Tetracone of Reflection

It’s been five days since my last post on the Opposite Arrows of Spacetime. Since then I’ve tried to figure out how to use what I have learned to apply to the concept of the Reflection K. But not for the first time, my quest to describe the Theory of Everything through reflections of elementary particles of energy (dots) is progressing slowly.

However, I think I’ve found a new mathematical tool for this quest. I call this tool the tetracone of reflection. It’s actually not exactly a logical next step in my latest discoveries, but a parallel discovery. I might not be able to explain the concept simply enough, but I’ll give it a try.

Each reflection consists of two dots approaching each other at an angle. I think I haven’t mentioned this angle, so I’ll give it a new Greek letter: this time ε, or epsilon. The length of the path of both dots needs to be equal. I’ll name this length A for simplicity. As the two dots approach each other at an angle of ε, the parallel component of this path is B = A cos ε. Similarly, the reflected component of the path is C = A sin ε.

Based on simplified logic, I thought that these values were enough, and I would get a cone of reflection from these values. But, looking at my Blender image of the reflections, I realized that there isn’t just one cone in this image. There is also a much smaller cone of reflection, where the height of the cone is D = A(1-cos ε). You get a couple of other lengths from the figure, but for now the values from A to D are sufficient. 

But the above image is just a triangle, not two cones, you might say. The problem comes from fitting this triangle to the 3D model of reflection. I don’t know at the moment how the triangle is placed at the moment to the model, so I need to know all of the options. And these options can be illustrated by rotating the above triangle around its vertical axis. This shape made of two cones of different sizes, but where the sum height of both cones is equal to the height of the slant of the bigger cone. While a bicone is a similar, it is comprised of two cones of equal height, so it’s not the same. I could call this rotated shape a dicone, because the term exists, but is not commonly used.

However, the dicone of reflection doesn’t describe reflection very well as the are no vectors for before and after the reflection. What is required is to mirror the shape to form a tetracone. In the rotating 3D image below one can clearly see the formation of the reflection K.

How this fits with the rest of the theory remains to be seen. But considering that any model that doesn’t include this shape must be incomplete, might also mean that with this shape included, I might finally be able to complete my model.

We’ll see soon enough…