I haven’t posted anything in almost two weeks, as I’ve been stuck in the accurate vector representation of refraction. The problem is that when you’re dealing with approximations, you can assume a spherical cow. This way you make a model which is close enough and you use it to solve the problem at hand. But if the problem at hand is making an exact model of the universe, you can’t stop with the spherical cow.
Rather, if your model is pretty close, but there’s a small error, you can’t just ignore the error and trod on regardless. This is more or less the problem that I encountered. You see, the mathematical model that I made for the geometry of the helical orbital of dots didn’t properly address the issue of motion.
Granted, there was always a rotational component to the shapes, but never a calculation showing that the dots (elementary particles of energy) would move the exact same length within a given time along the orbital. And if the dots didn’t move the same length, they couldn’t have the same speed. And if they didn’t have the same speed, then there would be no rational basis for the theory. So, I was in a bind.
I’ve just been constantly turning the problem over in my head and drawn projections in PowerPoint and 3 D images in Blender and I just couldn’t figure it out. And then I happened to watch a very short clip where Brian Cox explained what energy is, probably from this program. To paraphrase him, energy is the vector component towards time, or something like that. I think the explanation is a bit hand-waving, as to what energy really is, but the sentence lit a lightbulb in my head. A very indirect lightbulb, but still it made a difference.
If we consider that dots always move in curved trajectories, the curvature must always be the same. This means that if we have an entangled string of dots, the point of refraction must be the point where the dot has no secondary rotational component. Roughly, the deflection from the other end the Higgs helix touching the dot causes it to move tangentially to the average location of the dots. This is quite tricky to explain any more simply, so just bear with me.
So, if refraction causes curvature, what happens to the pair of the dot that is in direct contact with the the other end of the Higgs helix: i.e. the dot that isn’t in direct contact with the the other end the Higgs helix? Well, the linear arc of movement has to be shorter than with the dot in direct contact: otherwise there would be no curvature. But the overall length of the arc of movement has to be equal for both dots. This means, that the direct impact with the other end of the Higgs helix causes a rotational component around its pair. This can be illustrated with the below very simplified image:
In it, I have taken away probably too much information. The green spheres in the center define the location of the dots, whose movement in time we ignore for a while, just to keep things simple. And conversely the red arcs depict the movement of the inner and outer dots, whose spheres I’ve omitted to keep the focus in their trajectories. Except, the inner arcs, with two rotational components aren’t real in the most literal sense. Rather, the only the endpoints and the middle (intersecting with a green cylinder) depict real locations. Otherwise, I should instead draw a bent helix to depict the exact trajectory.
However, splitting the trajectory into two components we observe something curious: the paths of the rotational components of the neighboring dots aren’t at a 180 degree angle, which I’ve mistakenly thought this whole time. Rather, the rotational components are only at a 90 degree angle to each other!
This means that for the above image the outer dot rotates only around the y-axis (defined in Blender), whereas the inner dot revolves around the y axis, as well as the z axis. Except, at the point of contact with the other end of the Higgs helix the components around the y-axis and z-axis cancel each other out. Only at that very spot do the dots move parallel to the z-axis.
The next thing is to draw the projections depicting this and do a whole bunch of calculations to check if this really makes sense.
I could have shown a whole lot of other images that I had been messing around with, but at the moment, none of them seem as relevant. Now I just need to find out whether I’m finally 100 % correct. This might be last key to the final solution. But then again, I think this isn’t the first time I’ve said the same phrase.
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