Particles of Matter Have No Center

I start today’s post with a rather curious claim. Today I realized that a particle of matter cannot have a true center. This might seem a silly thing to say, as I’ve been showing equations of the saint Hannes knot and have shown this Excel plot of it:

The equations seem to be twisting around a sphere with a radius of R:

Surely this must mean that the center of this sphere is the center of the saint Hannes knot?

For a long time, I though this to be the case. However, this led to a very peculiar puzzle. If the dots revolve around the center of the particle does this mean that the distance of the dot from the center varies? In the above 2D plot this isn’t very clear, but in a rotating 3D model it becomes apparent that the dots cannot all be at an equal distance from the center.

This would mean that the speed of the dots would need to vary. I really tried to handwave this problem away, but to no avail. Only today it hit me. If in light dots refract around a center point that moves in a straight line, in matter the dots refract around a center point that is similarly knotted (or folded) as the orbital.

Below you see the illustration of the saint Hannes knot, with the moving point of refraction depicted as an identical green knot: 

While to the lay person, this moving point of refraction seems to offer no new insight, one would need to draw a line from the central knot to the each of the dots. If the shape of the central knot is correct (I’m not 100 % sure whether it is), the distance from the dot to its mirror image in the central knot is always R.

With this realization, the linear speed of each dot is c cos √5θ and the refractive speed is c sin √5θ, regardless of at what point of the saint Hannes knot the dot might find itself.

As is so often the case, I think I made a surprisingly important discovery today, even though I sort of thought there would be no big discoveries left. At least big discoveries that could be easily found by simple thought experiments.

This realization should help me write a much clearer Theory of Everything -manuscript.