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

[Whitefoot]

15 minutes ago, swansont said:

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

Or just use minutes instead of seconds.

That probably won't happen today.  I can see that a change from seconds to minutes obviously changes the value of the Boltzmann constant.  I think that base units of seconds are more consistent with the way these units and values have developed.

[Bufofrog]

2 hours ago, Whitefoot said:

pV = NkT would not hold if the various values were expressed in different units.

If I replace metric units with imperial I will still get the correct answers from this equation.  That is not true for the relationship you described.  Your relationship is a coincidence that is based on arbitrary units.

[Genady]

Excuse me for quoting myself, but in SI units the ratio between the Newton's gravitational constant and the Planck's constant is: 

On 2/23/2023 at 8:34 AM, Genady said:

G/h = 10^{number of Crocodilian species}

[swansont]

3 hours ago, Whitefoot said:

pV = NkT would not hold if the various values were expressed in different units.

Sure it would, as long as the proper units and values were used in conversion

[studiot]

Looking back over the years SF averages at least one thread per year about concidence/numerology in maths

http://blogs.scienceforums.net/ajb/2011/10/17/number-theory-and-numerology/

 

http://blogs.scienceforums.net/ajb/2011/10/17/number-theory-and-numerology/

 

 

and many more.

 

The answer has never wavered.

[Whitefoot]

19 minutes ago, swansont said:

Sure it would, as long as the proper units and values were used in conversion

I expressed myself wrong. I meant to say inconsistent units.

I am looking at a recalculation based on minutes, but this is not straight forward since time units enter into the Boltzmann constant, the Planck constant and the mass of the electron.

And apparently the kelvin. Since 2019 the kelvin definition has been based on the energy equivalent as given by Boltzmann's equation. From Wikipedia.

[swansont]

1 hour ago, Whitefoot said:

I expressed myself wrong. I meant to say inconsistent units.

I am looking at a recalculation based on minutes, but this is not straight forward since time units enter into the Boltzmann constant, the Planck constant and the mass of the electron.

It’s a factor of 60 if you express k in terms of minutes.

h and m don’t enter into it, since the change would cancel (time doesn’t appear in the result where these appear)

1 hour ago, Whitefoot said:

And apparently the kelvin. Since 2019 the kelvin definition has been based on the energy equivalent as given by Boltzmann's equation. From Wikipedia.

The redefinition didn’t change the values of any of the units.

 

The bottom line is that if you have units, your answer depends on what units you use. There’s no fundamental insight in such cases.

[Whitefoot]

19 minutes ago, swansont said:

The redefinition didn’t change the values of any of the units.

The redefinition bases the constant on an energy equivalent - introducing a dependence on time units, I think.

I've almost come around to agreeing that the numerical match won't hold up with a change of units.  But I'm going to try some calculations with factors of 60 to see what happens.

I'm referring to the redefinition of the kelvin.

39 minutes ago, swansont said:

h and m don’t enter into it, since the change would cancel (time doesn’t appear in the result where these appear)

I've already seen this since they define the size of the Compton radius, which supports your argument that the numerical match won't hold up.  I plan to do more calculating anyway and see what results.

[swansont]

14 minutes ago, Whitefoot said:

The redefinition bases the constant on an energy equivalent - introducing a dependence on time units, I think.

I've almost come around to agreeing that the numerical match won't hold up with a change of units.  But I'm going to try some calculations with factors of 60 to see what happens.

I'm referring to the redefinition of the kelvin.

The redefinition based units on defined constants rather than physical artifacts. A change of 1 degree was and is a difference in energy, it’s just that it used to be based on the temperature of water. 

[Whitefoot]

6 minutes ago, swansont said:

The redefinition based units on defined constants rather than physical artifacts. A change of 1 degree was and is a difference in energy, it’s just that it used to be based on the temperature of water. 

From another Wikipedia page:  The magnitude of the kelvin was redefined in 2019 in relation to the physical property underlying thermodynamic temperature: the kinetic energy of atomic free particle motion. The redefinition fixed the Boltzmann constant at precisely 1.380649×10⁻²³ joules per kelvin (J/K).

This suggests that there might be a dependence on time units for the kelvin.  Since the Boltzmann constant is now fixed, maybe it has no influence from time units.

I'm going to be trying calculations with or without a factor of 60 in various places and see what happens.

Thanks for the discussion - this gives me a new aspect to look at in the model.

[Bufofrog]

40 minutes ago, Whitefoot said:

Thanks for the discussion - this gives me a new aspect to look at in the model.

You are completely ignoring everybody's input.

[Whitefoot]

I've been paying attention to swansont's input - he's giving me something I can work with.  I'm not ready to just accept someone telling me it's a hopeless cause.

[Bufofrog]

7 minutes ago, Whitefoot said:

I've been paying attention to swansont's input

Are you though?

1 hour ago, swansont said:

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

 

[Whitefoot]

I have followed the arguments that a change of units will negate the numerical matches I'm finding.  swansont has given me some ideas I can use to take a closer look at my model.  In order to test it for a change of units, I have to know how the various constants depend on a change of units.  His comments have steered me mainly to Wikipedia to learn more about the physical constants, and now I have something to actually work with.

20 minutes ago, Bufofrog said:

You’re tweaking numbers to come up with an answer. 

The use of math for numerical evaluation is integral to science.

[studiot]

Coincidences occur both in calculations involving units as well as numbers and calculations involving only numbers.

 

14 hours ago, swansont said:

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

 

For instance If I buy rope as 1 shilling a foot the units are 1 per 1.

By a strange coincidence that is also 1 penny per inch  :  again 1 per 1.

 

Or think about area; an area 3 feet by 3 feet makes 9 square feet or 1 square yard  -   not a coincidence and also not very useful to measure electron areas

 

How about working in Barns ?

Quote

https://en.wikipedia.org/wiki/Barn_(unit)

barn (symbol: b) is a metric unit of area equal to 10⁻²⁸ m² (100 fm²). Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is also used in all fields of high-energy physics to express the cross sections of any scattering process, and is best understood as a measure of the probability of interaction between small particles. A barn is approximately the cross-sectional area of a uranium nucleus. The barn is also the unit of area used in nuclear quadrupole resonance and nuclear magnetic resonance to quantify the interaction of a nucleus with an electric field gradient. While the barn never was an SI unit, the SI standards body acknowledged it in the 8th SI Brochure (superseded in 2019) due to its use in particle physics.^[1]

 

Of course we can do without units

2³  is approximately equal to 3².

or better

3² + 4²  =  5²

and the net abounds with other coincidences

 

By the way I am still waiting for a response this my question.

 

On 9/23/2023 at 11:22 PM, studiot said:

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.

I originally had some trouble downloading your 5-page paper, but I have now managed to do this.

But if you will not read a 5- line reply from me, why should I read a 5-page paper from you ?

Can you point me to the page and paragraph that contains the answer to my question ?

Edited September 26, 2023 by studiot

[Whitefoot]

16 hours ago, swansont said:

Or just use minutes instead of seconds.

From swansont's suggestions, and some recalculations, I now agree that a change of units invalidates the numerical matches.  The recalculations suggest I'm not likely to fix the problem very soon. 

Thanks everybody for the feedback.

 

 

1 hour ago, studiot said:

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 addressed this in a previous post:

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.

[studiot]

56 minutes ago, Whitefoot said:

From swansont's suggestions, and some recalculations, I now agree that a change of units invalidates the numerical matches.  The recalculations suggest I'm not likely to fix the problem very soon. 

Thanks everybody for the feedback.

 

 

I addressed this in a previous post:

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.

 

I saw this alleged response the first time and understood your description.

Then I couldn't see how this addresses my query about symmetry and I still can't detect any refernce to symmetry in your reply.

Am I being thick or what ?

[Whitefoot]

1 hour ago, Whitefoot said:

a two dimensional surface with less symmetry than a true spherical one.

I assumed that pointing out the diagram was a representation of a 3D object answered the question.  As to the symmetry of a torus versus a sphere, I don't know if this affects the validity of the model or not.

[Whitefoot]

I'm posting here the diagrams that I neglected to post earlier (essentially the first two pages of my paper).  I think the proposed electron geometry may be of interest, despite my further calculations looking flawed.

 

 

The duplicated values are just a numerical check.

[HawkII]

Do you have any posts with all the information on it, so that newcomers can read it with ease of access?

[Whitefoot]

17 minutes ago, HawkII said:

Do you have any posts with all the information on it, so that newcomers can read it with ease of access?

A PDF of my 5 page paper is attached to the fifth post in this thread.  As nearly as I can tell, it is only downloadable if you are signed in.  As this thread has established, and I agree, calculations on the last 3 pages are flawed.

[studiot]

On 9/27/2023 at 10:34 PM, Whitefoot said:

A PDF of my 5 page paper is attached to the fifth post in this thread.  As nearly as I can tell, it is only downloadable if you are signed in.  As this thread has established, and I agree, calculations on the last 3 pages are flawed.

So the last thre pages (of 5) are flawed.

 

You have also agreed that at least the first page is also flawed and I invited you to correct it.

I presume you are therefore going to withdraw this paper and perhaps substitute it with something better.

 

When you do please be aware that your Fig 1 is very worrying.

Since you have identified the length Beta (and gamma) with the bohr radius, which is the radius of an atom, it follows that your model electron must be several times the size of an atom.

That is if Fig 1 represents you toroidal model of an electron.

You should also be aware that the Bohr radius is the radius of a hydrogen atom in the ground state.

Other electrons have different corresponding radii.

Alternatively if you are confusing quantum orbitals with the Bohr orbital model of the atom then this is even more difficult to square with your model.

Also to be considered is that the Bohr electron is in a bound state, whilst the Compton and Classical electrons are in essentially a free or unbound state.

There is a lot of Physics for you to account for.

 

There is a good summary of toroidal models and their faults from the original 1915 one to the present day here in pdf.

 

https://www.ptep-online.com/2018/PP-53-06.PDF

Edited September 28, 2023 by studiot

[Whitefoot]

20 minutes ago, studiot said:

You have also agreed that at least the first page is also flawed and I invited you to correct it.

I haven't agreed that the first page is flawed. I may have used the word 'radius' when the word 'length' is maybe more appropriate, but that's kind of moot.  The lengths associated with the electron have been traditionally referred to as radii, with the possible exception of what I call the Compton radius.

26 minutes ago, studiot said:

So the last thre pages (of 5) are flawed.

There are probably flaws there, not to imply that they are totally flawed. I have agreed that a change of units would invalidate the numerical matches I found.

 

28 minutes ago, studiot said:

I presume you are therefore going to withdraw this paper and perhaps substitute it with something better.

Not very soon - sorting out problems in the last 3 pages is not a simple thing. I don't think the first 2 pages need redoing. 

This part of the paper is simply showing how 3 lengths associated with the electron can also be associated with the geometry of a self-intersecting circular torus. There are no subtle problems with unit changes and there is no conflict with known science, since there is not yet an established physical model of the electron.  

37 minutes ago, studiot said:

Since you have identified the length Beta (and gamma) with the bohr radius, which is the radius of an atom, it follows that your model electron must be several times the size of an atom.

From the later part of the paper, I am suggesting the electron is comprised of some much smaller quantum, traversing a circular helical curve that wraps around a toroidal surface. The torus is not physical, it defines the shape of the geometry. The electron then is mostly empty space.  In an atom, the nucleus would be at the center of such electrons, and therefore the Bohr radius comes out just right.  I didn't develop these added details in the paper.

Thanks for the PDF.  I have seen some of the toroidal models.  I haven't seen any that identify the 3 electron lengths with a self-intersecting circular toroidal  geometry as I've done here.

[Whitefoot]

Some questions by studiot made it clear I need to better describe my electron model.  This is to elaborate a bit on my post.  This material is not in my paper.
 
The proposed electron is comprised of a quantum traversing an orbit that is a self-intersecting circular toroidal helix.  The electron orbit has an outermost radius equal to the Bohr radius.  The electron classical radius is roughly 13850 times larger than the moving quantum proposed to make up the electron.  The proposed electron then is mostly empty space.  The electron classical radius gives half the width of the intersection at the center of the electron orbit.  It is well established that hydrogen nuclei are smaller than the electron classical radius.  In an atom, the nucleus would be at the center of electrons as modelled here.

The first figure roughly illustrates the electron orbit with the gray helical curve.  The pitch of the helix, analogous to a thread pitch, is not yet determined in my paper.  The intersection at the center of the toroidal space is way too small to show up in this figure. The second figure is only included to give a bit of perspective on the first figure.

 

On 9/28/2023 at 2:46 PM, studiot said:

You should also be aware that the Bohr radius is the radius of a hydrogen atom in the ground state.

 

[studiot]

21 minutes ago, Whitefoot said:

The electron orbit has an outermost radius equal to the Bohr radius

Your section shows it is (nearly) twice that.

23 minutes ago, Whitefoot said:

The proposed electron is comprised of a quantum traversing an orbit that is a self-intersecting circular toroidal helix.

Quantum of what ?  (those pesky units again)

 

Orbiting what?

 

Geometry is all very well, but what about the Physics?