α as angular rigidity of the electron: references?

[Roberto Pavani]

TL;DR

Are there references treating α as a mechanical/geometric property (angular rigidity) of the electron rather than just a coupling constant?

The fine-structure constant α appears whenever the electron resists forced reorientation by an external field:

- Anomalous moment: precession deficit per cycle, $(g-2)/2 = \alpha/(2\pi) + \ldots$
- Zeeman: forcing the spin to align with $B$ costs energy $\Delta E = g,\mu_B,B,m_s$; the factor $g \neq 2$ reflects the same internal structure, but measured as a static energy cost rather than a dynamic precession

- Larmor radiation: power loss when forced to orbit, $P \propto \alpha,\omega^2$

In all cases α quantifies how much the electron "resists" being forced to rotate; operationally, an angular rigidity or stiffness.

Has this interpretation been discussed formally?
I'm looking for references that treat $\alpha$ as a geometric/mechanical property of the electron (rigidity, angular inertia, spin stiffness) rather than purely as a coupling constant.
Classical electron models (Abraham, Lorentz) or more modern approaches (form factors, Berry phase, spin transport) would all be relevant.

 

[pines-demon]

The fine-structure constant α appears whenever the electron resists forced reorientation by an external field:

- Anomalous moment: precession deficit per cycle, $(g-2)/2 = \alpha/(2\pi) + \ldots$
- Zeeman: forcing the spin to align with $B$ costs energy $\Delta E = g,\mu_B,B,m_s$; the factor $g \neq 2$ reflects the same internal structure, but measured as a static energy cost rather than a dynamic precession

- Larmor radiation: power loss when forced to orbit, $P \propto \alpha,\omega^2$

In all cases α quantifies how much the electron "resists" being forced to rotate; operationally, an angular rigidity or stiffness.

Can you provide more specific formulas? I feel that you can shove $\alpha$ anywhere where $e^2$ is found and get any interpretation you want.

For example, Larmor power formula can be written using $\alpha$ but that introduces a $\hbar$ that was not there making it look like if its a quantum formula (it is not). In the case of the Zeeman effect it seems that you need to divide by a factor of $e$ (elementary charge) in order to make it work, what does that imply?

 

[Roberto Pavani]

Sure. More specifically: $\alpha = e^2/(4\pi\varepsilon_0,\hbar c)$ can be rewritten as the ratio of the electron's self-field energy at the Compton scale to its rest energy.

I'm asking whether anyone has formalised this as a mechanical property; a "spin stiffness" or "angular rigidity", rather than just a coupling constant.

For example, in condensed matter there's the concept of spin stiffness $\rho_s$ (energy cost per unit twist of the magnetisation).
Has anyone applied a similar concept to the free electron's spin in QED? Or in classical electron models (Poincaré stresses, Abraham–Lorentz)?

I'm not proposing a new interpretation. I'm asking if this one already exists in the literature.

 

[pines-demon]

I'm not proposing a new interpretation. I'm asking if this one already exists in the literature.

Sure but your original post does not tell me why would that be the case. It is like asking if $e^2$ is related to rotation somehow.

 

[Roberto Pavani]

Sure but your original post does not tell me why would that be the case. It is like asking if $e^2$ is related to rotation somehow.

You're right that $\alpha$ appears everywhere in EM, so the question needs sharper motivation. Here it is:

The Schwinger result $(g-2)/2 = \alpha/(2\pi)$ has a specific physical content: it's the precession deficit per cycle of the spin relative to the orbital motion.
This is operationally identical to how one defines a torsional stiffness in mechanics: the angular lag per cycle of a driven oscillator relative to the driver, normalised by $2\pi$.

In condensed matter, the spin stiffness $\rho_s$ (Hubbard model, Heisenberg model) is defined exactly this way: energy cost per unit twist angle.

My question is whether anyone has written a paper making this analogy explicit for the QED electron, connecting $\alpha/(2\pi)$ to a spin stiffness in the condensed-matter sense.

If no such reference exists in the established literature, that's a useful answer too.

 

[jedishrfu]

Your post seems to be related to your Zenodo papers. I’d like to remind you that these questions are okay as stand-alone questions but not if they bring in your unpublished Zenodo papers. PF rules explicitly state that we only discuss peer-reviewed papers from reputable journals. Sadly, posting on zenodo does not count as either a published paper nor as a reputable journal.

If the discussion does extend into your Zenodo papers then the PF mentors will be forced to delete your relevant threads and give you a personal speculation warning or personal theory site ban.

Please take some time to read our site global guidelines.

 

[Roberto Pavani]

Understood, thanks for the heads-up. To be clear: I have not linked or referenced any personal work in this thread. The question is purely about existing published literature on the analogy between $\alpha$ and spin stiffness. If no such reference exists, that's a perfectly valid answer.

 

[PeterDonis]

The question is purely about existing published literature on the analogy between $\alpha$ and spin stiffness.

What leads you to believe that there is any such analogy in the first place? Evidently you are not aware of any published literature about any such analogy, since you're asking the question. So what is making you ask the question?

 

[arivero]

I think you could benefit of reading "§ 1. Die Keplersche Ellipse in der Relativitatatheorie." as a initiation to alpha,

and then the discussions about how lucky was Sommerfeld having the atom right even when ignoring Spin; it is said that somehow two algebraic issues cancelled out.