In today’s post I might have cracked the geometrical conundrum behind the reflection of elementary particles of energy (dots). In my last post, I coined the term “inter-helical reflection”, but when I reread the post I must admit, the post isn’t an easy read. The term was supposed to mean that dots in a helix move in a way that they get reflected by the same helix. Or more specifically, I said “they [dots] are reflected from the dots in front, as well as behind, in the same helix”. This idea relied on the idea that dots would never form a uniform helix but bounce back and forth from the dot behind to the dot in front.
This idea was marvelous. Except for the fact that it didn’t work. That it didn’t work, wasn’t at all obvious. The only way for me to see this was to draw two intertwined helices in Blender and try to visualize the back-and-forth bouncing. Once I’d created the image, it didn’t take too long for me to realize that this sort of bouncing was not possible. I’m not able to explain why easily, so I’ll let you figure that out as an exercise, as they say in mathematics.
However, the back-and-forth bouncing wasn’t a bad idea at all. The problem was that I still didn’t understand what was bouncing from what. In these situations, I find it most helpful to just play around with the 3D models until things start making sense. And here I got my next Eureka moment: what if the handedness of the helix shifts upon each reflection?
So, what would this look like? We can begin with two right-handed helices below:
Then, we can imagine that the path of each of the dots is a left-handed helix, but with extremely low angle of twist. When he dots move half a turn along the above helix, the yellow dots and blue dots trade place and these “future dots” form a left-handed helix, which immediately reflects the dots to a path with a right-handed helix and again with extremely low angle of twist.
The connections are this time marked with green cylinders to indicate that the two original helices are split in two.
When you combine these two helices, you get this funky shape:
I haven’t yet added any curving to this image, to keep it simple. For the same reason, I also haven’t added arrows to show the paths of movement for the dots. However, if I were to show the paths, they would be linear (horizontal) vectors connecting yellow dots to blue dots and vice versa.
If you squint your eyes, you might be able to see that each of the yellow-blue dot pairs (both horizontal and vertical ones) form a sort of a hinge. This should at least in principle mean that when one hinge opens a bit, another can close a bit, negating their overall effects. This way the sum of the two paths: yellow to blue dot plus blue to yellow dot, should always be √8 times the radius of a dot.
I must admit, I haven’t checked whether this is the really the case. If the assumption holds, this is almost certainly the mechanism how dots can at the same time be reflected back and forth and form closed loop toroidal helical orbitals.
So, once again, I might be very close to the final mathematical proof for the theory of everything, or I’ll find a new reason why my idea is wrong. As always, I’m going to be brutally honest with you, whichever option proves to be the truth.
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