I began to write today’s post without knowing exactly where I’m heading. My aim was to multiply the image from my last post about the bending of spacetime, with the aim of hopefully solving the n-body problem. If I succeed, this will possibly open a new field of mathematics and possibly worthy of an Abel prize. However, there’s no Abel prize awarded for an interesting idea. I really would need to prove this mathematically to be eligible. So, for now it’s still a dream, but not a distant dream. At the end of the post I did find a solution, but what I’ve written below has not been edited to make it seem that I knew what the solution was when I started…
The next problem I need to solve in understanding the nature of reflections of elementary particles of energy (dots), is how do spacetime tetragons connect. For a while after writing my last post, I thought that the only thing that I needed was to copy-paste one tetragon after another, after shifting their place by √8 times the radius of a dot. This idea was somewhat doable, but I ended up needing to arrange the dots in the shape and the arrows connecting the dots. Or more specifically, I could only copy one such shape after the other, if I actually changed the shape altogether. And this just didn’t seem right.
But after pondering the problem for a while, I realized that shifting the shape by √8 times the radius of a dot towards the direction of the movement of the dots wasn’t enough. Because in reflection, a component of the movement of the dots is reversed. This means that besides shifting, the shape also must be rotated by 180 degrees along the axis of the common movement of the dots. Like this:
And this is what the shape looks like when rotated:
So is this it? Is this the solution to the Theory of Everything and the n-body problem? It is beginning to look inevitable. In my last post I said possibly. This time I say probably. I can’t say definitely, until I’ve verified the hypothesis by mathematics. However, there really isn’t any reason why this wouldn’t be it.
The trickier question is, how long will it take for me to verify the hypothesis. It will either be very fast, or I might hit another speedbump on the way. The biggest unanswered question is whether the angles of reflection in this shape make sense. I haven’t addressed this problem in any of my posts yet.
I think I’ll leave today’s post as a teaser. I won’t necessarily address the problem of the angles in my next post, as there are still plenty of other unresolved questions left. What I would like to be able to do would be to draw the above structure in all three projections (x-y, x-z and y-z), with proper space and spacetime vectors. This should produce a lot more mathematical rigor to the theory, which is still rather intuitive and messy…
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