http://geocalc.clas.asu.edu/pdf/SpacetimePhysics.pdf by David Hestenes shows geometric algebra applied to the celebrated Dirac relativistic wave equation. To me the interesting the thing is that Hestenes shows that the common belief that spin emerges from relativity is not correct. I don't claim to understand it, but he seems to be saying that spin is an observed fact built into the equation. It doesn't emerge from anything, it was introduced in a subtle way that was overlooked until now. While Hestenes frames no hypothesis he seems to imply that the electron could actually be rotating. Wolfgang Pauli believed this to be impossible because the surface of the electron would then be moving faster than the speed of light. But if the radius of the electron is small enough then this isn't the case, is it? And if it has extent into non-obvious smaller dimensions then the electron can be much more compact. If the basic unit of the dimensions is very small such as perhaps the Plank length, the electron could have a very small yet positive radius while having a surprisingly large surface area, this presumably being connected to the wavelength, which is certainly much longer than the radius.

Scattering experiments have shown that the radius is very small. I have the impression that physicists on the whole have given up and declared the electron to be a point particle with zero radius, then used dodgy math to get rid of the resulting infinities. One of the goals of string theory is to get rid of these.

It is certain that quantum spin is orientable, so it occurs in an even dimensional space. This rotation can't include time, because such a rotation would be hyperbolic. Hestenes simply declares a bivector of spin. Actually since the size of the bivector is a constant this is a one dimensional space embedded in a 2D space, but such a 1D space is orientable so it doesn't matter.

Hestenes is partial toward the zwitterbewegung interpretation, in which on very small scales the electron has a random component to its movement.