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An electron is described often enough as a cloud. It has the quantum property called spin, which does not mean actual spinning. Regardless of that property, if it is something with size that occupies volume can this thing rotate? I imagine in a rotating frame of reference it must appear to rotate but I suspect I am wrong about this somehow.

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  • $\begingroup$ chemistry.stackexchange.com/questions/58020/… $\endgroup$
    – bleuofblue
    Apr 5 at 6:46
  • $\begingroup$ An electron is not a 'cloud'. $\endgroup$
    – my2cts
    Apr 5 at 9:12
  • $\begingroup$ Nobody knows if an electron is actually spinning or not: we do not have a model besides a point charge. $\endgroup$
    – my2cts
    Apr 5 at 9:12
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    $\begingroup$ In a rotating frame of reference anything may appear to rotate. $\endgroup$
    – my2cts
    Apr 5 at 9:12

5 Answers 5

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Electrons are quantum mechanical entities, and in the mainframe standard model of particle physics point particles, no dimensions, with the quantum numbers and mass shown in the table.

An electron is described often enough as a cloud.

This statement is wrong, any wave model at the quantum level is a probability wave .

The "cloud" statement is a description of electrons in quantum mechanical bound states about a nucleus, see for example the measured electron positions for a hydrogen atom, they resemble a cloud

enter image description here

but they are its locations, not sequential tracks, but orbitals.

Since no orbits , one cannot set up a system to see if it rotates, although it has the spin rotational quantum number, which can be measured in experiments to have a specific direction, so in that general sense it does rotate.

Spin quantum numbers have been assigned to elementary particles and composites of elementary particles in order to keep angular momentum conservation at the quantum level also, and this is continually validated up to now.

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  • $\begingroup$ "Since no orbits , one cannot set up a system to see if it rotates, although it has the spin rotational quantum number, [...]" really doesn't rock? $\endgroup$
    – Gert
    Apr 5 at 12:05
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In nonrelativistic particle-based QM, spin has to be put in by hand, and makes little sense.

But in quantum field theory, spin is actual spinning of the field. See Hans C. Ohanian, "What is spin?", Am. J. Phys. 54 (6), June 1986, online here. Here's an excerpt from the abstract:

According to the prevailing belief, the spin of the electron [...] is a mysterious internal angular momentum for which no concrete physical picture is available, and for which there is no classical analog. However [...] it can be shown that the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron. [...] Furthermore, a comparison between calculations of angular momentum in the Dirac and electromagnetic fields shows that the spin of the electron is entirely analogous to the angular momentum carried by a classical circularly polarized wave.

So electrons do rotate, more or less.

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    $\begingroup$ So Wolfgang Pauli 'makes little sense'? $\endgroup$
    – my2cts
    Apr 5 at 9:16
  • $\begingroup$ I feel it is rather profound and understated that an electron or probably any fundamental particle cannot rotate. A proton could, I think, since it has structure. I think when we try and collapse the wave function so that it occupies a point it can't be rotating. Rotating implies a radius which implies structure. I don't know if its truly a point but you can't pin it down cause of Heisenberg. The idea that the electron generates an energy flow and that spin is the rotation quantized of that energy flow resonates with me. $\endgroup$ Apr 5 at 18:08
  • $\begingroup$ @my2cts I don't really understand your comment. Obviously I didn't say that Pauli the person doesn't make sense, or anything about him. Ohanian quotes him as saying that spin is essentially quantum-mechanical and can't be understood classically. Ohanian argues he was wrong, and I think Ohanian is right. $\endgroup$
    – benrg
    Apr 5 at 18:14
  • $\begingroup$ I don't really understand your sentence 'In nonrelativistic particle-based QM, spin has to be put in by hand, and makes little sense.' Does it mean that the Pauli hamiltonian makes little sense? It probably also refers to the fact that the Dirac equation predicts g=2 for leptons. For baryons g#2 and again spin must be 'put in by hand'. $\endgroup$
    – my2cts
    Apr 6 at 6:52
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Electrons in QM don't have a determined volume. They are considered as waves. When you measure the position of it, you find a point where the wave collapses. Then, your electron becomes a point, which has no volume. So, usually, when the wave has not collapsed, it doesn't make sense to describe a volume as we don't know the position (it could be at every point of space). As you can not define a volume, it makes no sense to talk about rotation as it needs an axis and a certain volume. A point can not rotate physically.

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A electron has no known inner structure so it's a point as far as we're concerned. A rotation of a point couldn't be observed so a point can't rotate.

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It is a misconception to think an electron is physically some sort of cloud. Indeed, the probability density for measuring it at some point in spacetime is not a point, but that is not something material, but only mathematical formalism.

Thus, asking if the cloud can rotate is like asking if a Gaussian or a sine function can rotate.

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