In my last post I showed that the arcing of the orbital is related to its twisting. More specifically, I showed that a full 360-degree arc translates to a 2 x 180 = 360-degree twist of one half of the elementary particle. Or a 180-degree arc translates to a 2 x 90 =180-degree twist, as seen below.
But what do the 2 x 180 and 2 x 90 calculations mean in this context? As far as the movement of the elementary particles goes, they still aren’t at the starting point after moving 360 degrees in the arc, but in some sense, they don’t have to be, because they are at the starting point of the neighboring elementary particle. This pair of particles behaves in some sense as a single particle. But this property can be relevant in future considerations, but I’m not yet sure how.
And what does this twisting and arcing mean for the bending of the orbital into the complex shape of the hydrogen molecule, as seen below?
What this must mean is that the angles of the connections of the arcs should match at the point of connection. But what else?
I was thinking that something that something has to change at the point where a circular arc with one curvature changes to another. But what can it be, if the only thing to change is the curvature and the twist, which are known to be interconnected? And then two things hit me, pretty much at the same time, so I’m not sure which one was first. The number of turns has to be astronomical where the period of a helix is just a few elementary particles long, which doesn’t fit at all with the concept that in a proton it’s diameter and that of a single turn are the same. This has to mean that the number of turns in a proton would have to be much smaller than in one half of a hydrogen molecule. This would indicate that the number of turns would somehow disappear. But this is a very problematic concept with regards to topology. Unless, you have a reversal of the direction of twist at the point where one circular arc transitions to another!
While this concept is very tricky to explain in an adult way, i.e. in mathematics, it’s dead simple in the kids way. What we have is a balloon animal twist. You begin with a tube-shaped balloon, with no twist. Then you take hold of one bit and twist it, so that the sides on either side are not moving. The two nodes on either sides of the twisted segment have mirror twists, so that when you release the middle node, it will unravel, leaving no twists left.
But in the case of a molecular orbital, we don’t really have very visible nodes. The change from one state to another is just visible in the curvature of the arc. But we don’t have a linear balloon. What we begin with is a circle and ten segments for a hydrogen molecule. Simplified like this:
Except you the segments aren’t of equal size, and you don’t have a circle. The whole concept of the intersection of the hydrogen atoms in a hydrogen molecule is quite tricky and will have to be left for a later date.
Ok, so why don’t we have an equal number of turns? Why is the sum of the lengths of the circular arcs of one curvature different to the sum of the lengths of another curvature? The answer must come from basic geometry. The equations I came up for the hydrogen molecule, back still when I thought they were for the supramolecular shell, show that this is the way you can twist a circle into to spherical orbitals. The sum of lengths of the two sizes of arcs just aren’t equal because the mathematics says they cannot be equal. So, if we have a case, where the these twisted double-helices unravel, they turns will ‘annihilate’ except for the relatively small number of turns that is the difference of the number of turns between the two sizes of arcs.
There are so many other questions that this eureka moment raises that I won’t be able to address them all in this post. But one elephant in the room is the question of how on earth doesn’t orbital immediately unravel into a proton, if there are several points of discontinuity with sudden changes in twist in the orbital? I only have an intuitive answer at the moment. And my intuition says it’s the connection of two halves into a single hydrogen molecule that keeps them so tight that they can’t unravel. But this is way too vague for me to know whether I’m right or wrong.
I think I’ve exhausted my creative juices for today. In my next post I’ll probably start thinking about the connection of the two sides of a hydrogen molecule. That will probably be another key to its fine structure.
I feel like I’m at the very last steps of a marathon, with the finishing line hovering in sight. But I’ve been wrong before. There’s always another even higher peak to climb when you think reached the highest one.
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