It’s been again quite a while since my last post. This usually means that I’ve been working on challenging mathematical riddle. It’s again about refraction, but this time with geometrical precision.
In this riddle, we begin with the actual refraction, θ, which in matter is very close to, but not exactly, zero. However, to illustrate the phenomenon, we must increase θ to a value that’s large enough to see.
But then there’s the fact that with zero refraction, the angle between three neighboring dots is 60 degrees and not zero degrees, so the angle between three neighboring dots is actually 60 degrees plus the angle of refraction.
But with refraction, θ isn’t the only important angle. You see, refraction also causes a second angle to form, which I call the angle of dot displacement, or φ. This is the angle by which the vertically neighboring dots are displaced, if all three original dots are viewed in the same plane.
Then there is also a third angle of γ, which is kind of hard to explain. This angle is the displacement from the plane where the original three dots were.
Below you see these three angles illustrated in the x-z and y-z projections.
I think I’ve already solved the equations for how φ is derived from θ and how γ is derived from θ and φ. However, I haven’t yet tested whether these values are correct, so I won’t go too deep into the details in this post.
So, this is what I’m going to do next. I will see whether my mathematics add up and whether I’m able to finally come up with the vectors of refraction, which should hopefully allow me to draw the Higgs helix just with vectors the angle of refraction.
If I’m correct, this shape is such, where the angle of refraction begins with a non-zero number, drops to zero at the halfway point, and then climbs back to the same non-zero number as in the beginning.
The only way for me to know whether I’m correct is to come up with the vector equations that produce this helicity. However, if I’m able to produce these equations, I would have to say that the probability of me being wrong anymore about the nature of matter is very low.
However, this post is more like a teaser of a more comprehensive theory that I may or may not be able to formulate. If you don’t understand what the picture with circles, ellipses and lines, with the Greek letters and equations are about, it’s not because you couldn’t understand the concepts. It’s more that I haven’t honed the theory sufficiently to make it understandable to everyone.
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