[PaulTalbot (OP)]

In a recent preprint, I wonder if the minimum mass, the Hubble constant and the proton radius could be calculated precisely using the observed ratio of the electrostatic force to the gravitational force?
The value of the minimum mass would be Mmin ≈ 1.7206 × 10^^-68 kg, and that of the Hubble constant, H ≈ 72.013 km s-1 Mpc-1. The proton radius can also be calculated using similar assumptions: rp ≈ 0.8264 fm.
Since I am looking for some feedback on this hypothesis, your comments are welcome.
The 4 page preprint is attached (PDF).
Thank you.

[Origin]

I wonder if the minimum mass

Minimum mass of what?

the Hubble constant and the proton radius could be calculated precisely using the observed ratio of the electrostatic force to the gravitational force?

Electrostatic force of what and the gravitational force of what?  You could pick values for the electrostatic and gravitational forces so that they would equal the Hubble constant ant the radius of a proton, but I don't see what use that would be.
I don't see any physical reason that these different phenomena would be related like that.

[Bored chemist]

The Hubble constant is pretty close to 1/ the age of the universe.
So it changes.
The radius of the proton doesn't.

https://en.wikipedia.org/wiki/Hubble%27s_law#Hubble_time

[PaulTalbot (OP)]

Minimum mass of what?

The value of M_min corresponds to the Wesson’s mass (m_E ≈ 2 × 10 ⁶⁸ kg), i.e., the quantum of mass calculated by Pr. Wesson [10] in 2003 using the constants c, h and Λ (the cosmological constant).

[PaulTalbot (OP)]

Electrostatic force of what and the gravitational force of what?

The ratio, say β, of the electrostatic force to the gravitational force between an electron and a proton is
β = e² / 4π ε₀ G m_e m_p.                                                           (4)
ε₀ is the vacuum permittivity.
G is the gravitational constant .
m_e is the mass of the electron.
m_p is the mass of the proton.
In the last century, Paul Dirac popularized this β ratio in a cosmological context [8] [9]. It still gets attention because of its high value (β ≈ 2.268 66 × 10³⁹). The gravitational force is tiny compared to other forces.

[PaulTalbot (OP)]

 

The Hubble constant is pretty close to 1/ the age of the universe.
So it changes.
The radius of the proton doesn't.

The decreasing value of the Hubble constant is indeed suggested by the conformal model ΛCDM.
Now, in my opinion, this conformal model is falsified by observation, since the observed value of H is way too high.
Moreover, how do we know if the proton radius is really constant?
Why couldn't it slowly vary with time?

[Halc]

The value of M_min corresponds to the Wesson’s mass (m_E ≈ 2 × 10 ⁶⁸ kg), i.e., the quantum of mass calculated by Pr. Wesson [10] in 2003 using the constants c, h and Λ (the cosmological constant).

Yes, it seems Wesson attempted to determine a quanta of mass.

In the last century, Paul Dirac popularized this β ratio in a cosmological context [8] [9]. It still gets attention because of its high value (β ≈ 2.268 66 × 1039). The gravitational force is tiny compared to other forces.

You're giving refereces 8 & 9 which don't correspond to any bibliography.

You are obviously copying directly from the works of others without giving credit. This plagiarism violates site rules.
Please edit your posts with credits properly given.

The decreasing value of the Hubble constant is indeed suggested by the conformal model ΛCDM.

That very model suggests that H will actually settle down to a constant value of around 57 km/sec/mpc, which is straight exponential expansion.

[Bored chemist]

Moreover, how do we know if the proton radius is really constant?
Why couldn't it slowly vary with time?

Because that would have an effect on the spectra of atoms.
But we see the emission from atoms from a long time ago, and that (hypothetical) effect is not found
So we know that the radius of the proton has not changed.
So we know , from direct experimental observation, that your idea is wrong.

And now what we do is look at how you react to that fact.
Do you behave like a scientist and thank us for pointing out the glitch which makes your  idea impossible, or do you behave like a schoolkid.

[PaulTalbot (OP)]

You're giving refereces 8 & 9 which don't correspond to any bibliography. You are obviously copying directly from the works of others without giving credit. This plagiarism violates site rules.

There must be a misunderstanding. The text you refer to is part of the preprint I submitted in my original post (a 4-page attached PDF, relatively quick to read). The bibliography is included in the document.
I am new to this forum, so I thougth I could get some feedback before publishing.
Since the text is already available in the original post, I won't repeat it.
However, for those who just want to have a quick view, please find attached a chart of the assumed relations between   
the refered physical constants.

[Origin]

Since I am looking for some feedback on this hypothesis, your comments are welcome.

I looked at your PDF and it appears to me that what you are doing is called numerology.  That is you are taking a bunch of unrelated constants and combining them in such a way that you get known quantities.  In other words the equations have no physical meaning they are essentially just a bunch of random numbers put together to equal a predetermined quantity.

[Bored chemist]

You're giving refereces 8 & 9 which don't correspond to any bibliography. You are obviously copying directly from the works of others without giving credit. This plagiarism violates site rules.

There must be a misunderstanding. The text you refer to is part of the preprint I submitted in my original post (a 4-page attached PDF, relatively quick to read). The bibliography is included in the document.
I am new to this forum, so I thougth I could get some feedback before publishing.
Since the text is already available in the original post, I won't repeat it.
However, for those who just want to have a quick view, please find attached a chart of the assumed relations between   
the refered physical constants.

And now what we do is look at how you react to that fact.
Do you behave like a scientist and thank us for pointing out the glitch which makes your  idea impossible, or do you behave like a schoolkid.

OK, so you went with the schoolkid option.

[PaulTalbot (OP)]

Because that would have an effect on the spectra of atoms.
But we see the emission from atoms from a long time ago, and that (hypothetical) effect is not found
So we know that the radius of the proton has not changed.
So we know , from direct experimental observation, that your idea is wrong.
And now what we do is look at how you react to that fact.
Do you behave like a scientist and thank us for pointing out the glitch which makes your  idea impossible, or do you behave like a schoolkid.

First, I would like to thank all those who take the time to read this thread. So far, all replies have been and will continue to be thanked, as long as they stay polite.
I asked a question about the proton radius and I assume you answered it correctly.
Now, if you read the preprint, you will notice that all physical values are referred to as constants, including the proton radius. So, your conclusion about my idea is unjustified. It was just a question.
Please note that I try to answer the replies one by one.

[Origin]

Now, if you read the preprint, you will notice that all physical values are referred to as constants, including the proton radius. So, your conclusion about my idea is unjustified.

When I said you were doing numerology and not physics I was referring to things like this from your paper.
You wrote:
The Hubble constant H (of dimension T-1) would correspond to the minimum frequency:
fmin = H.

Let's think about this for a second, what is the frequency of a constant?  There is no frequency of a constant.  The Hubble constant is the speed of the expansion of space per Mpc.  A constant speed doesn't have a frequency.

You then take the formula for the energy of a photon  and substitute in the bogus frequency of the Hubble constant.

None of that makes any physical sense and that is just the first couple of equations.

[Halc]

Now, if you read the preprint, you will notice that all physical values are referred to as constants, including the proton radius.

Despite its name as 'the Hubble constant', it isn't a constant. For a zero energy solution of the universe, H would be exactly 1/t where t is time. The value has the same units as 1/t.

So, your conclusion about my idea is unjustified.

What conclusion exactly was that? I don't remember making one about your idea.

I looked at the paper a bit.
The first 'constant' is this M_min which lacks a reference. The H value (references given in introduction) is given to far more precision than is justified by the range of values in the references.  Looking at really distant galaxies doesn't count since they're way in the past when the value of H was considerably different.

I'm just saying that you're not justifying the sort of precision that the paper claims.

Origin is right, you're substituting variables of different units into equations, rendering them meaningless. You're using the energy formula for a photon and applying it to something that isn't a photon.

[PaulTalbot (OP)]

What conclusion exactly was that? I don't remember making one about your idea.

Sorry Halc, I think I mistakenly quoted some text from someone else. The conclusion was that I was a schoolkid because I wondered if the proton radius was really constant. Frankly, I wish I were a schoolkid, so at least, I would be younger. Fortunately, we are on the lighter side of the forum.

[PaulTalbot (OP)]

When I said you were doing numerology and not physics I was referring to things like this from your paper.
You wrote: The Hubble constant H (of dimension T-1) would correspond to the minimum frequency: fmin = H.
...
None of that makes any physical sense and that is just the first couple of equations.

OK, maybe I should have presented myself first and explain why I make such assumptions.
I am a computer scientist, an IT architect or if you prefer, a system designer interested in cosmology and the world we live in. I look at the Universe as a global system, not a simple object. This is why I am so intrigued by the relations between physical quantities.To get the idea, you can look at the attached chart: the MELT-hc network. It is part of a book I wrote on the subject (The Cosmospheric Principle).

This kind of illustration is typically used by system designers, and a network-type structure is quickly detected. The physical quantities (M:Mass, E:Energy, L:Length and T:Time) are represented by circles, and the relations by arrows, each with a boxed formula. Each arrow indicates the direction of the relation expressed by the formula linking two quantities. This direction is arbitrary and can be reversed by changing the formula. For example, the relation E = M c², Einstein's famous formula can be written M = E/c².
The MELT-hc network shows known equations that express the wave nature of energy and mass. The value of L then corresponds to a wavelength, and that of T, to the period of this wave. In this model, the relation L = c T links time to space in the same way that E = M c² links mass to energy. In fact, all the relations of the model have this same universal status.
The relation E = h/T is a reformulation of the Planck-Einstein relation (E = h f), expressed as a function of time (T). The relation L = h/M c is the Compton wavelength associated with a mass M, and so on. These relatively simple relations can be deduced from each other. They involve two extremum values:
•   the minimum action (h), and
•   the maximum speed (c).
This explains the name of the network: MELT-hc.

[Bored chemist]

That's still numerology.

[Bored chemist]

The fact that it fails on dimensional analysis is beside the point unless he can explain why something constant is the same as something that's changing.

[PaulTalbot (OP)]

OK, I am glad that there are so many replies, so thank you again for all those comments.
I here try to answer some of them, but one at a time.

Origin is right, you're substituting variables of different units into equations, rendering them meaningless. You're using the energy formula for a photon and applying it to something that isn't a photon.

In his 1924 thesis «Recherches sur la théorie des quanta» (Research on the theory of Quanta), Louis de Broglie broadened the interpretation of the Planck-Einstein relation which was then limited to electromagnetic phenomena. It assumes the existence of a periodic phenomenon associated with mass:
«One can thus conceive that because of a great law of Nature, to each piece of energy of proper mass m, is linked a periodic phenomenon of frequency ν such as we get: hν = mc². This hypothesis is the basis of our system.» (Broglie, 1924)
This hypothesis was quickly adopted by the scientific community and confirmed by the electron diffraction in 1927.

[PaulTalbot (OP)]

OK, so you have the relative strength of these two forces down to 5 significant digits, which is strange since the values are in different units.  Gravity between two objects is a function of their mass, and EM force between the same two objects is a function of their charge. So this number you've quoted is fairly random. You do the same calculation between say an electron and a positron and you get a different ratio. I got several different answers for the relative strengths of them, and they can't even agree on the order of magnitude, let along a figure to several digits, which again, being in different units, is largely meaningless.

I think you are right about the choice of particles. There seems to be something special about the electron-proton couple, as if they were two sides of the same coin. The same thing applies to the positron-antiproton couple.
In the chapter 2 of his 1974 paper "Cosmological Models and the Large Numbers Hypothesis", Paul Dirac uses this same ratio:
"The electric force between the electron and the proton in a hydrogen atom is e²/r². The gravitational force between them is Gm_p m_e/r². Their ratio is the dimensionless number e²/Gm_pm_e. Its value is about 2 x 10³⁹."
In those times, the charge was expressed in esu (electrostatic unit of charge also called statcoulomb or Franklin), so the electric constant was 1 instead of 1/4π ε₀. This may lead to a confusion about the dimension of charge, that was then different. The Dirac's paper is attached to this post.
The Dirac's hypothesis about the variation of G over time has not held up well. Nevertheless, some scientists, including myself, follows in the footsteps of Dirac, searching for a meaning of dimensionless numbers.