Whitefoot

I don't have an answer to your question. I haven't yet been able to do more with this than what is in the paper. The CMB temperature found in the paper is specifically that found due to being measured in the Solar System frame of reference. It seems conceivable that the toroidal orbit as modeled here may change size in different reference frames, or at different temperatures. Since there is not yet a known size or physical picture of electrons, this is not at odds with known science.

Since the Cosmic Microwave Background radiation permeates the universe, I don't think it's unreasonable that the Boltzmann constant might be connected with a surface area associated with electrons. The need to fine-tune to get a very accurate match may only mean that there is more involved than just a simple area calculation, which doesn't seem surprising. Being of a skeptical nature, I won't deny that I could be fooling myself with a fudge-factor. The way numerical matches are falling into place, however, makes me think the fine-tuning is reasonable.

The paper under discussion is attached as a PDF at the fifth post of this thread. The diagram on the first page is a 2D representation of a cross-section of a 3D self-intersecting torus. The intersection is shown large to illustrate how three lengths, analogous to the three electron radii, can be seen as part of the geometry of a self-intersecting torus. The discussion in the paper analyzes this better than I can do by repeating it here. The second diagram in the paper is also a 2D representation of a cross-section of a 3D self-intersecting torus, with a tiny intersection. This is roughly drawn to scale when the three electron radii are used in the torus geometry. The diagrams also show that there are actually two radii that define the torus, and combinations of them make up the electron radii. The Compton radius is more typically called the reduced Compton wavelength, or Compton length. Further on in the paper, calculations of surface area are based on the 3D torus, using base units of meters. Initially, what I call the outer toroidal surface area, is numerically close to twice the Boltzmann constant. This suggested some fine-tuning to see if a better match could be achieved. From here on, the calculations probably make the paper difficult to follow. I arrived at the formulations by trial and error - there is no particular theory involved here. Accurate numerical matches were achieved by using a ratio that led to a temperature equal to the Cosmic Microwave Background temperature. This may seem arbitrary, but associating the CMB temperature with the Boltzmann constant doesn't seem unreasonable. The Inner surface area, the area of the small intersection at the center of the torus, numerically equals ten times the mass of the electron. I consider this to be what I call a numerical artifact. The number must come from related values, but I don't think it can be physically meaningful. Particle mass shouldn't be directly related to area, since particle mass increases at smaller sizes. The exact value was targeted by the fine-tuning, however. As part of the fine-tuning process, a small quantum of roughly 2.035E-19m radius is deduced to be traversing an orbit defined by the torus. I consider that this may possibly be the beginning of a physical model of the electron.

swansont I use the values of the 3 electron radii to calculate the surface area of a self-intersecting torus. Numerically, half of this gives roughly the Boltzmann constant. If you have the PDF I attached, further calculations are used to fine-tune the match in values, leading to a temperature which matches the CMB temperature. I won't deny that these might conceivably be numerical artifacts, but several numbers roughly just fall into place. Do you have the PDF? Can you tell me if there is a better way to post the paper? Genady, It seemed easiest to just have the entire paper available, though having the first page with diagram would have been useful. I don't know how to post this stuff, though, and I still don't know if it was correct to post the PDF as I did a couple posts ago.

My use of the word toroidal may be a bit loose. The geometry of the paper is a self-intersecting circular torus. I just attached a PDF of the paper with diagrams, but I don't know if that is the correct way to post. Can anyone let me know how to post the paper?

It would be difficult to carry on a discussion without having the content of the paper available. How can I attach a PDF? Can it be added to this thread, or would it be a new post? "fit to a toroidal geometry" refers to the 3 radii fitting to a specific geometry, presumably an orbit. Best shown by the diagram in the paper. When the toroidal surface area is found in square meters, half the result is numerically equal to the Boltzmann constant. I don't make any connection to other units. 1-electron-geometry-AW.pdf I just attached a PDF. I don't know if this was done correctly. Can anyone inform me how this should be done?

You're right about the Bohr radius - my statement is a bit sloppy.

There are three radii associated with the electron: The Bohr radius, Compton radius and Classical radius. These radii have never been associated with any physical electron geometry. They can actually be fit to a toroidal geometry, in a way not presented in other speculative toroidal electron models. When all values are expressed in base units, half the outer toroidal surface area equals the Boltzmann constant. Things are never that simple of course, leading to a paper that is 5 pages, PDF format. The paper is publicly available at Zenodo and has not been published or peer reviewed. Some currently unrecognized numerical findings about electrons are presented. There is no attempt to disprove any existing science. May I post a link to Zenodo? (I know that is against the rules.) Or can I reasonably paste a 5 page PDF into a post?