It looks like a paper but it’s rather a printable - and hopefully readable - article about a well-defined part of our VM theory. In two formats: see comment below. Thus preventing this thread floating to the top with every minor change in contents.
ABSTRACT
This paper is the third one in a series of articles about the Variable Mass theory. Earlier publications in the VM series are: 1. Atomic Time, Orbital Time and the Variable Mass Theory and 2. The Variable Mass Theory and Gravitational Paradoxes. The main content of the first two papers is supposed to be more or less familiar to the reader. Length Contraction is a feature of Variable Mass. It will be argued that Length Contraction with VM is observationally equivalent with the expansion of Empty Space. In this way a couple of mathematical tools that are useful for our theory can be outsourced to the (nowadays common) expanding universe model. Conditions are investigated for which a Static Euclidean Universe has a radius larger than the Schwarzschild Radius. We find that a SEU with constant non-zero mean mass density can only exist if it is finite. As Variable Mass is entering the stage, the playground becomes completely different. Especially relevant is the discovery of an Observability function $f_O(x)$ . Giving rise to an Observable Universe, which more lucidly may be called a Black Hole Bubble, because it moves through cosmos along with the observer in its center. A value for the radius of the Black Hole Bubble is calculated. This value is reasonably close to the radius of the Observable universe as accepted by the mainstream. A solution for Olbers’ paradox is given. Especially for a universe without a Big Bang it is desperately needed. It turns out that there is an absolute maximum of 28.5 for the intrinsic cosmological redshift. The paper is finished with a value for the MOND acceleration which is unique for VM.
Comments are quite welcome !! I am prepared to change contents in the article accordingly.
HTML and PDF: paper_3.pdf , up to date 2026-08-15.
The paper will be published eventually on viXra too. The viXra version can NOT always be made up to date.You had this ‘disclaimer’ in paper II as well, I’m just wondering:
I don’t understand exactly what you are trying to say. If the universe is infinite, how can it not contain everything? Is this because you talk about “potential infinity” (sort of like Leibniz) rather than “completed infinity” (e.g. Cantor)?
This seems very metaphysical. Which I don’t find to be a problem.
I put forward for discussion that the “universe was a bad idea”:
There’s nothing too inherently wrong with the “universe” idea, but it very much muddies the basic concepts with which we are to assemble reality as we know it, in an academic capacity.
In a physics context, things have masses, relative positions and momenta (velocities). Does the Universe have these properties? Not in any meaningful way to us. So the Universe shouldn’t be considered a thing like normal physical things.
It seems to me that if you carry that line of thought into the metaphysical, then the Universe doesn’t exist the way normal things exist. If anything, the Universe is just a nickname for existence itself.
IOW. Things that exist, belong to the set of things that exist. Does the set of things that exist belong to itself?
@RedshiftDrift , @mikehelland . >Is this because you talk about “potential infinity” (sort of like Leibniz) rather than “completed infinity” (e.g. Cantor)?
Exactly !! Infinitum Actu Non Datur.
@RedshiftDrift .
From the last update in section 6 of the paper we quote.
Resulting in $\rho_c \approx 8.1\times 10^{-27} kg/m^3$, corresponding with $\approx 5/m^3$ hydrogen atoms. Which is not very deviant from mainstream results. How does this compare with an electron density of 0.3 for STz (and 0.5 for NTL) ? Aren’t your electrons bound to (hydrogen) atoms ? Or do you assume that common matter is only 10% of all matter ? With other words: does Tired Light implicitly assume Dark Matter ?
STz predicts a free electron density $n_e = 0.29/m^3$. At $T = 6$ GK, electrons are not bound to anything; they are free. Plasma physics predicts that the IGM is mostly neutral, so for protons $n_p = 0.29/m^3$ and $\rho \approx 4.6\times 10^{-28} \ kg/m^3$.
However, these protons are likely accompanied by heavier nuclei such as helium and others. If, for example, we have 75% protons and 25% ${\rm He}^{++}$, then five electrons are associated with three protons plus one alpha particle, for a total mass of about 7 times the proton, or $\rho \approx 6.5\times 10^{-28} \ kg/m^3$. I don’t know the ratio between the various nuclei, that’s a nuclear physics calculation I can’t do accurately. If there are heavier nuclei, then that mass-density will increase a little, but not above $\rho < 10^{-27} \ kg/m^3$.
There are also some cold regions of the IGM where hydrogen is not ionized. This produces absorption seen as the Lyman-alpha forest on the spectrum of quasars. I don’t have the exact values for that, but the density of neutral hydrogen is probably around $0.1/m^3$, so a mass density $\rho_{HI} < 1.6\times 10^{-28} \ kg/m^3$. (@tiredlyndon would be able to give a more accurate value from his 2015 paper.)
Therefore, STz predicts a slightly higher number density than interpreted by mainstream from observations, which claims that the “average density of ordinary matter in the Universe is believed to be 0.2–0.25 atoms per cubic metre”. STz does not need dark matter nor dark energy.
The following section has been deleted from the last version.
Cosmological Quantities
Values for the Hubble parameter are copied from (9) and (10) in the current publication [3].
$$ H = \sqrt{w.8\pi\mbox{ }G\rho_c} \quad \mbox{with} \quad w=0.3883945571 \quad \Longrightarrow \quad \rho_c = \frac{H^2/w}{8\pi\mbox{ }G} $$
MAPLE calculation:
Resulting in $\rho_c \approx 8.1\times 10^{-27} kg/m^3$, corresponding with $\approx 5$ hydrogen atoms $m^{-3}$. Which is not very deviant from mainstream outcomes. It is possible to calculate for the total mass of our Observable universe as well, with (5), (8), (9) and (10) in mind.
$$ M_O = \int_0^{R_O} \rho_c e^{-H/c.r} 4\pi r^2.dr = \left(\frac{c}{H}\right)^3 4\pi\rho_c \int_0^W e^{-\xi} \xi^2.d\xi $$
$$ = \left(\frac{c}{H}\right)^3 4\pi\rho_c \left[-e^{-\xi}(\xi^2+2\xi+2)\right]_{\xi=0}^W = \left(\frac{c}{H}\right)^3 4\pi\rho_c \frac{2-e^{-W}(W^2+2W+2)}{W}.W $$
$$ = \left(\frac{c}{H}\right)^3 4\pi\rho_c\mbox{ }f_O(W).W = \left(\frac{c}{H}\right)^3 \frac{H^2}{2wG} . wW $$
$$ M_O = \frac{c^3W}{2GH} $$
Resuming our MAPLE calculation:
Giving $M_O \approx 3.0 \times 10^{53}\mbox{ }kg\mbox{ }$, which is twice the magnitude as found on the internet as $\approx 1.5 \times 10^{53}\mbox{ }kg\mbox{ }$.
Attention is paid to the MOND theory by Mordehai Milgrom. Quote from the original paper: tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration - below an acceleration constant $a_0$ [ .. ]. It is found that $a_0\approx (1.2\pm 0.2)\times 10^{-10}\mbox{ }m\mbox{ }s^{-2}$. It has been pointed out from the very advent of MOND [ .. ] that this is a cosmologically significant acceleration. We have the near equalities
$$ \mbox{[ .. ]}\quad 2\pi\mbox{ }a_0\approx cH_0\quad\mbox{[ .. ]} $$
Back to our own theory. Using the formulas (3), (11) and the one for $M_O$ above we subsequently have
$$ R_O = \frac{2GM_O}{c^2} \quad ; \quad R_O = W\frac{c}{H} \quad ; \quad M_O = \frac{c^3W}{2GH} $$
The above formulas are mutually consistent, because
$$ M_O = \frac{c^2R_O}{2G} = \frac{c^2}{2G}.W\frac{c}{H} = \frac{c^3W}{2GH} $$
Next we calculate the acceleration $a_0$ in an orbit at the horizon of our Observable universe.
$$ a_0 = \frac{M_O\mbox{ }G}{R_O^2} = G\frac{c^3W}{2GH}.\left(\frac{H}{c.W}\right)^2 = \frac{Hc}{2W} $$
Bearing in mind that [ .. ] while being in the MOND regime implies $\mbox{ }MG/R^2\lesssim a_0\mbox{ }$. Now imagine that there are hypothetical observers at our dimensionless $x=W$ coordinate, corresponding with the maximum $w$ of the Observability function according to (9). The Cosmological principle then says that quantities that are measurable in principle at our horizon are measurable as well at their horizon. The latter is precisely the place where we are ourselves. This ensures that, for example, a minimal acceleration in cosmos is universally valid. It will be conjectured by now that our $a_0$ is precisely the MOND $a_0$. As far as I know, the following possibilities - except the last one - have been proposed.
$$ a_0 = Hc \times \begin{cases} 1/6 & \approx 0.16667 \ 1/(2\pi) & \approx 0.15915 \ 1/(2W) & \approx 0.14777 \end{cases} $$
Suppose that we want to calculate the age $(-T_O)$ of stars at the edge of our Observable universe. That age must be expressed, of course, in Orbital Time, because the age of the universe in Atomic time is simply eternal. Employing Narlikar’s Law as formulated with (10) in [1] we get an outcome that is consistent with the age of the universe according to (11) in [1].
$$ \left[1+\frac{1}{2}H T\right]^2 = \frac{m}{m_0} = e^{H t} \quad ; \quad 1+\frac{1}{2}H(-T_O) = \sqrt{e^{-H/c.R_O}} = \sqrt{e^{-W}} $$
$$ T_O = 2\left(1-e^{-W/2}\right)\times\frac{1}{H} \quad \Longrightarrow \quad \mbox{age} \approx 1.63 \times \mbox{(Hubble time)} \lt \frac{2}{H} $$
References
Interesting calculation Louis, “average density of ordinary matter in the Universe is believed to be 0.2–0.25 atoms per cubic metre”https://en.wikipedia.org/wiki/Friedmann_equations#Density_parameter. STz does not need dark matter nor dark energy. Beyond me, but was this calculation done assuming the universe was expanding and the BB is correct? Just a thought Lyndon
From: Louis Marmet @.> Sent: 27 June 2026 04:23 To: a-cosmology-group/acg @.> Cc: tiredlyndon @.>; Mention @.> Subject: Re: [a-cosmology-group/acg] Variable Mass Theory and Observable Universe (Discussion #377)
STz predicts a free electron density $n_e = 0.29/m^3$. At $T = 6$ GK, electrons are not bound to anything; they are free. Plasma physics predicts that the IGM is mostly neutral, so for protons $n_p = 0.29/m^3$ and $\rho \approx 4.6\times 10^{-28} \ kg/m^3$.
However, these protons are likely accompanied by heavier nuclei such as helium and others. If, for example, we have 75% protons and 25% ${\rm He}^{++}$, then five electrons are associated with three protons plus one alpha particle, for a total mass of about 7 times the proton, or $\rho \approx 6.5\times 10^{-28} \ kg/m^3$. I don’t know the ratio between the various nuclei, that’s a nuclear physics calculation I can’t do accurately. If there are heavier nuclei, then that mass-density will increase a little, but not above $\rho < 10^{-27} \ kg/m^3$.
There are also some cold regions of the IGM where hydrogen is not ionized. This produces absorption seen as the Lyman-alpha forest on the spectrum of quasars. I don’t have the exact values for that, but the density of neutral hydrogen is probably around $0.1/m^3$, so a mass density $\rho_{HI} < 1.6\times 10^{-28} \ kg/m^3$. @.***https://github.com/tiredlyndon would be able to give a more accurate value from his 2015 paper.)
Therefore, STz predicts a slightly higher number density than interpreted by mainstream from observations, which claims that the “average density of ordinary matter in the Universe is believed to be 0.2–0.25 atoms per cubic metre”https://en.wikipedia.org/wiki/Friedmann_equations#Density_parameter. STz does not need dark matter nor dark energy.
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Not so much interesting - in my humble opinion - rather annoying instead: mean mass densities differ a factor of 10, depending on the Gravitational XOR Optical approach, even for a Static Euclidean Universe. And I have no idea how to reconcile these two world views.
Yes the number comes from the Big Bang model, the link’s name is revealing: “Friedmann_equations#Density_parameter”.
The reason I requested your assistance is because you published a paper where you count absorption bands by H I clouds in the Ly-alpha forest of quasars as a function of redshift.
With that absorption and the number of clouds, can you get an average column density for H I ?
@HanDeBruijn you write:
but how is the Hubble constant you define as $H = \sqrt{w.8\pi\mbox{ }G\rho_c}$ actually obtained from observations? What is the meaning of $\rho_c$ in that equation? Is it only the the density of matter or could it include the gravitational potential energy of all interacting galaxies? Depending on how the variables you use are interpreted, there may be a way to reconcile these values…
@RedshiftDrift .
Two elaborate heuristics/derivations of the $H^2 \sim \rho_c$ relationship are presented in a new document:
HTML and PDF: paper_3a.pdf , up to date 2026-07-13.
Another - primitive - heuristic is found in section 3, preceding (4) of the current paper and from there proceeding to (10). It’s purely theoretical, not from observations. These are formulas for the mean mass density, not for the Hubble constant.
$$ H^2 = \frac{4}{3}\pi.G.\rho_c \quad ; \quad H^2 = \frac{8}{3}\pi.G.\rho_c \quad ; \quad H^2 = w.8\pi.G.\rho_c \quad ; \quad w=0.3883945571 $$
I find it typical that Einsteinian derivations consequently give double (e.g. 8 vs. 4) the results of Newtonian derivations. Fortunately, the $\rho_c$ factor cancels out in calculations that I consider the most important, but the question still stands: >What is the meaning of $\rho_c$ in that equation? Is it only the the density of matter or could it include the gravitational potential energy of all interacting galaxies? Depending on how the variables you use are interpreted, there may be a way to reconcile these values…
@HanDeBruijn
So $\rho_c$ is the mean baryonic mass density. You treat the potential energy separately. Then, for the variable mass to vary sufficiently rapidly to match $H_0$, you need a higher value of $\rho_c$.
But you write “It seems to be wise to anyway not identify under all circumstances our $H$ with the common $H_0$” and then write somewhere else [edited] “This means that the Hubble parameter is business as usual, namely $H \equiv H_0$”.
Your annoying “factor of 10” may just be because you haven’t formally decided what causes the variable mass! Is it only the baryonic mass in the universe?
You also reach the well known conclusion that the total energy content of the universe is nil. But this is actually not verified observationally, unless dark matter is added. Does dark matter help VM to get rid of the factor of 10?
P.S. Your numbering is mixed up; the website have sections 1, 2, and 2, with references as sec. 5(!)
@RedshiftDrift . >P.S. Your numbering is mixed up; the website have sections 1, 2, and 2, with references as sec. 5(!)
Thanks !! I’ve made the necessary corrections. Thanks too for the well known link.
P.S. Your write somewhere else link is mixed up. It must refer to paper_3b instead of paper_1.
Hi Louis, Thanks for the link to the paper. Wow! 40 quid to access one of Lyndon’s papers! Coming up in the world. That paper was referring to the original paper I presented at the CCC2 conference (I enjoyed it there) 2009 and published in the ASP proceedings file:///C:/Users/lyndo/Downloads/413-0003%20(2).pdf Long time ago. Not sure it will give you what you are looking for. I will have a think. But the point I was making, is that this density of matter is a prediction of the BB model (not an observation) and so even if you got this number what does it prove? Since we don’t believe in the BB and consequently any prediction it makes. Lyndon
From: Louis Marmet @.> Sent: 29 June 2026 20:08 To: a-cosmology-group/acg @.> Cc: tiredlyndon @.>; Mention @.> Subject: Re: [a-cosmology-group/acg] Variable Mass Theory and Observable Universe (Discussion #377)
was this calculation done assuming the universe was expanding and the BB is correct? - @tiredlyndonhttps://github.com/tiredlyndon
Yes the number comes from the Big Bang model, the link’s name is revealing: “Friedmann_equations#Density_parameter”.
The reason I requested your assistance is because you published a paperhttps://doi.org/10.1142/9789814719063_0046 where you count absorption bands by H I clouds in the Ly-alpha forest of quasars as a function of redshift.
With that absorption and the number of clouds, can you get an average column density for H I ?
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Yes, CCC-2 was a long time ago, and it was very enjoyable. I had forgotten that your paper was about hydrogen cloud separation since when I talked with you, I was more interested in understanding NTL. For those who’d like to read it, Lyndon’s paper is here https://aspbooks.org/a/volumes/article_details/?paper_id=30535 (the link to your computer drive isn’t accessible :laughing:) Indeed, in that paper you count the hydrogen clouds and discuss their separation, but there is no estimate of the H I column density in each cloud. So the number I’m looking for is not explicit.
The BB number doesn’t prove anything, agreed, I’m just mentioning this to @HanDeBruijn to show that from the same observations, the model we use to analyze data can give different numbers. (Although a factor of ten is starting to be difficult to explain.
I’m sorry, but I don’t really see how your Variable Mass Theory works as a solution. To me, it doesn’t look like Variable Mass so much as Expanding Mass. So instead of Expanding Space, it seems like you’re proposing Expanding Mass. But then why wouldn’t photons also have mass increase? Photons would become more energetic, and any “expanded mass JWST” couldn’t detect any photon shift at all.
So I’m afraid I can’t get behind the De Brujin Expanding Mass Theory. And if your response is going to be that photons don’t have mass, only energy, then I’d ask why is your theory only Expanding Mass without Expanding Energy? And if your answer is that photons are a conveniently privileged exception where their energy doesn’t expand, then I would say bon voyage.
@ericcosmos . >I don’t really see how your Variable Mass Theory works as a solution.
Of course you don’t. Because it requires properties that you (and many others here) do not seem to have: curiosity in the first place.
That sentence alone proves that you didn’t even have a brief glimpse through my article.
That theory does not exist. And the author does not exist either. Oh Lord, please help me to keep my big mouth shut until I know what I am talking about.
Same to you. And next time I will think twice.
Who wrote this? I’m just curious.
I wrote this and it’s wrong. Thank you for noticing !!