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.