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In the paper What is spin?, Am. J. Phys. 54 (1986) 500, by Hans C. Ohanian, spin is described as a circulating flow of energy in the wave-field of a particle. Is this the generally agreed upon explanation of intrinsic angular momentum or just a fringe theory?

(A similar thread exists on Reddit, but I couldn't find a satisfactory discussion there.)

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    $\begingroup$ I must admit this is very weird, for me. When I studied this subject I was taugh that spin (and helicity) is just a degree of freedom that appeared in quantising a particular irreducible representation of the Lorentz group. That's a very good question. $\endgroup$
    – QuantumBrick
    Commented Oct 9, 2016 at 18:58
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    $\begingroup$ I've never heard anyone criticize the paper for incorrectness, but it also only appears as a footnote. None of my texts or instructors spent any time on it. I've never dug in to try to figure our why that should be, but the response feels like people find the result to be difficult to generalize or it is more complicated without making new predictions. It could be perfectly correct, but more difficult than is justified by the value it offers and it would get a response like that. But that is social guess work based on people knowing it is there and not bothering with it. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Oct 9, 2016 at 23:34

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Ohanian's paper shows that spin can be understood as a circulating flow of energy, and is a wave property, valid in both classical and quantum mechanical formulations, rather than inherently and mysteriously "quantum mechanical" in nature. A fine point not needed for calculations that can be ignored by the pragmatic experimental physicist. But to me (and apparently the author) it's comforting to have physical intuition so lacking in much of conventional qm.

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I read the abstract.

The basic reason it is not referred to or used is that main stream physics has elementary particles as point particles in the standard model and any wave nature attributed to the particle is on the probability distribution of its location in space and time.

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.

A point particle can have no circulating flow of energy. So it may be a correct mathematically description but not within the language/model of mainstream particle physics at present.

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  • $\begingroup$ Ohanian derives this flow of energy and charge currents from standard QM does he not? $\endgroup$
    – B T
    Commented Jul 14, 2021 at 4:41
  • $\begingroup$ I have no access, but I doubt he is using QFT of standard model. from the abstract: "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 " . quantum fields in SM carry no angular momentum. $\endgroup$
    – anna v
    Commented Jul 14, 2021 at 5:51
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    $\begingroup$ @annav I'm bothered by the notion of a "particle" with zero dimension. It seems to contradict the perspective of matter as quantized fields. Here's a link: physics.mcmaster.ca/PHYS3MM3/notes/whatisspin.pdf $\endgroup$
    – DWin
    Commented Jul 25, 2021 at 23:38
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    $\begingroup$ It seems you are somewhat arbitrarily picking and choosing which mathematical objects to consider "physical". I'm assuming it's the Dirac function is being considered to imply pointlike reality for electrons, but the planewaves are said to be "just mathematical" and not in need of interpretation. (And I don't understand why fields are not thought to have energy.) $\endgroup$
    – DWin
    Commented Jul 27, 2021 at 0:32
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    $\begingroup$ It is the Feynman diagram + particular QFT that has these assumptions/axioms. Energy is "field+creation and annihilation operators". that involve energy. The field itself is like a coordinate system. $\endgroup$
    – anna v
    Commented Jul 27, 2021 at 3:32
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It answers the question: what does "spinor" have to do with "spin"? How does "spinor" turn into "spin"? Ohanian tells us that, when the spinor is coupled to momentum and mass as in the Dirac equation, then this coupling causes the wave to have an automatic self-rotation characteristic even when we are supposed to have something "sitting still". That self-rotation orbital angular momentum is the spin, and it is the magnetic moment.

Outside of fundamental particle physics, we have the "2D Dirac materials" in which the wave motions happen far slower than the speed of light yet they impart an emergent spin onto the electron. When waves move on a honeycomb lattice, for certain special regions of momentum space we get an effective spinor out of the A and B sublattices, coupled to momentum. When the A and B sublattices differ (as in a layer of MoS$_2$) then this introduces a 'Dirac mass' term. It is often thought that this 2D Dirac equation is merely a fun mathematical analogue without further physical meaning but no: the Dirac equation has no choice but to produce self-rotation in the waves, turning that effective spinor into a real 2D spin with angular momentum and significant magnetic moment. See these refs:

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