The Electron is a Möbius Double Donut

In my last post I figured what is the physical phenomenon behind the compactification in the predominant String Theory, the M-theory. In M-theory the strings loop into extra dimensions, because there isn’t space in the regular three space and one time dimension for these loops.

If we do not expect quantum mechanics to apply to the elementary particles, dots, making up these loops, we don’t have to introduce extra dimensions. Rather, quantum mechanics is an emergent property of these loops forming according to classical mechanics of dots moving at a constant speed of light, with only their direction changing.

There is still one problem. Electrons have this odd phenomenon that they have a spin of ½, meaning that they need to spin 720 degrees to complete a full cycle.

But if the electron is a simple donut, like I stated in my previous post, such a simple structure would not have this property. But as I said:

Am I a 100 % sure this is the structure of an electron? Not really. But considering that before I had absolutely no idea of the structure of an electron, this is a good starting point to figure out whether I’ve gone wrong somewhere. It’s always easier to falsify a concrete claim than vague suggestions.

So could an electron be a donut, but not a simple donut? Rather a donut that would need to rotate 720 degrees to get to its initial state. I took the closest cord at hand, a cell phone power cord and started twisting it this way and that and almost immediately I realized that the simplest structure that isn’t a single donut is a double donut (duh!). So, I took the blender file for the simple donut and cut it into semicircles, or more precisely half-tori, and started tweaking with sizes and angles until I came up with the shape below.

Interestingly, this is the tube equivalent of the Möbius strip. Or more precisely, half of this double donut is equivalent to a Möbius strip.

The dots in the loops can be considered equivalent to this Crab, used in the Wikipedia illustration of the moebius strip. This is, after a 360 degree spin, the dots have come roughly to the same spot where they started from, but on the wrong side of the loop. So, we need to add a second loop (and a second 360 degree spin) right next to the first one for the dots (or the crab) to find their way back to where they started.

And how do I know this is what happens? You can call it intuition. Next, I need to figure out whether I can introduce more mathematical rigor to this intuition. I think I can. This seems like a problem that is solvable.