In my last post where I introduced the difference between a hydrogen atom and a proton being that the hydrogen atom is composed of a double helical pair of strings, whereas a proton is the fusion of the two string, where one turn is removed. This removing of a single turn causes the fused double helices to ‘inflate’ into a sphere.
However, it’s not really ‘inflating’, as one would imagine, as no additional length is introduced to the string. What I currently think happens is that in the beginning, the loss of the turn (i.e. the electron) causes the orbital, previously bent to a collection of circular arcs like this:
to be tightened into a single circle, like this:
This can be described with the double helical sphere equation as:
Where, Amin must be the diameter of the elementary particle (probably Planck length), and G is zero. As I noted before, P is the number of turns in the double helix.
But remember when I said that this ring isn’t stable and inflates? Well actually, while true, in some sense I think it’s the opposite. A ring will probably always expand to a sphere, but when the Hydrogen orbital comprises of circular arcs interconnected at an angle, these arcs cannot expand to a sphere.
And how exactly does the double helical ring expand to a sphere? As the number of turns stays the same, we can make the ring into a sphere by increasing either Amin, or G, or both.
This way the topology, or the number of twist, doesn’t change in the expansion. And what about the length of the string? Roughly speaking, if the diameter of the double helical ring is D, then the length of the string making it up is 2πD. The twisting actually increases this length a bit, but let’s ignore that for now.
And what about the sphere? The diameter of the semi-circular arcs is between Amin and Amin + │2π(P+1)/2│G, with the average diameter being Amin + πPG/2. If Amin is close to Planck length, then the average diameter can be approximated to πPG/2. When the ‘sphere’ has P semi-circular arcs, the length of the string is π²2P²G/2.
And as the lengths should be equal, we get 2πD = π²P²G/2. or D = πP²G/4.
So why does the above sphere look so ugly? Because I used a helix with just 19 turns to make it. Already this, with 19 quasi-circles, should have a diameter roughly 9.5 times smaller than the uninflated double-helical ring.
We can make a very rough estimate for the number of rings in a proton by comparing the sizes of a proton and of a hydrogen molecule. The charge radius of a proton is 0.833 fm, whereas the Van der Waals radius of a hydrogen molecule is 120 pm, or 120 000 fm. If we split this in half, the ratio of a single hydrogen atom is 60 000 fm. So, we get a rough ratio of 72 000. In the above example the number of turns is twice the ratio of radii, or roughly 144 000 turns. This is way above anything I think my computer can handle in Blender. But already with 399 turns we get a sphere like this:
However, take note that the numbers I use now are still ballpark estimates and the equations aren’t accurate yet. This is just to get a sense of the scale.
Also, in the same vein, an electron has a length of ~1/1836 of a proton, if we compare masses. However, I’m not yet sure what this means topologically. There are some grounds to believe that the electron has just as many turns, if not more, than a proton. This is due to the electron being so small, that it is sometimes considered a point particle. Assuming an electron having an equal number of turns to a proton, the radius of an electron would be roughly 0.45 attometers. The Wikipedia page on point particles states that an electron is smaller than an attometers, so this working hypothesis seems to be good enough. It should be noted that the same page says that the expected value for the size of an electron is exactly zero. This means that we can’t say anything more concrete about the size of the electron than it being less than an attometer.
If this is the case, the electron/proton twisting off a supramolecular shell has to follow a mechanism, where two halves of a hydrogen atom begin to twist, but somehow most of the length of the string flows to the proton-side, leaving the electron with a whole lot of twist, but not a lot of length. What all of this means, I’ll have to explore in another post.
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