I have some numerical findings about electrons that I think are new:

[Whitefoot]

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?

[studiot]

27 minutes ago, Whitefoot said:

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?

Welcome you seem to be observing the rules here and I for one woulf like to view you speculation.

 

However I am puzzled by your introduction since my understanding of the Bohr radius is that it is an orbital radius. The other two, of course, refer to measures of the electron size in interactions.

[Whitefoot]

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

[swansont]

Posting a link is not against the rules, but the rules require that the discussion can take place without clicking on the link.

Can you explain what you mean by the radius being “fit to a toroidal geometry”

“When all values are expressed in base units, half the outer toroidal surface area equals the Boltzmann constant”

How do you get from square meters to J/K? (or, in base units, kg-m^2/sec^2 K)

 

[Whitefoot]

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?

[HawkII]

Quote

I have some numerical findings about electrons that I think are new:

49 minutes ago, swansont said:

Can you explain what you mean by the radius being “fit to a toroidal geometry”

Spoiler

What is the difference between a toroid and a torus?

 

 

 

 

If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid, as in a square toroid.

 

Spoiler

 

 

 

 

 

 

Edited September 23, 2023 by HawkII

[Whitefoot]

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?

[swansont]

58 minutes ago, Whitefoot said:

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

So it’s numerology. You’re tweaking numbers to come up with an answer. 

[Genady]

I don't believe that it is necessary to read 5-page paper before start of a discussion. You could post a paragraph or two, attach a diagram from your paper, show the final result, etc., and then add details as needed depending on how the discussion progresses. 

BTW, you have only one allowed post left for the first day of membership.

[Whitefoot]

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.

[studiot]

32 minutes ago, Whitefoot said:

I use the values of the 3 electron radii to calculate the surface area of a self-intersecting torus.

Having already acknowledged that your 3 electron radii are not all electron radii, I am disappointed you have not made the relevant correction either to your paper or to your postings here.

In fact more "loose wording" has been pointed out by others.

Also I don't know whether your speculation is mathematical or physical ?

In other words can you provide a some physical reasoning as to why an electron might present as a two dimensional surface with less symmetry than a true spherical one.

I worry about this because some behaviour of observed quantum mechanics (in spectroscopy for example) relies on the assumed spherical symmetry of the electron.
That is it has no preferred direction in 3D space.

 

[Whitefoot]

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]

On 9/23/2023 at 5:37 PM, Whitefoot said:

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.

Such fine-tuning is ad hoc. The colloquial term is “fudge-factor”

[Whitefoot]

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.

[swansont]

The CMB temperature is not constant. Were electrons bigger in the past?

[Whitefoot]

29 minutes ago, swansont said:

The CMB temperature is not constant. Were electrons bigger in the past?

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.

 

[swansont]

1 hour ago, Whitefoot said:

The CMB temperature found in the paper is specifically that found due to being measured in the Solar System frame of reference

And measured in the present day. As I said, it’s not a constant. Unrelated to any property of the electron.

Furthermore, any relationship between terms that have units depend on the units chosen. Boltzmann’s constant has a different value if you choose non-SI units. There’s no significance to this. It’s numerology.

 

[Whitefoot]

54 minutes ago, swansont said:

And measured in the present day. As I said, it’s not a constant. Unrelated to any property of the electron.

Furthermore, any relationship between terms that have units depend on the units chosen. Boltzmann’s constant has a different value if you choose non-SI units. There’s no significance to this. It’s numerology.

 

I know I haven't made the connection between units, but the accurate numerical match seems like more than coincidence. The match applies when the Boltzmann constant is expressed in base units of meters, grams and seconds. The electron surface area is expressed in square meters.

From Wikipedia: "Immediately after the Big Bang, the universe was a hot, dense plasma of photons, leptons, and quarks..."   This is not incompatible with the model. Large electrons with toroidal forms dependent on temperature could easily be present in a hot, dense plasma.
 
I'm not assigning numbers to letters of the alphabet and trying to decipher the Mark of the Beast.

[Bufofrog]

5 minutes ago, Whitefoot said:

I know I haven't made the connection between units, but the accurate numerical match seems like more than coincidence. The match applies when the Boltzmann constant is expressed in base units of meters, grams and seconds. The electron surface area is expressed in square meters.

It is absolutely a coincidence.  You are not understanding the comment about units.  If I were to change the units from meters to furlongs and time from seconds to fortnights, then your connection would disappear, but an real connection like pV = NkT would still hold with a unit change.

[Whitefoot]

12 minutes ago, Bufofrog said:

It is absolutely a coincidence.  You are not understanding the comment about units.  If I were to change the units from meters to furlongs and time from seconds to fortnights, then your connection would disappear, but an real connection like pV = NkT would still hold with a unit change.

I am using units consistently in my calculations.     pV = NkT would not hold if the various values were expressed in different units.

[swansont]

32 minutes ago, Whitefoot said:

I know I haven't made the connection between units, but the accurate numerical match seems like more than coincidence. The match applies when the Boltzmann constant is expressed in base units of meters, grams and seconds. The electron surface area is expressed in square meters.

But those units are arbitrary. If you chose imperial units there would be no match. If we chose a different value for the second, or the Kelvin, there would be no match. 

 

32 minutes ago, Whitefoot said:

From Wikipedia: "Immediately after the Big Bang, the universe was a hot, dense plasma of photons, leptons, and quarks..."   This is not incompatible with the model. Large electrons with toroidal forms dependent on temperature could easily be present in a hot, dense plasma.

Atoms formed when the universe was much warmer than it is today.  There’s no evidence they were any different than they are today, but if there was it would be up to you to provide it.

 

32 minutes ago, Whitefoot said:

I'm not assigning numbers to letters of the alphabet and trying to decipher the Mark of the Beast.

No, you’re trying to assign meaning based on accidental similarities of number combinations.

[Whitefoot]

1.  The units aren't arbitrary. I made the proper conversion into base units for the Boltzmann constant. That way the units in my paper are consistent.

2.  From CERN:   "In the first moments after the Big Bang, the universe was extremely hot and dense. As the universe cooled, conditions became just right to give rise to the building blocks of matter – the quarks and electrons.... It took 380,000 years for electrons to be trapped in orbits around nuclei, forming the first atoms."

It may have taken 380,000 years because the electrons were initially in a highly expanded state due to the high temperatures. Since my model is not far enough advanced yet, I can't make any useful numerical arguments related to the early universe.

3.  See nr 1.   The numerical matches seem like a highly improbable accident.

[swansont]

It’s not a matter of consistency and conversion.

The second was originally dependent on earth rotation. The duration, division into 24 hours and the subsequent division by 60, and 60 again, is arbitrary. Similarly for Kelvins, based on water properties and 100 degrees separation between freezing and boiling.

 

 

[Whitefoot]

The units in a calculation have to be consistent to get meaningful results.  Within my calculations, using consistent units makes accidental numerical matches fairly improbable.

 

   I can see no obvious reason why the numerical matches wouldn't hold up with a consistent change of units.

[swansont]

17 minutes ago, Whitefoot said:

The units in a calculation have to be consistent to get meaningful results.  Within my calculations, using consistent units makes accidental numerical matches fairly improbable.

 

Then do a consistent calculation using other units. Try imperial.

Or just use minutes instead of seconds.