Hi !

An unknown physicist named Thomas Lockyer has produced an absolutely astonishing calculation. 🦄

He calculates the proton/electron mass ratio to the first seven significant digits.

For the record, the Standard Model is able to produce the first two significant digits at best.

Lockyer's calculation does not contain any bias that would allow it to obtain the desired result because it is a finite sum (of increasing energies) with each member increasing by a ratio sqrt(2).

He uses only physical constants (CODATA values).

The starting point of the calculation is the magnetic moment of the electron.

For more details, Google "A Photon-Based Vector Particle Model for Proton and Neutron Masses" + PrePrints.

This isn't numerology... although on another forum, a physicist (he introduced himself as such, so I'm willing to believe him) told me it is.

What do you think?

Edited September 18Sep 18 by Ser Gio

34 minutes ago, Ser Gio said:

What do you think?

You need to explain the idea.

Ironically perhaps, that's what's not supposed to happen on these forums. Somebody asking for opinions on an idea that hasn't been introduced. 😀

Edited September 18Sep 18 by joigus
minor correction

1 hour ago, Ser Gio said:

For more details, Google "A Photon-Based Vector Particle Model for Proton and Neutron Masses" + PrePrints.

Moderator Note

This is not an acceptable tactic. Things for discussion need to be posted here, Not links, not uploads, and not “go Google this”

Do you want me to transcribe part of the document here ? Ok, I'll try, but later because it will take some time to summarize it...

Moderators will tell you.

BTW, is this the Thomas Lockyer that you mention?:

https://inspirehep.net/authors/1701596

4 minutes ago, Ser Gio said:

Do you want me to transcribe part of the document here ? Ok, I'll try, but later because it will take some time to summarize it...

The abstract will do to start:

This work presents a simplified geometric model for the proton-to-electron mass ratio (mp/me), achieving a remarkable precision of seven significant figures (mp/me ≈ 1836.1521964, relative error −2.6 × 10−7) matching CODATA’s 1836.15267343. Building on T.N. Lockyer’s Vector Particle Physics (2000), the model eliminates an ad hoc QED-inspired correction, improving precision from six to seven significant figures in double-precision arithmetic. Rounding errors do not allow us to verify whether this model predicts a better outcome. The neutron-to-electron mass ratio (mn/me ≈ 1838.68982960, error 3.35 × 10−6) achieves six significant figures, consistent with the model’s structure.

This work is your work, right? Based on Lockyers paper from the 70s? Not sure why you're having trouble summarizing it. We have LaTex available maths if you need it.

No, the theory is by Thomas N. Lockyer. Summarizing this theory is not easy, as it is presented in pieces scattered throughout his book.

I would like to be able to copy a few chapters in full, but I don't think I have the right. I would have liked to ask his permission, but he died long ago.

I think I have the right to send excerpts privately. I can take photos of the pages and send them by email.

To verify his calculations, I translated his BASIC program (in the appendix to his book) into JavaScript. I had posted it on a blog. Contact me privately and I'll give you the address. With this program, I verified that you can't cheat to find the desired mass.

I'll be too busy in the next few days, but then I'll come here to post the calculations in Latex.

I will also give you some indications for anyone who wants to try to find the mass of the Muon or the Tauon by postulating a structure of the same kind. I tried for a long time but I did not succeed. I ended up considering that the mass of these particles had another reason for being. But if someone is able to calculate the mass of the Muon or the Tauon in the manner of Lockyer, this will call into question my theory (which I do not like very much) and I will be very happy to explore this new direction.

9 minutes ago, Ser Gio said:

No, the theory is by Thomas N. Lockyer. Summarizing this theory is not easy, as it is presented in pieces scattered throughout his book.

I would like to be able to copy a few chapters in full, but I don't think I have the right. I would have liked to ask his permission, but he died long ago.

I think I have the right to send excerpts privately. I can take photos of the pages and send them by email.

To verify his calculations, I translated his BASIC program (in the appendix to his book) into JavaScript. I had posted it on a blog. Contact me privately and I'll give you the address. With this program, I verified that you can't cheat to find the desired mass.

I'll be too busy in the next few days, but then I'll come here to post the calculations in Latex.

I will also give you some indications for anyone who wants to try to find the mass of the Muon or the Tauon by postulating a structure of the same kind. I tried for a long time but I did not succeed. I ended up considering that the mass of these particles had another reason for being. But if someone is able to calculate the mass of the Muon or the Tauon in the manner of Lockyer, this will call into question my theory (which I do not like very much) and I will be very happy to explore this new direction.

It seems you don't have anything to discuss on the forum at the moment, then.

See you around, perhaps.

2 hours ago, Ser Gio said:

No, the theory is by Thomas N. Lockyer. Summarizing this theory is not easy, as it is presented in pieces scattered throughout his book.

But you have a paper with an abstract.

Are you prepared to defend his work and answer questions about it?

I don't think I can copy Latex formulas here.

Is there a way to preview a message before posting it ?

Okay, let's test a Latex formula:

\begin{equation}

m = \frac{e^2}{m_e 4 \pi c^2 \lambda'_e d \epsilon_0}, \quad d = \frac{1 - \sqrt{2}/2}{2} - \frac{a_u}{\sqrt{2}}, \quad a_u = 2 \left( \sqrt{1 + \frac{\alpha}{2\pi}} - 1 \right).

\end{equation}

EDIT : ok the test failed.

But let's get back to the point:

I told you about a calculation proposed by T. Lockyer that gives the proton/electron mass ratio with the first seven significant digits correct. You have several options:

- You can look at the calculation itself to verify that there's no fraud, then, after checking, try to understand what it can tell us about physical reality, or you can shrug your shoulders and tell yourself that T. Lockyer has a very, very low chance of stumbling upon such precision by chance, but he won the lottery.

- You want to understand the theory behind his calculation: in this case, the best thing would be to buy his book, but there are very few in circulation, and certainly not enough for everyone who might be interested.

You also have the option of reading the article I wrote on the subject, but it only presents the formulas that produce the final calculation, without the full theory behind it. I didn't dare; the article would never have been accepted on PrePrints, and it would require recopying a large portion of his book, which I don't think is allowed.

In his model, the proton has a cubic structure (yes, that was almost enough for me to close the book too). Within this cube are other cubes indented like Russian dolls, with sides successively reduced by a factor of sqrt(2).

To explain the cubic aspect, he starts with the structure of the photon, decomposed into two mutually perpendicular waves (electric and magnetic). Arranged in a certain way, these waves form a cube of standing waves. But he must correct the side length of the first cube by a factor he deduces from the proton's magnetic moment (which slightly 'shrinks' the size of the cube => decrease in wavelengths => increase in the energy of all waves => increase in the final mass of the proton (about 5%).

That's what I can tell you for now. I can try taking a photo of a few pages from the book and posting them here: is that a problem?

I can also take a photo of the BASIC code of the program he put at the end of his book and which I translated into JavaScript to check if there was an ad hoc parameter introduced to improve the accuracy.

For your information, he did indeed add a small, ad hoc correction to his calculation, in keeping with the Standard Model, which I removed. To my surprise, instead of breaking the result, it greatly improved it: from the first 6 exact significant digits, we go to the first 7.

I can also give you my JavaScript program to save you time.

A long time ago, I tried to discuss this calculation in a forum, and was laughed at: it was numerology, and there was no point even being interested in it. And as usual, "personal theories are forbidden from discussion here," even though it wasn't a personal theory since it was first published in the 1970s, I believe (my book was published in 1992). (What good is a forum if not for adults to discuss topics that interest them?)

I don't pretend to tell you why this calculation is important or not: that will be up to each of you to make up your own mind.

Edited September 24Sep 24 by Ser Gio

1 hour ago, Ser Gio said:

I don't think I can copy Latex formulas here.

https://www.sciweavers.org/free-online-latex-equation-editor

https://editor.codecogs.com/

Regarding the book, you can’t ask a dead man’s permission, but if you believe it of great value, could you track who owns the rights now and ask them?

Copyright Exceptions:

You may be able to use limited excerpts under specific exceptions for non-commercial uses like private study, non-commercial research, or criticism. However, the amount you can copy must be "fair and reasonable“.

if this site is about discussion and critique i think you should be able to paste what is required as long as ‘fair and reasonable’ but better check yourself. Not a lawyer of copyright law.

On 9/24/2025 at 12:33 PM, studiot said:

https://editor.codecogs.com/

On 9/24/2025 at 12:33 PM, studiot said:

https://www.sciweavers.org/free-online-latex-equation-editor

https://editor.codecogs.com/

Okay: I can't just copy the Latex formulas from my article, I'd have to retype them one by one in this editor? And all the theory too... That would be a huge time-consuming process, which I don't have because I'm still working on other publications.

On 9/24/2025 at 12:39 PM, BuddhasDragon23 said:

Regarding the book, you can’t ask a dead man’s permission, but if you believe it of great value, could you track who owns the rights now and ask them?

Copyright Exceptions:

You may be able to use limited excerpts under specific exceptions for non-commercial uses like private study, non-commercial research, or criticism. However, the amount you can copy must be "fair and reasonable“.

if this site is about discussion and critique i think you should be able to paste what is required as long as ‘fair and reasonable’ but better check yourself. Not a lawyer of copyright law.

I think this is the best solution. I'll take some photos to post here.

On 9/24/2025 at 5:22 AM, Ser Gio said:

Is there a way to preview a message before posting it ?

There’s a sandbox area for testing such things

On 9/24/2025 at 5:22 AM, Ser Gio said:

In his model, the proton has a cubic structure (yes, that was almost enough for me to close the book too). Within this cube are other cubes indented like Russian dolls, with sides successively reduced by a factor of sqrt(2).

Cubic structure made of…what?

How does the proton mass depend on this?

On 9/24/2025 at 5:22 AM, Ser Gio said:

To explain the cubic aspect, he starts with the structure of the photon, decomposed into two mutually perpendicular waves (electric and magnetic). Arranged in a certain way, these waves form a cube of standing waves. But he must correct the side length of the first cube by a factor he deduces from the proton's magnetic moment (which slightly 'shrinks' the size of the cube => decrease in wavelengths => increase in the energy of all waves => increase in the final mass of the proton (about 5%).

What do photons have to do with protons. What is the confining structure that gives you a standing wave?

On 9/24/2025 at 5:22 AM, Ser Gio said:

A long time ago, I tried to discuss this calculation in a forum, and was laughed at: it was numerology, and there was no point even being interested in it. And as usual, "personal theories are forbidden from discussion here," even though it wasn't a personal theory since it was first published in the 1970s, I believe (my book was published in 1992). (What good is a forum if not for adults to discuss topics that interest them?)

You’re free to explain how it’s not numerology.

And it is a personal theory, even if it’s not yours, but you have to be prepared to defend it.

Here are the principal pages.

Note that I have a JavaScript program available for anyone who would like to try it out.

If only electrons could capture neutrinos as those posted pages show, we wouldn't need the neutrino detectors we currently employ.

I notice that these pages mention several times that the electron as a cube is a model. I can't find anywhere they say the electron is a cube.

However I also can't find anywhere where they distinguish between free electrons and bound electrons or expound the Pauli principle.

How do uncharged photons give rise to the charge in an electron? How are they confined? What is the size of the electron and how does this compare to experiment?

His theory was written long before anyone knew what neutrinos were (do we already know that?).

Basically, neutrinos correspond to the missing mass in certain nuclear reactions.

And just as Lockyer's theory shows, the proton and the neutron are particles made of energy, he imagined that the inner layers were made of neutrinos.

But for me, that wasn't at all what interested me: it was the calculation itself that contained the shadow of a reality I wanted to understand.

Like you, the 'cube' didn't seem possible to me; it was more of a computational artifice, a model. Moreover, a little further into the calculation, the nested 3D cubes become nested circles (the cube was used to explain the radius of the concentric circles, in particular sqrt(2). But sqrt(2) can have other origins.

The charge is in the first layer of the proton (the positron, which serves as a container for the energy).

Charges generate fields, which are the origin of forces. This is precisely what needs to be explained.

All the questions raised by such a structure (like Russian dolls) have been the basis of my reflections for a very long time, and little by little, I have been putting the pieces of the puzzle together.

This will be what I will discuss in my future posts here, if you are interested.

Note: If you double levels 1 and 2, you get the mass of a neutron.

Haha, I know you're scratching your head! It's more fun than learning (or reciting) theories by heart. This is where you have to step out of your comfort zone. 🤨

On 9/25/2025 at 9:03 PM, studiot said:

If only electrons could capture neutrinos as those posted pages show, we wouldn't need the neutrino detectors we currently employ.

They did ! But at a temperature > 10^12 K. Can we reproduce the conditions of the early universe in the laboratory ?

Lockyer calls it neutrinos. I prefer to call it energy. I don't know exactly the way energy travels as 'neutrinos'

I talk about positrons capturing energy here: https://ai.vixra.org/abs/2508.0014

1 hour ago, Ser Gio said:

They did ! But at a temperature > 10^12 K. Can we reproduce the conditions of the early universe in the laboratory ?

Lockyer calls it neutrinos. I prefer to call it energy. I don't know exactly the way energy travels as 'neutrinos'

I talk about positrons capturing energy here: https://ai.vixra.org/abs/2508.0014

This rings alarm bells. It makes no sense to equate neutrinos with "energy". Anyone with training in physical science knows energy is a property of a system, not stuff. And how could "energy" have spin?

If positrons capture energy, it must be the energy of something. Of what, then?

On 9/27/2025 at 1:23 PM, exchemist said:

This rings alarm bells. It makes no sense to equate neutrinos with "energy". Anyone with training in physical science knows energy is a property of a system, not stuff. And how could "energy" have spin?

If positrons capture energy, it must be the energy of something. Of what, then?

I don't understand your objection: during primordial nucleosynthesis, matter was created from energy. We also know the equivalence E=mc^2.

But it seems to me that you support the separation between matter and energy, is that it?

If so, we each have a different postulate, and it's normal that we don't arrive at the same conclusions.

The postulate that matter = energy is not 'my' postulate; I inherited it from the scientific literature. It explains many physical phenomena, nuclear reactions for example: the enormous amount of energy produced comes from the conversion of mass into energy. (But since the energy produced wasn't enough to explain all the missing mass, we came up with neutrinos.)

I'll leave it to Lockyer to call the nested energy layers of his model 'neutrinos'. At his time, this may have been a good idea. But what interests me is the calculation, not the words that we put on it.

PS : A better argument: we know how to create a positron/electron pair (with Spin ;-)) from energy (laser) : the conversion of radiation into matter is indeed a possible physical phenomenon, it's not a postulate.

________________________________________________________

In the article submitted to PrePrints, the JavaScript code I attached was unfortunately modified for security reasons and became unusable.

Last year, I wrote a blog post just to explain this calculation. Here you'll find the script ready to use (and instructions for those unfamiliar with JavaScript).

Here's the link; you just need to replace each § with a / (slash), and each * with a . (dot)

https:§§science-wide-open*blogspot*com§024§10§relative-mass-proton-electron*html

Edited September 28Sep 28 by Ser Gio

1 hour ago, Ser Gio said:

I don't understand your objection: during primordial nucleosynthesis, matter was created from energy. We also know the equivalence E=mc^2.

That is if you accept the hypothesis of 'primordial nucleosynthesis' , which I do not.

Both energy and mass are properties of something as exchemict says.

When that something undergoes some process the equation you mentioned keeps an accounting of the sum of these properties.

But it would be better if you used it in its differential form

ΔE = Δmc²

As befits a process.

Otherwise you are suggesting that there are 'absolute' vlaues to mass and energy, both of which are frame dependent.

On 9/27/2025 at 12:23 PM, exchemist said:

If positrons capture energy, it must be the energy of something. Of what, then?

1 hour ago, Ser Gio said:

I don't understand your objection: during primordial nucleosynthesis, matter was created from energy. We also know the equivalence E=mc^2.

But it seems to me that you support the separation between matter and energy, is that it?

If so, we each have a different postulate, and it's normal that we don't arrive at the same conclusions.

The postulate that matter = energy is not 'my' postulate; I inherited it from the scientific literature. It explains many physical phenomena, nuclear reactions for example: the enormous amount of energy produced comes from the conversion of mass into energy. (But since the energy produced wasn't enough to explain all the missing mass, we came up with neutrinos.)

I'll leave it to Lockyer to call the nested energy layers of his model 'neutrinos'. At his time, this may have been a good idea. But what interests me is the calculation, not the words that we put on it.

PS : A better argument: we know how to create a positron/electron pair (with Spin ;-)) from energy (laser) : the conversion of radiation into matter is indeed a possible physical phenomenon, it's not a postulate.

________________________________________________________

In the article submitted to PrePrints, the JavaScript code I attached was unfortunately modified for security reasons and became unusable.

Last year, I wrote a blog post just to explain this calculation. Here you'll find the script ready to use (and instructions for those unfamiliar with JavaScript).

Here's the link; you just need to replace each § with a / (slash), and each * with a . (dot)

https:§§science-wide-open*blogspot*com§024§10§relative-mass-proton-electron*html

My understanding is that the primordial nucleosynthesis involved chiefly a plasma of electrons, positrons and γ-ray photons, i.e. radiation. It makes no sense to speak of energy as if it's a free-standing entity. Elementary particles and radiation are physical entities however.

As for E=mc², that simply says that energy is associated with mass. Both mass and energy are properties of some physical system or entity. You can't have a jug of mass, nor can you have a jug of energy. So when you speak of either you need to say what system or entity they are properties of.

On 9/26/2025 at 4:53 AM, Ser Gio said:

His theory was written long before anyone knew what neutrinos were (do we already know that?).

I thought his theory was from the 1970s.

On 9/26/2025 at 4:53 AM, Ser Gio said:

Basically, neutrinos correspond to the missing mass in certain nuclear reactions.

Not mass, since mass isn’t conserved (so it’s harder to say it’s missing in a nuclear reaction) but other properties, like energy and angular momentum, and the fact that the electron energy has a continuous spectrum, which is related to conservation of momentum.

On 9/26/2025 at 4:53 AM, Ser Gio said:

And just as Lockyer's theory shows, the proton and the neutron are particles made of energy, he imagined that the inner layers were made of neutrinos.

“made of energy”?

On 9/26/2025 at 4:53 AM, Ser Gio said:

But for me, that wasn't at all what interested me: it was the calculation itself that contained the shadow of a reality I wanted to understand.

If the model is flawed, any calculation that stems from it is suspect.

On 9/26/2025 at 4:53 AM, Ser Gio said:

Like you, the 'cube' didn't seem possible to me; it was more of a computational artifice, a model. Moreover, a little further into the calculation, the nested 3D cubes become nested circles (the cube was used to explain the radius of the concentric circles, in particular sqrt(2). But sqrt(2) can have other origins.

The charge is in the first layer of the proton (the positron, which serves as a container for the energy).

Is “container for the energy” your phrasing or his? You’re using descriptions that I would not expect from someone who had studied physics at any advanced level

On 9/26/2025 at 4:53 AM, Ser Gio said:

Charges generate fields, which are the origin of forces. This is precisely what needs to be explained.

Yes, and it’s this explanation that we’re asking for. The actual physics at play.

On 9/26/2025 at 4:53 AM, Ser Gio said:

All the questions raised by such a structure (like Russian dolls) have been the basis of my reflections for a very long time, and little by little, I have been putting the pieces of the puzzle together.

This will be what I will discuss in my future posts here, if you are interested.

No it won’t.

Our rules preclude building on non-mainstream physics, without providing the solid foundation first. You’ve got to establish the validity of the model first.

Regarding nucleosynthesis: if nucleosynthesis was based on more elementary material constituents, we are simply postponing the question: where does their synthesis come from? Personally, I prefer to think that energy is an essential building block in the construction of matter rather than imagining that these building blocks appeared from 'nothing,' or rather, from a "singularity."

As for the rest, I don't intend to dwell on Lockyer's theory. I have presented a calculation that should, in my opinion, pique the curiosity of anyone who has studied physics at any advanced level...

But I'm not forcing anyone to find it interesting. Some may find it interesting, or not. That's their choice.

Edited September 28Sep 28 by Ser Gio