Today’s post won’t be long. It’s just a simple observation that you don’t need a separate tightening of a knot that is made of elementary particles of energy moving at the speed of light.
In my last post, I presented an image of a twisted knot, whose ends flare outwards.
This is what I suggested represents a molecular bond. However, I you take the same exact knot, but stretch the ends as tight as possible, you get this shape:
Topologically this is exactly the same structure, even if you assume that the strings continue in a way that the ends meet.
But isn’t this knot extremely loose, as there doesn’t seem to be anything holding it in place? The answer is that for each of the strings, the ‘relaxed’ state, where the strings would be the loosest would be in an orbital that passes through the center of the knot. So, it’s the geometry of the knot itself that prevents it from unraveling. The only way to unravel the knot is to get energy (more string) from outside of the system so that the knot can unravel. This input of energy from outside to unravel knots is the basis of all chemistry and physics.
The curious thing is that I’ve felt quite lazy these past few days, as I haven’t allowed myself just to toil away with equations and exact representations. But I think the reason was that the final problem that I was tackling wasn’t exactly about mathematics, but about something even more fundamental. I was struggling to understand the interaction between quasi-independent particles of matter. That is, everything that I previously done regarding the mathematics of the Theory of everything was about the interactions of particles of energy (dots) within a single particle of matter or light.
So, is this a culmination of the theory? Not exactly. More like reaching a peak on a mountain and realizing that there is an even higher peak looming ahead of you. And who knows whether that peak is the highest one?
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