Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion?

[jamesfairclear]

Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion?

[swansont]

Any alignment of an angular momentum vector is determined locally (it's with respect to the atom), so yes, the direction would have to change in a rigid body. But most electrons are paired up in multi-electron atoms, and there is nuclear spin to consider as well, so the amount of torque needed to achieve this is going to be quite small compared to what's necessary to rotate the body itself.

We can see that this is the case because we can see it happen with a permanent magnet, which depends on unpaired electrons having a certain orientation within the material. The magnetic field depends on the orientation of the magnet, so if it is rotated, the spin orientation must have changed as well.

 

[jamesfairclear]

  On 12/21/2021 at 2:16 PM, swansont said:

Any alignment of an angular momentum vector is determined locally (it's with respect to the atom), so yes, the direction would have to change in a rigid body. But most electrons are paired up in multi-electron atoms, and there is nuclear spin to consider as well, so the amount of torque needed to achieve this is going to be quite small compared to what's necessary to rotate the body itself.

We can see that this is the case because we can see it happen with a permanent magnet, which depends on unpaired electrons having a certain orientation within the material. The magnetic field depends on the orientation of the magnet, so if it is rotated, the spin orientation must have changed as well.

 

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Would you expect the quantity (the speed) of angular momentum to vary?

[swansont]

  On 12/21/2021 at 3:19 PM, jamesfairclear said:

Would you expect the quantity (the speed) of angular momentum to vary?

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Not for any of the individual particles, since it's quantized.

The only pathway for changing them is flipping the spin of an electron or causing an excitation of an electron to a state with a different orbital angular momentum. I'm not sure how that could happen just by re-orienting a rigid body. There would need to be a corresponding interaction down on the atomic level, and I can't think of a direct connection between the two.

[jamesfairclear]

  On 12/21/2021 at 3:19 PM, jamesfairclear said:

Would you expect the quantity (the speed) of angular momentum to vary?

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Can I then consider the angular momentum of the electron to be an invariant quantity (like c) such that it will be the same value regardless of whether the body is relatively stationary on Earth or moving away from Earth at 0.99c?

[studiot]

  On 12/21/2021 at 4:31 PM, jamesfairclear said:

Can I then consider the angular momentum of the electron to be an invariant quantity (like c) such that it will be the same value regardless of whether the body is relatively stationary on Earth or moving away from Earth at 0.99c?

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Note swansont's  first response, I have emboldened the relevant part

  On 12/21/2021 at 2:16 PM, swansont said:

Any alignment of an angular momentum vector is determined locally (it's with respect to the atom)

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So you are both working in the frame of reference of that individual atom.

If you want to reconsider from another point of view (Earth) you will need to do the transformations.

[exchemist]

  On 12/21/2021 at 4:31 PM, jamesfairclear said:

Can I then consider the angular momentum of the electron to be an invariant quantity (like c) such that it will be the same value regardless of whether the body is relatively stationary on Earth or moving away from Earth at 0.99c?

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The spin angular momentum is an intrinsic property with a fixed value. Orbital angular momentum is not.

I'm not a relativity expert but I would not have thought that linear relative motion would affect the observed angular momentum.  

[swansont]

  On 12/21/2021 at 6:31 PM, exchemist said:

The spin angular momentum is an intrinsic property with a fixed value. Orbital angular momentum is not.

I'm not a relativity expert but I would not have thought that linear relative motion would affect the observed angular momentum.  

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It's all quantized, though, and so a photon being absorbed or emitted changes the angular momentum of an atom by the angular momentum of the photon, which is h-bar.

 

[exchemist]

  On 12/21/2021 at 6:39 PM, swansont said:

It's all quantized, though, and so a photon being absorbed or emitted changes the angular momentum of an atom by the angular momentum of the photon, which is h-bar.

 

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Yep.