First. Theory by Amitabha Ghosh and Han de Bruijn (@HanDeBruijn) as summarized in this reply.
Here are published (GitHub/book) formulas linking the Hubble parameter $H$ to a mean mass density $\rho_c$ of the universe.
$$ H = \sqrt{\chi G \rho_c} \quad \mbox{with} \quad \chi = 8\pi \times \begin{cases} 1/8 & (: \mbox{OI}) \ 1/6 & (: \mbox{Mach}) \ 1/3 & (: \Lambda\mbox{CDM}) \ 0.3883945571 & (: \mbox{UAC}) \end{cases} $$
Three of these formulas - (OI) , (Mach) , (UAC) - are for a steady state model (SEU) and only (ΛCDM) is for an expanding universe.
Instance selected:
$$ H = \sqrt{\frac{8}{3}\pi G \rho_c} \qquad (1) $$
where $G=$ gravitational constant.
Second. Tired Light theories by Louis Marmet (@RedshiftDrift) and Lyndon Ashmore (@TiredLyndon) as copied from the STz thread.
$$ H_{STz} = \frac{2}{\pi}\frac{\alpha h^2}{m_e^2 c} n_e(STz) \qquad ; \qquad H_{NTL} = \frac{1}{\pi}\frac{\alpha h^2}{m_e^2 c} n_e(NTL) $$
And so
$$ H_{STz} = H_{NTL} \quad \Longrightarrow \quad n_e(STz) = \frac{1}{2} \times n_e(NTL) $$
Instance selected:
$$ H = \frac{2}{\pi}\frac{\alpha h^2}{m_e^2 c} n_e \qquad (2) $$
where $\alpha=$ fine-structure constant, $h=$ Planck constant, $m_e=$ electron mass, $c=$ speed of light, $n_e=$ electron density.
Third. Theory by Patrick G. Tonin (@PatrGT), Sahil Gupta (@sahil5d) and Robin Booth (@rajbooth). From the Jeans contraction thread:
$$ H_0(Tonin) = \frac{m_e c^2}{h}.\pi.\frac{Gm_p^2}{\hbar c} = \frac{1}{2}.\frac{Gm_p^2m_e c}{\hbar^2} = \frac{1}{2}H_0(Booth) $$
It is seen that the theory by @PatrGT (and @sahil5d too) gives exactly half of the $H_0$ value by @rajbooth.
Instance selected:
$$ H = \frac{G m_p^2 m_e c}{2 \hbar^2} \qquad (3) $$
where $m_p=$ proton mass, $\hbar=h/(2\pi)$ .
Is it possible to reconcile all of the three different theories? Or at least make a unification of well chosen instances out of the three categories?
My attempt
First we need an estimate for the electron density $n_e$. This is done by using the equation (1), more or less along the lines in an STz reply.
$$ n_e = \rho_c/(\tau m_p) = \frac{H^2}{(8/3) \pi G} / (\tau m_p) $$
Here an extra factor $\tau$ is introduced. According to AI >Most of the atoms in the universe are hydrogen and helium. Hydrogen has 1 nucleon (1 proton), and helium has 2 protons and 2 neutrons, for a total of 4 nucleons. The average is closer to 2 when considering all atoms.
Which would make $\tau = 2$, but we decide to let the mathematics go instead by using (2).
$$ H = \frac{2}{\pi}\frac{\alpha h^2}{m_e^2 c} n_e = \frac{2}{\pi}\frac{\alpha h^2}{m_e^2 c} \frac{H^2}{(8/3) \pi G . \tau m_p} $$
$$ 1 = \frac{3\alpha H [h/(2\pi)]^2}{m_e^2 c G.\tau m_p} \quad \Longrightarrow \quad H = \frac{G m_p^2 m_e c}{2\hbar^2}\frac{(2m_e/m_p)}{3\alpha}.\tau = \frac{G m_p^2 m_e c}{2\hbar^2} $$
where the last equality is according to (3). Consequently
$$ \frac{(2m_e/m_p)}{3\alpha}.\tau = 1 \quad \Longrightarrow \quad \tau = \frac{3}{2}\alpha\frac{m_p}{m_e} \approx \frac{3\times 1836}{2\times 137} = 20 $$
Which is not even close to $\tau = 2$ ! This would mean that the redundancy of heavy elements in the universe is, say, ten times higher than commonly assumed. (Making combinations of other instances in the three categories is left as an exercise for the reader)
Hi Han, Thank you for your efforts to link the different theories. The simple way to link Louis’s formula and mine is to postulate the following: electron density = 2 x Universe density / 3 x alpha x electron mass x (proton/electron mass ratio)squared Using formula no7 in my paper for the Universe density, you get a value of 0,279 m-3 With this, all formulas just match nicely and if it is correct it would give us a noval nice formula for the electron density ! Patrick
Alternatively by replacing the universe density by 3xH0squared/8PiG (formula 7), you get electron density = H0 squared / 4 x Pi x alpha x electron mass x (proton/electron mass ratio)squared x G
Thanks Patrick for working that out ! ( I think Louis will be glad with the outcome $\approx 0.279\mbox{ }m^{-3}$ ) Formally:
$$ n_e = \frac{2\rho_c}{3\alpha.m_e.\mu^2} = \frac{H_0^2}{4\pi.\alpha.m_e.\mu^2.G} \quad \mbox{with} \quad \mu = \frac{m_p}{m_e} $$
It looks better like that, thanks Han !
Check, check, double check. Calculations with MAPLE.
Giving for the electron density : $n_e = 0.3010355989\mbox{ }m^{-3}$ 😀
The formula for the dimensionless factor $f$ below is from a reply in the STz thread:
$$ f = \frac{4\sigma}{c}\Theta_{CMB}^4/(n_e.m_e c^2) $$
It is the energy density of the CMB divided by the mass-energy density of electrons in there.
Resulting in : $f = 1.69514234$ .
what is your point ? I don’t know what this f factor is supposed to do …
I know what the “f factor” stands for. May get banned if I spell it out😁 David Hine
Following the equations in my paper, one could also rewrite the above equations as follows, giving a fairly precise value for the electron density without involving H0
$$ n_e = \frac{m_e.\pi^3.\mu^2.G}{c^2.\alpha.\lambda_e^4} = 0.279 \mbox{ }m^{-3}$$
@RedshiftDrift , any thoughts on this ?
I submitted a paper, 48 days ago, which has not been reviewed yet… I think they are having problems finding reviewers who know something about quantum mechanics, plasma physics and astrophysics. (They even asked me, by mistake, to review my own paper! 🤣 🤣 )
Except for NTL, every other theory uses the gravitational constant $G$, which indicates that they are derived from some sort of relativistic time-variations of space (expansion) or other physical parameters. Therefore, they cannot be reconciled with with STz and NTL since they have a different physical basis. A numerical agreement does not mean ‘reconciliation’!
In my paper (I’ll post it when it is accepted) I propose a number density $n_e$ derived from optical physics, without any link to gravity since STz redshift is an optical effect.
$$ n_e = 2\pi \lambda_e \big[ 2\pi\zeta(3) \big]^{4/3} \ \left( \frac{k_B T_{CMB}}{hc} \right)^4 = 0.29089 \pm 0.00024 \mbox{/m}^3, $$
where $\zeta(3) = 1.2020569…$, and the uncertainty is defined by the uncertainty on the optical measurement of $T_{CMB} = 2.72548 \pm 0.00057 \mbox{ K}$. (This is a refined version of the reply in the STz thread mentioned by @HanDeBruijn). It follows from the physics that $T_{CMB}$ is defined by $n_e$, so if we could measure $n_e$ precisely, we could calculate $T_{CMB}$.
This is close to your exact values, but $n_e$ differs by an amount larger than the uncertainty I quote.
Inserting this value of $n_e$ in the equations given in arXiv:2410.02036 gives the Hubble constant
$$ \mathcal H_0 = c\Sigma_z n_e = 73.59 \pm 0.06 \mbox{ km/s/Mpc}, $$
where $\Sigma_z \equiv 2\alpha \lambda_e^2/\pi$ is the STz cross-section. Indeed, this does settle the Hubble tension in favour of the so-called “late universe” value.
P.S. Advertisement: any volunteer to review my paper? I can suggest you as a reviewer for the journal Galaxies. P.P.S. I must have another look at your paper @PatrGT re. the value of $n_e$…
@RedshiftDrift Good luck, Louis! Galaxies is a good choice I think. I submitted there once and had a mostly fair treatment from them. 48 days seems like a long time to be sitting there. I wonder if your abstract is a bit too technical and scaring reviewers away.
@RedshiftDrift maybe you could try https://www.qeios.com/ or https://prereview.org/en-us for reviews I also recommend https://arxiv.org/abs/2504.03424 https://arxiv.org/abs/2509.15453 https://arxiv.org/abs/2509.06917 Those are for feedback not publishing except somewhat qeios. For publishing not ideal but maybe mdpi.
Hi Louis. I think you have selected me in error regarding your paper about Hubble’s Constant being published. I am the guy that submitted (on the GitHub A Cosmology Group) a novel way of calculating Ho by using a simple equation:-
2 x one Mpc x C, divided by Pi to the power of 21 = 70.94 k/s/Mpc
For this equation oneMpc is 3260000 light years C is 299792.458 k/s Pi is 3.142…………
I also sent a screenshot of an online calculator displaying the equation, which I attach, and is safe to open
The post number allocated to my post on the “A cosmology Group Forum” is # 337.
My name is David Hine and my email is:- @.***
I will be happy to help you if I can, but I am purely an interested amateur in cosmology, and know only the “old school” way of doing algebra. The SI system is almost unknown to me and makes little to no sense. My equation is NOT accepted as the way to find Ho, but it works, with no errors in its “old school” algebra maths format. Please let me know if I can help you in any way. With very kind regards, and VERY good luck with getting your Hubble paper peer read and published !!. Please let me know how you get on with your Hubble paper, and please stay in touch. David Hine. P. S. I normally get banned from places when I present my equation, and so far, NONE of the reasons for banning that Ho equation makes any sense to me at all. I partly blame the SI system of maths, because it’s almost impossible with SI to “knowingly or not knowingly” mix up and confuse the algebra maths proceedure in cosmology equations (due to the large numbers), so giving false answers. On Sunday 17 August 2025 at 16:13:55 BST, Louis Marmet @.***> wrote:
I submitted a paper, 48 days ago, which has not been reviewed yet… I think they are having problems finding reviewers who know something about quantum mechanics, plasma physics and astrophysics. (They even asked me, by mistake, to review my own paper! 🤣 🤣 )
Except for NTL, every other theory uses the gravitational constant $G$ , which indicates that they are derived from some sort of relativistic time-variations of space (expansion) or other physical parameters. Therefore, they cannot be reconciled with with STz and NTL since they have a different physical basis. A numerical agreement does not mean ‘reconciliation’!
In my paper (I’ll post it when it is accepted) I propose a number density $n_e$ derived from optical physics, without any link to gravity since STz redshift is an optical effect.
$$n_e = 2\pi \lambda_e \big[ 2\pi\zeta(3) \big]^{4/3} \ \left( \frac{k_B T_{CMB}}{hc} \right)^4 = 0.29089 \pm 0.00024 \mbox{/m}^3,$$
where $\zeta(3) = 1.2020569…$ , and the uncertainty is defined by the uncertainty on the optical measurement of $T_{CMB} = 2.72548 \pm 0.00057 \mbox{ K}$ . (This is a refined version of the reply in the STz thread mentioned by @HanDeBruijn). It follows from the physics that $T_{CMB}$ is defined by $n_e$ , so if we could measure $n_e$ precisely, we could calculate $T_{CMB}$ .
This is close to your exact values, but $n_e$ differs by an amount larger than the uncertainty I quote.
Inserting this value of $n_e$ in the equations given in arXiv:2410.02036 gives the Hubble constant
$$\mathcal H_0 = c\Sigma_z n_e = 73.59 \pm 0.06 \mbox{ km/s/Mpc},$$
where $\Sigma_z \equiv 2\alpha \lambda_e^2/\pi$ is the STz cross-section. Indeed, this does settle the Hubble tension in favour of the so-called “late universe” value.
P.S. Advertisement: any volunteer to review my paper? I can suggest you as a reviewer for the journal Galaxies. P.P.S. I must have another look at your paper @PatrGT re. the value of $n_e$ …
— Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you commented.Message ID: @.***>
Hi Matt and Louis. Often in ground breaking theoretical physics it often takes a very long time for new approaches to be appreciated. Entreched mindsets, planned agendas and scientific establishments do not like being challenged, especially by those who operate independently and carve their own path. As Matt said, “that could be scaring “over cautious” reviewers away“. Anyway, dear Louis, don’t let anyone succeed in derailing your new paper, and all the best stuff in cosmology has its roots in the “abstract”!! With very kind regards and respect to Matt and Louis, David Hine. On Monday 18 August 2025 at 16:39:26 BST, Matt Edwards @.***> wrote:
@RedshiftDrift Good luck, Louis! Galaxies is a good choice I think. I submitted there once and had a mostly fair treatment from them. 48 days seems like a long time to be sitting there. I wonder if your abstract is a bit too technical and scaring reviewers away.
— Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you commented.Message ID: @.***>
It’s been frustrating, but now I see: the Hubble Tension is part of my Theory !!
References are
I should have known this for a long time. In Tired Light (TL) theories, such as the Stimulated Transfer redshift (STz) theory by @RedshiftDrift, the Hubble parameter can be precisely calculated. I thought that the same should be done with the Variable Mass Theory. With VM, however, there is a relationship between the Hubble parameter $H$ and an Age $A$. In combination with Arp’s findings this his means that the Hubble parameter $H$ can be - and shall be - different for different physical phenomena and/or objects. Mathematically:
$$ H = \frac{2}{A} \quad \mbox{or} \quad A = \frac{2}{H} $$
An obvious example of the tension is in the age of the earth and the age of the universe, whatever the latter might mean.
By the way, the Variable Mass Theory (Han) is in concordance with the Time Dilated Past hypothesis by @mikehelland (Mike), apart from what’s in a name ( $\tau \leftrightarrow T$ ) and
$$ \large 1+H\tau = e^{Ht} \quad \mbox{(: Mike)} \qquad ; \qquad 1+\frac{H}{2}T = e^{\frac{H}{2}t}\quad \mbox{(: Han)} $$
Here is an update about calculating Ho, the Hubble Horizon Distance and the cosmology reason causing the “Hubble Tension iassue”, assuming the Ho readings are accurate:-
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Hubble Constant (Ho) fixed to light speed, C and calculated as 71 k/s/Mpc
My name is David Hine, and here is an interesting Hubble Constant equation that “fixes” Ho to local light speed, C.
Ho is now “fixed” to local light speed, C by this simple Ho equation worked in the old algebra style of Maxwell:-
Astronomers measuring Ho give the “ballpark” values of Ho, and now we have an Ho equation that “fixes” Ho to local light speed, C, which has to be much more precise.
Note:- In the numerator, distance (Mpc) is multiplied by speed (k/s), and that is NOT an error in this situation, as the “distance squared” does not affect the numerical value of the Ho redshift by “spreading out” (as any light source does) when viewing that redshift for Ho along just one dimension only.
The dimensionless denominator Pi^21 sets the scales of this Ho equation correctly into the Dynamic Aether framework. The Dynamic Aether Framework is not the static aether that the Michleson-Morley experiment could not detect, but the Dynamic Aether that Faraday knew caused electrical “reluctance”, and that Maxwell used for his electric and magnetic “inertia” constants used in his equations to calculate light speed. C..
In this equation, directly input the values below:-
oneMPC is 3260000 light years
C (local) is 299792.458 k/s
Pi is 3.142……….
With very kind regards, David Hine.
Email:- dhine2999@yahoo.com
=============================================================================================
Note:- This Hubble Horizon Distance equation prevents falsifying the terminology by declaring light years as years only.
In this equation, directly input the values below:-
one Mpc is 3260000 light years
C (local) is 299792.458 k/s
One billion is 1,000,000,000 light years, used to give the answer in convenient units of billions of light years.
===========================================================================================
Note:- In the “Dynamic Aether Framework” of the Ho calculating equation in which Ho is “fixed” numerically to C, the “Hubble Tension issue” is caused by the LOCAL VALUE of C in the observed space regions being directly affected by the presence of huge galaxies, black holes. or void areas, RELATIVE to the observer.
One idea that may be gaining traction is to solve the Hubble Tension/Crisis is that primordial magnetic fields present in the pre-recombination plasma “would generate baryon inhomogeneities and speed up the recombination process, bringing the CMB-deduced value of H0 closer to that found from distance ladders.”
Nature Astronomy https://www.nature.com/articles/s41550-025-02737-x https://arxiv.org/abs/2503.09599
Even with fancy MHD simulations and MCMC runs, they were only able to increase the value of the Hubble constant to H0 = 70.0 km/s/Mpc ± 1%, still far from the correct value 73.59 km/s/Mpc.