Last time I managed to write down the equations for the x-axis and y-axis values for the electron but had to do a bit of lattice trickery to come up with the scheme below.
This was a nice beginning, but next I needed to figure out how would the lattice transformation be translated to the equations.
First of all the equations for x and y would need to be revisited:
But I forgot to include the z coordinates, which are:
The z-coordinates are automatically included in the Blender image, as it’s not drawn exactly from equation, but from bending a helix for 720 degrees.
Next, we need to address the lattice issue. First of all, while the original lattice deformation seemed to produce something reasonable, it wasn’t actually based on anything very concrete. Rather, it was a way to offset the bending helix. However, if one is to actually think about what is happening when one twists a helix for 720 degrees. The original crooked lattice doesn’t make that much sense.
Rather, the lattice would have to be symmetrical. And not symmetrical in just random way, but in a way that the helix closes in on itself on the outside of the formed sphere, once the helix has been bent for 720 degrees. Otherwise, an electron couldn’t really unravel and interact properly. What this lattice deformation means is that it changes the amplitude of the helix as a function of the angle. Thus, I only had to change A from constant to a variable, with the equation:
where Amax is the maximum amplitude, θmax is the maximum angle, when the string has turned the full number of turns, C is the ‘choke factor’, which determines the slope of the decrease of the amplitude an Acorr is a correction factor. As equations go, this is quite ‘ugly’, but does the job.
When I chose the values P = 99, Amax = 100, C = 3 and Acorr = 66 ⅔, I could plot the below projections:
Looking at the above plots, it’s at the same time important to realize that they are very much accurate in their mathematics, but not necessarily descriptive of anything true. That is, none of the constants that I picked are based on any experimental observations or on deeper knowledge on the nature of the electron.
The only thing I can say for sure is that with the above equations I can describe a quasi-spherical shape with a piece of string that does not intersect with itself and where the string can have a thickness. If the string comprises of elementary particles moving at the speed of light, they are free to do so without hindrance from the other elementary particles in the string, apart from them determining the path of movement of the individual elementary particles, or dots.
When I went back to blender and created the lattice to replicate this ‘choking’ of the helix before turning 720 degrees, I got the ‘quasi sphere’ below (with 199 turns in the helix). I have no way of knowing how deep the ‘choking’ goes: whether an electron has helically advancing strings to the very center of the ‘quasi sphere’ or whether the strings are confined closer to the surface. But there seems to be something that’s almost certainly true. The strings cannot form a uniform layer onto the surface of the sphere. The ‘funky’ turning pattern at the poles indicates that even when the turning pattern would continue to the very core of the ‘quasi sphere’, the number of strings in this ‘stack’ can be only 1/π of the number of strings that could be tightly stacked onto the surface of the sphere. Also the 720 degree turn actually means that the surface of the turned cylinder forms more like a sea-shell structure than a conventional spherical surface.
So what can we say about this electron model? As far as I understand, it is consistent with all experimental observations of the electron and doesn’t violate any known laws of nature. And as captain Barbossa said in the Pirates of the Caribbean, the probabilistic nature of the electron is ‘more like a guideline’. Except this is the last stumbling block. Frankly, I don’t really know whether this model explains the probabilistic-looking experimental observations of the quantum world, or whether there lurks an experiment that shows that this proposed model of the electron cannot be true.
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