In my last post I presented the equations required to form a knot in a Higgs boson: an elementary particle of matter with no angular momentum that doesn’t form bonds with other Higgs bosons, or with any other particles.
Because the mathematics was just so clear, I decided to start writing a manuscript of the findings and apply this knotting to hydrogen atoms as well. The only difference being that these knots would knot with other knots, forming a large chain of knots.
So, I started writing an abstract for the manuscript but stopped at a point where I was supposed to say that the equations apply to the knotting of hydrogen atoms into molecules.
You see, the concept of one knot being directly applicable to a different situation is easier said than done. I just couldn’t say that the knot applies to the structure of the molecular bond without actually trying to visually check whether it does. So, as always, I went to blender and opened the file “Saint Hannes Knot”. At first, I duplicated the image, moved the duplicate right next the original and twisted the duplicate by 90 degrees around their common axis. And this is what I got:
At first, I was quite elated. This clearly shows that knotting is topologically feasible. However, it became almost instantly obvious that for proper knotting of two hydrogen molecules, I couldn’t push the entangled string together so that they would overlap. This is not how knots work. To make a proper molecular knot, I would have to come up with an equation where the four loops at the intersection twist around each other, forming a knot, but still sustaining the general shape of the hydrogen atom outside of the knot.
And to make matters even more confusing, the topology shown above means that the knotting I envisioned before, cannot be right. I assumed that different loops would form pairs than the above structure indicates. If you look closely at the image of the molecular bonding image of the Theory of Everything -manuscript, you see that bonding loops are parallel to each other. This is especially clear in image f.
However, if we follow the shape of two knots placed next to each other, the loops that bond are at 90-degree angles (orthogonal) to each other:
This might not be a trivial observation. Rather, I think only once I solve the problem of the molecular knot can I say anything meaningful about how the dots move from one atom to another.
So, as I often say, today’s post was just a teaser. Now that I know what the problem to be solved is, the next step is to solve it. The solution might be easy and fast, or conversely it might take weeks or even months. But I’m pretty confident I’ll be able to solve this as well.
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