[PaulTalbot (OP)]

Sorry, I had forgotten the attached paper.

[Origin]

Nevertheless, some scientists, including myself, follows in the footsteps of Dirac, searching for a meaning of dimensionless numbers

I didn't realize you were a scientist.  Could you explain how the Hubble constant can have a frequency and what that frequency is?  Thanks.

[Bored chemist]

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.

Let me know when you plan to get to this one.

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)]

Could you explain how the Hubble constant can have a frequency and what that frequency is?  Thanks.

The fact is that the dimension of a rate is the same as that of a frequency (T^-1). In the case of the Hubble constant, it is expressed as a speed divided by a length so we get [H] = (L T^-1) / L = T^-1. It is not a frequency as such, but it is assumed to be the smallest possible value of a physical quantity of dimension T^-1.
By the way, I consider myself as a low level computer scientist. Since I am not a physicist, I am not qualified to provide pertinent advice on the subject matter. Moreover, my view of the physical world is unconventional.

[PaulTalbot (OP)]

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.

The fact is that the possible variation of physical constant is a complex and unresolved issue:
https://en.wikipedia.org/wiki/Time-variation_of_fundamental_constants [nofollow]
If some of them are varying over time, it should be very slowly, because there is no obvious observation supporting this hypothesis. I do not pretend to solve this enigma in my preview, so I am just wondering if some of them could vary.

[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.

The fact is that the possible variation of physical constant is a complex and unresolved issue:
https://en.wikipedia.org/wiki/Time-variation_of_fundamental_constants
If some of them are varying over time, it should be very slowly, because there is no obvious observation supporting this hypothesis. I do not pretend to solve this enigma in my preview, so I am just wondering if some of them could vary.

Yes.
But they would all have to vary in carefully specified ways in order to not be obvious.

And your idea doesn't fit with that

[Origin]

 

The fact is that the dimension of a rate is the same as that of a frequency (T-1).

That is not correct, the dimensions of the rate in this case is L/t.

In the case of the Hubble constant, it is expressed as a speed divided by a length so we get [H] = (L T-1) / L = T-1.

You can't just cancel out the Lengths since one of the units is km and the other is Mpc.  Using unit analysis you can easily convert Mpc to km and then you will end up with the reciprocal of the age of the universe.

It is not a frequency as such, but it is assumed to be the smallest possible value of a physical quantity of dimension T-1.

What do you mean by, "it is assumed to be the smallest possible value of a physical quantity of dimension T-1"?
I agree it is not a frequency and certainly multiplying the Hubble constant by by the Planck constant is not going to give you anything useful.

[PaulTalbot (OP)]

I am as well, although I've never suggested to anybody that I'm a scientist.

I have a degree in computer sciences from Université Laval and a specialization in computer security from Université de Sherbrooke. This may not be impressive but enough to confirm my scientific background.

[Origin]

I have a degree in computer sciences from Université Laval and a specialization in computer security from Université de Sherbrooke. This may not be impressive but enough to confirm my scientific background.

It would be much more useful to address the questions about your ideas rather than discussing our educational backgrounds.

[PaulTalbot (OP)]

It would be much more useful to address the questions about your ideas rather than discussing our educational backgrounds.

Your are 100% right, this is precisely what I expected.

That is not correct, the dimensions of the rate in this case is L/t.

From: https://en.wikipedia.org/wiki/Hubble%27s_law [nofollow]
"Hubble constant is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy 1 megaparsec (3.09×10¹⁹ km) away, and its value is about 70 (km/s)/Mpc. However, the SI unit of H₀ is simply s⁻¹, and the SI unit for the reciprocal of H₀ is simply the second. The reciprocal of H₀ is known as the Hubble time. The Hubble constant can also be interpreted as the relative rate of expansion. In this form H₀ = 7%/Gyr, meaning that at the current rate of expansion it takes a billion years for an unbound structure to grow by 7%."

[PaulTalbot (OP)]

What do you mean by, "it is assumed to be the smallest possible value of a physical quantity of dimension T-1"?

This is an assumption of the preview. If there is a minimum value for the physical quantities action, charge and temperature, then maybe some other physical quantities may be minimally limited too.

[PaulTalbot (OP)]

My choosing different particles was meant to illustrate the meaninglessness of comparing the one force with another, since they're not functions of the same thing.  So there's an insanely large difference between the gravitational and EM attraction between a positron and an electron, yet the gravitational force between a pair of billiard balls is probably more than the EM force between them. So does that mean that gravity is stronger than EM? No, it just means the ratio between them is in different units and is thus a meaningless comparison.

In both cases, the attractive force is expressed in newtons (of dimension M L T^-2). As for the choice of particles, it is the same one that Dirac made in his paper attached to my previous post. I understand that this may seem arbitrary, but once again:

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."

The following link explains the process in details:
https://courses.lumenlearning.com/physics/chapter/18-3-coulombs-law/#:~:text=The%20ratio%20of%20the%20magnitude,G%20%3D%202.27%20%C3%97%2010%2039%20. [nofollow]

[Origin]

This is an assumption of the preview. If there is a minimum value for the physical quantities action, charge and temperature, then maybe some other physical quantities may be minimally limited too.

That may or may not be true.  But there is no reason to think this is true :
The Hubble constant H (of dimension T-1) would correspond to the minimum frequency:
fmin = H.

[Origin]

However, the SI unit of H0 is simply s−1, and the SI unit for the reciprocal of H0 is simply the second.

That's nice, but the bottom line here is treating the Hubble constant like a frequency and multiplying it by Planck's constant is meaningless.

[PaulTalbot (OP)]

That's nice, but the bottom line here is treating the Hubble constant like a frequency and multiplying it by Planck's constant is meaningless.

Once again, this is an assumption. If H is the minimum value for any physical quantity of dimension T^-1, then this should apply to frequency as well. So there should exist a minimum frequency bounded by the same value.

[Origin]

If H is the minimum value for any physical quantity of dimension T-1

That is a mighty big if.  This all still just looks numerology with no basis in anything real.

[PaulTalbot (OP)]

That is a mighty big if.  This all still just looks numerology with no basis in anything real.

I would like to deal with the numerology question first and then with the "big if" in a next post.
This kind of research looks like solving a puzzle, and yes, some numbers are involved in the process. It may thus be associated to a special kind of numerology, but there are strict rules to comply with:

1 - The assumed relations must comply with dimensional analysis, that is both sides of the equations must have the same dimension. Many questions have been posted on the subject, and it is OK. If you believe that some of the assumed relations do not comply with this rule, please let me know.

2 - The assumed relations should not conflict with already known and validated relations like E=mc². The use of such equations is highly recommended.

3 - The use of dimensionless numbers like π, α (the fine structure constant) or β (the electrostatic to gravitational ratio) is allowed. The same rule applies to simple coefficients or exponents like 2 or ½. The use of complicated numbers like 127y^59α must be justified or ideally avoided. I haven't read about this last rule, but it seems obvious to me.

4 - The assumed relations must comply with observation and ideally could allow some predictions that can be tested. This is part of the scientific process.

Do you agree with those rules?

[Origin]

Do you agree with those rules?

Not really, the important point is to show that the equations actually correspond with a physical phenomena.

[PaulTalbot (OP)]

Not really, the important point is to show that the equations actually correspond with a physical phenomena.

And where does that rule come from?

[Origin]

Not really, the important point is to show that the equations actually correspond with a physical phenomena.

And where does that rule come from?

Common sense?  If the equations don't correspond to something physical then it is just math and not physics.