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

[Whitefoot]

1 hour ago, studiot said:

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

My model shows that the Bohr radius is equal to beta plus gamma.  In the model, gamma is the length from the center of the toroidal space to the center of the circle defining the toroidal space.  Beta is the radius of the circle.  Beta plus gamma, the Bohr radius, gives the length from the center of the toroidal space to the outermost radius of the toroidal space.  For an atom, with the nucleus at the center of the toroidal space, the outermost radius of the electron orbit is at a length of one Bohr radius.

My section in diagram 1 of the paper may give an erroneous appearance, but the lengths there are greatly exaggerated for illustration.

1 hour ago, studiot said:

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

Since the calculated radius of this object is quite small, 2.035E-19 meter, for now I'm calling it the quantum rather than make up some new terminology. 

Orbiting in space. 

I'm only connecting the lengths associated with an electron with a possible geometry.  I'm not able to explain all of physics yet.  Since a toroidal helix can have one of two chiralities, toroidal models can fit with the existence of matter and antimatter.

 

Edited September 30, 2023 by Whitefoot

[swansont]

37 minutes ago, Whitefoot said:

My model shows that the Bohr radius is equal to beta plus gamma.  In the model, gamma is the length from the center of the toroidal space to the center of the circle defining the toroidal space.  Beta is the radius of the circle.  Beta plus gamma, the Bohr radius, gives the length from the center of the toroidal space to the outermost radius of the toroidal space.  For an atom, with the nucleus at the center of the toroidal space, the outermost radius of the elctron orbit is at a length of one Bohr radius.

My section in diagram 1 of the paper may appear that way, but the lengths there are greatly exaggerated for illustration.

But beta and gamma are terms that you’ve defined, related to the Bohr radius; these are not tied to anything outside your model. Your model doesn’t “show” this; that’s a tautology, i.e. circular reasoning.

1 hour ago, Whitefoot said:

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

How does this compare with the experimentally observed charge distribution of the electron (electric dipole moment no larger than ~4 x 10^-30 e-cm)

[Whitefoot]

36 minutes ago, swansont said:

But beta and gamma are terms that you’ve defined, related to the Bohr radius; these are not tied to anything outside your model. Your model doesn’t “show” this; that’s a tautology, i.e. circular reasoning.

Within the context of my model, beta plus gamma, terms that I have defined, correspond to the Bohr radius.  Is this a semantics complaint?

36 minutes ago, swansont said:

How does this compare with the experimentally observed charge distribution of the electron (electric dipole moment no larger than ~4 x 10^-30 e-cm)

I'm not able to answer your question.  I haven't even been able yet to figure out how charge arises from the model.  I haven't even been able to account for spin or other known electron properties.

Edited September 30, 2023 by Whitefoot

[Whitefoot]

3 hours ago, studiot said:

Your section shows it is (nearly) twice that.

Going back a ways, I can improve my answer.  At first I said:

My section in diagram 1 of the paper may give an erroneous appearance, but the lengths there are greatly exaggerated for illustration.

I'm now adding:  Since gamma is the length from the center of the circle to the center of the torus, the section in Fig 2 shows that beta+gamma is almost equal to twice beta, but not quite, when using values for the electron.  I think this is where you may get the impression that it is twice the correct value, but within the model beta+gamma still corresponds to the Bohr radius.

From the model, beta-gamma equals the classical radius, which is a very small difference.  That's beta minus gamma.

Edited October 1, 2023 by Whitefoot

[studiot]

46 minutes ago, Whitefoot said:

Going back a ways, I can improve my answer.  At first I said:

My section in diagram 1 of the paper may give an erroneous appearance, but the lengths there are greatly exaggerated for illustration.

I'm now adding:  Since gamma is the length from the center of the circle to the center of the torus, the section in Fig 2 shows that beta+gamma is almost equal to twice beta, but not quite.  I think this is where you may get the impression that it is twice the correct value, but within the model beta+gamma still corresponds to the Bohr radius.

Yes, you are correct.
I confused myself there.

I understand the sectional geometry given in your Fig1, along with the necessary exaggerations for clarity,  though I welcome your later additions to improve communications.
In particular your article should start by saying a nucleus is at the centre of your donut.

But as far as I can see the choice of alpha and gamma are arbitrary so you should make clear at the outset how you have divided up the fixed Bohr radius.

I asked you " orbiting what ?" and you have now added a nucleus for the first time. Thank you.

But what happens if there is no nucleus or the nucleus is from another atom, say He⁺ or Li⁺⁺ ir Be⁺⁺⁺ ?

The energy level depends upon the square of the atomic number and the Bohr radius is define for one electron systems.

How does this affect you numerical coincidences for these and all the other atoms, since their ground state radii will be different?

I also asked you what was orbiting and you have simply called it a quantum, which is a poor nomination since a quantum is not necessarily small but should be a very specifically defined amount of something, which you have not provided.

This is a crucial question because of the Physics.

If this something has mass the question of its speed immediately becomes important since its mass appears in the physical equations.

If you are thinking of the model with a photon travelling at the speed of light, then the problem becomes

Can then electrons exist without an associated nucleus to produce this toroid and helix ?
I ask this because I can easily produce a beam of electrons free of any nucleus. so how can an electron be a photon trapped in a toroid ?

 

 

[Whitefoot]

1 hour ago, studiot said:

But as far as I can see the choice of alpha and gamma are arbitrary so you should make clear at the outset how you have divided up the fixed Bohr radius.

Page 1 of the paper shows RI/RC equal to RC/RB equal to the fine structure constant alpha.  That is (Classical radius)/(Compton radius)  equals  (Compton radius/Bohr radius) equals the fine structure constant alpha.  This is well established physics - ancient in fact.  I didn't work thru the algebra, but the calculations for beta and gamma are shown on page 2.

The diagram of Fig 1 shows that (beta-gamma)/Rc  equals  Rc/(beta+gamma) for a self-intersecting torus.

The matching ratios:
   (Classical radius)/(Compton radius)  equals  (Compton radius/Bohr radius)
                                 (beta-gamma)/Rc  equals  Rc/(beta+gamma)

suggest that the lengths associated with the electron can conceivably fit the geometry of a self-intersecting circular toroidal helix.  I haven't seen this proposed in other toroidal models.

1 hour ago, studiot said:

But what happens if there is no nucleus or the nucleus is from another atom, say He⁺ or Li⁺⁺ ir Be⁺⁺⁺ ?

I am assuming even free electrons have these orbits - that somehow it is a stable geometry.  I don't know if the radii change, since I don't have numerical results to back this up, and I don't have results that would apply to other atomic orbitals.  I haven't been able to go beyond what is in my paper and what we have discussed in this thread.

1 hour ago, studiot said:

I also asked you what was orbiting and you have simply called it a quantum, which is a poor nomination since a quantum is not necessarily small but should be a very specifically defined amount of something, which you have not provided.

From a previous post:  Since the calculated radius of this object is quite small, 2.035E-19 meter, for now I'm calling it the quantum rather than make up some new terminology.  I'm just not inclined to make up new words.  That number refers to the radius of an object treated as a sphere in the calculations.

1 hour ago, studiot said:

If this something has mass the question of its speed immediately becomes important since its mass appears in the physical equations.

I haven't yet been able to solve for speeds and resulting mass.  That's the main direction I've tried to go with this.

1 hour ago, studiot said:

In particular your article should start by saying a nucleus is at the centre of your donut.

My paper was focused on the electron and I wasn't even thinking about atoms at the time.

Edited October 1, 2023 by Whitefoot

[swansont]

11 hours ago, Whitefoot said:

I am assuming even free electrons have these orbits - that somehow it is a stable geometry.

Why would they? If they aren’t moving in a straight line, there must be a force.

[Whitefoot]

1 hour ago, swansont said:

Why would they? If they aren’t moving in a straight line, there must be a force.

I haven't been able to solve that.  Maybe interacting with the Higgs field would lead to an optimal orbit.

From Wikipedia:  "The Higgs field is a field of energy that is thought to exist in every region of the universe. The field is accompanied by a fundamental particle known as the Higgs boson, which is used by the field to continuously interact with other particles, such as the electron. Particles that interact with the field are "given" mass..."

Given the two chiralities possible for a toroidal helix, I think the geometry is a natural fit with the existence of matter and anti-matter.  I know toroidal models have been attempted for a long time, but I haven't seen this particular geometry described before.

Suggesting a geometry is probably about as far as I will be able to go with the model with my limited knowledge of physics.

[Whitefoot]

On 9/30/2023 at 3:12 PM, swansont said:

But beta and gamma are terms that you’ve defined, related to the Bohr radius; these are not tied to anything outside your model. Your model doesn’t “show” this; that’s a tautology, i.e. circular reasoning.

Looking back over the posts, I don't think I adequately responded to this.  Excerpted from my paper page 2:

The 2nd and 3rd lines  show that beta and gamma of my model are tied to the Compton radius and the fine structure constant alpha, both physical constants.  The Compton radius is more commonly called the reduced Compton wavelength.

[swansont]

1 hour ago, Whitefoot said:

The 2nd and 3rd lines  show that beta and gamma of my model are tied to the Compton radius and the fine structure constant alpha, both physical constants. 

The Bohr radius and Compton radius and are related to each other by a factor of the fine structure constant, as you note, so beta and gamma are still terms you’ve defined; one is a little bigger than half of the Bohr radius, one is a little smaller.

[Whitefoot]

3 minutes ago, swansont said:

so beta and gamma are still terms you’ve defined

Yes, I've defined them to show the possible fit to the geometry of a self-intersecting toroidal helix.

[swansont]

25 minutes ago, Whitefoot said:

Yes, I've defined them to show the possible fit to the geometry of a self-intersecting toroidal helix.

You could pick another small increment to add and subtract, and you would have a different torus. So what? There’s no physics here. It’s still just playing around with numbers.

[Whitefoot]

But it wouldn't be a toroidal helix compatible with lengths related to the electron.  The ratios  Rclassical/Rcompton = Rcompton/Rbohr = alpha suggest this specific geometry.

[swansont]

26 minutes ago, Whitefoot said:

But it wouldn't be a toroidal helix compatible with lengths related to the electron.  The ratios  Rclassical/Rcompton = Rcompton/Rbohr = alpha suggest this specific geometry.

Nothing suggests you have to subtract or add anything to the Bohr radius to form a torus. There’s nothing physical attached to this (you’ve acknowledged the classical radius has no physical significance), you’ve suggested no experimental repercussions of it, and have admitted you haven’t looked at ramifications that have been brought up which would confirm there’s nothing physical to this.

It’s up to you to make an experimental connection to show that this isn’t more numerology.

[Whitefoot]

The first page of my paper shows the compatibility of the ratios of electron radii with the ratios found in the geometry of a self-intersecting torus.  This only shows the conceivability of a possible connection.

I'm not able to make experimental predictions from what is only the beginning of a proposed model.  I haven't been able to take it farther than what I currently have.

I am adding the first page of my paper here again for readers who probably aren't familiar with it:  Click to enlarge.  Note that when the electron radii are used, the self-intersection of the torus will be tiny.  It is shown large here for illustration.

Edited October 3, 2023 by Whitefoot

[swansont]

When you have some physics to add, you can request this be unlocked.