc. Spin is just another one of these intrinsic properties with units of angular momentum.

I might be mistaken, but wasn't the origin of the spin attribute related to accounting for the electrical center of the nucleus moving around such that the electron was not subject to a pure Columb field, and avoiding considering the electron as a point particle?

bahamagreen said:
I might be mistaken, but wasn't the origin of the spin attribute related to accounting for the electrical center of the nucleus moving around such that the electron was not subject to a pure Columb field, and avoiding considering the electron as a point particle?

Actually its a deep and general result of Quantum Field Theory:
http://www.worldscientific.com/worldscibooks/10.1142/3457

Thanks
Bill

Spin is the intrinsic angular momentum of a particle. It can be seen from the coupling of a spin 1/2 particle to the EM field that a particle has intrinsic angular momentum in the Dirac equation due to Lorentz invariance. Spin 1/2 particles transform under the SU(2)*SU(2) of the Lorentz group. A representation includes the mass and spin of a particle

Spin also shows that a particle can have an intrinsic magnetic dipole moment even if it is not charged (the neutron is spin 1/2).