In my last post I talked about the drawing of a spacetime tetragon to help visualize the movement of elementary particles of energy (dots). In the post I said:
If we just consider a pair of dots in neighboring helices to always have the same distance upon reflections (green cylinder in the video below) and the direction being traveled being the same (depicted in purple arrows in the video), we get a rather interesting tetragon, where the dots begin on one circular plane and are transferred to another circular plane.
After this text I showed a video, where the neighboring dots are separated by empty space. While this idea of a gap between the dots had been against my initial intuition, the existence of such a gap seemed inevitable based on the requirement that the neighboring dots must pass each other at the halfway point, according to the time gap hypothesis.
However, upon closer inspection of the idea of the spacetime tetragon, I realized that the gap is something very different to what I had initially thought. Or better yet, the gap becomes a non-gap, if you bend the cylinder connecting the neighboring dots:
When you do this, you end up with a situation where each dot can indeed be reflected by two neighboring dots at once. While this might not sound like much, it is actually a very significant mathematical realization. I can’t know for sure whether someone else has figured out this before in some other context, but at least for me this is the first time I can really explain reflection of three connected particles. Curiously, this sounds a bit like the three-body problem. According to Wikipedia:
In physics, specifically classical mechanics, the three-body problem involves taking the initial positions and velocities (or momenta) of three point masses that orbit each other in space and calculating their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.
It seems this is a solution of a specific kind of a three-body problem, where you realize that the answer requires the reframing of the question. And if you reframe the question, the question becomes that of the n-body problem. According to Wikipedia:
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.
Here we observe an apparent difference to our case. The above sentence states that celestial objects interact with each other gravitationally. The whole Wikipedia article ignores the energy-mass equivalence, as if gravity wasn’t derived from it. Apparently, this is due to an innocuous sentence in the Wikipedia article:
Physics has two concepts of mass, the gravitational mass and the inertial mass.
And continues:
The gravitational mass is the quantity that determines the strength of the gravitational field generated by an object, as well as the gravitational force acting on the object when it is immersed in a gravitational field produced by other bodies. The inertial mass, on the other hand, quantifies how much an object accelerates if a given force is applied to it. The mass–energy equivalence in special relativity refers to the inertial mass.
This means that the definition of mass is too vague. The only reasonable thing to do is to sever the definition of absolute mass of a dot from the rest mass of particles of matter, which is the sum of the masses of a collection of dots at apparent rest.
Anyhow, this is getting a bit too deep for a simple post. I’ll show you what this reflection structure with a bent connecting cylinder looks from above:
and from the front:
The inevitable reflective rotation of the dots around two axes becomes apparent in the above image. The smaller (vertical) rings with a radius a bit above that of a single dot define the rotation around the large axis, or the average radius of the particle of matter, whereas the larger (horizontal) rings define the rotation around an axis with a radius of √(2+√2)r, where r is the radius of the dot. The latter allows dots to be in in an orbital that apparently intersects itself, when the smaller axes allow the dots at the intersection to be reflected from each other.
And this is what the shape looks like when it’s rotating:
And next, the million-dollar question: “is this the final solution to the Theory of Everything?” If you’ve read any of my posts, you’ll probably know my answer: “possibly, but I need to check the mathematics.” Even though the shape looks perfect, it has to follow the laws of reflection. If I can make dots move at the speed of light along the shape and show that the angles of reflection are correct, then this is both the solution to the Theory of Everything and at least one solution for the n-body problem. If I wasn’t too old, the solution should be enough for the Fields medal. But that would require me to have a solution. And I don’t have it yet…
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