Circular Reflection

In today’s post in my quest to understand the Theory of Everything by the reflection of elementary particles of energy (dots), I might have finally solved the way reflection along two axes works. And the solution is much simpler than I could have thought. In recent posts, such as the “Future Particle”, my hypothesis was that the dots of neighboring helices bounce off each other, switching the handedness of the two helices with each reflection.

While this hypothesis seemed rather good, I couldn’t progress forward with it. I thought that going back to basics would help and realized that you can explain tilting of a plane, if instead of the plain being infinite, it is rather a small circle.

However, this realization didn’t lead me to the direction I originally thought. Rather, it brought me back over a year, to the point where I considered that the location of moving dots could be explained with a jagged shape, where half of the dot-dot connections would be with the neighboring dot and half with the dot either behind or in front:

So, why did I forget the above shape for over a year? The problem is that without a second axis of reflection, the dots would need to move a longer distance the farther from the center they are to maintain the same angular velocity.

So, what do we need? The dots need to revolve around two centers, where the revolution is a sum of two orthogonal vectors of reflection. The vector that is responsible for the revolution around the main axis, with an average distance of R, always points to the center. The second vector must be orthogonal to the vector of non-reflected motion and the reflection towards the center. If you’ve read enough of my posts, I assume the radius of this second reflection to be √(2+√2) times the radius of a dot. You’ll have to search for older posts to learn why. The second reflection vector must be non-zero, even when the dot is at the farthest point from the center of the particle of matter. However, the second reflection vector must increase in size the closer to the center the dot is. That’s because the distance traveled by a dot from one point of reflection to the next must be identical. I’m sure the mathematics for this isn’t too difficult, but it’s too late for me to figure it out (without major errors, that is).

So, how are the dots connected to each other in this shape rotating around a spot in the center? While the above simplification ignores the second radius of reflection altogether, which flattens the image, the video below isn’t too far off the mark:

It’ll take some time for me to figure out the details, but this shape looks extremely promising. While I might be wrong, there’s a chance that I just might be able to figure out the proper mathematics of reflection of this shape within a week or two.

Or then again, this might be a dead end, and I might need to get back to the drawing board once again…