In my last post I said I had the correct equations for the refracting of vector representation of elementary particles of energy. So, the only thing I had left was to place the values from my equations of the vector representation of no refraction.
Well, that is what I did. I won’t bore you too much with the details of what needed to be done. In short, it involved the X-Y projection of the refraction image, as seen below.
With a couple of extra steps, I was able to just take the equations that produce accurate no-refraction plot, like this:
And introduce the angle of refraction (φ) to get a twist, like this:
Here, I made the φ small enough (0.27°), so that with about 1400 vectors, I got a 180° twist to the entangled vectors. Had φ been larger, there would have been a higher twist and with a smaller φ the twist would have been smaller.
The above shape in X-Y projection is obtained when the first vector is along the z-axis. When viewed in the X-Z projection, the twisted entangled vectors have a tilt around the y-axis.
And when viewed in the Y-Z, projection, a very peculiar shape is observed:
The above shape is obtained with a twist of 180°. But we see that part of the shape is already duplicated. With a twist of 90° we observe the simplest element:
However, we also see that there are partial arcs as well, both in the figure with 90° and 180° twists. Only with a twist of 360°, or a full circle, the arc beginning at x = 0, y = -0.5 returns back to y = 0.5:
There’s so much going on in the above picture, that I’ll highlight the arc for you:
This looks great! However, there is still an unanswered question: we can clearly see the twisting around the common axis, with a curvature of r. However, in the above image, we don’t really see the secondary curvature.
I think the secondary curvature is only visible when the number of vectors is extremely high and φ is extremely small. I think the solution must be in the arcs you observe in the above image. While in the 2D-projections, the arcs seem two-dimensional, they are of course three-dimensional in reality. I have an intuition that when φ gets extremely small, something curious happens.
The 90° arcs you see in the 90° twist image, fuse into near-circular helices and you get the Higg’s helix:
Currently this is still a hypothesis. I have no evidence to back this intuition. However, I have a good feeling that I’ll be able to prove this pretty soon.
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