index $ \def \MET {\quad \mbox{with} \quad} \def \SP {\quad \mbox{;} \quad} \def \hieruit {\quad \Longrightarrow \quad} \def \slechts {\quad \Longleftrightarrow \quad} \def \EN {\quad \mbox{and} \quad} \def \OF {\quad \mbox{or} \quad} \def \half {\frac{1}{2}} $

[ ... ] the galaxies were larger in proportion to their spacings than they are at present. Indeed for $|\tau|$ given by $$ \left(\frac{\tau_0}{\tau}\right)^2 \ge \left(\frac{\mbox{Spacing}}{\mbox{Radius}}\right)_\mbox{Present day} \qquad (38) $$ the galaxies [ on the other side ] were overlapping each other. The right-hand side of equation (38) has an average value of about 300. Let's check that number with help of Wikipedia: Most of the galaxies are 1,000 to 100,000 parsecs in diameter (approximately 3000 to 300,000 light years) and separated by distances on the order of millions of parsecs (or megaparsecs). For comparison, the Milky Way has a diameter of at least 30,000 parsecs (100,000 ly) and is separated from the Andromeda Galaxy, its nearest large neighbor, by 780,000 parsecs (2.5 million ly.) Sticking to the latter we have $780,000 / 30,000 = 26$, which is quite different from Hoyle's $= 300$ estimate. Making this whole exercise difficult to believe. But wait!

From Wikipedia we quote: The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089. This would mean that (see Length Contraction) galaxies certainly were overlapping each other, at least according to Hoyle's theory: $$ \frac{L}{L_0} = \left(\frac{\mbox{Spacing}}{\mbox{Radius}}\right)_\mbox{Present day} = \frac{m_0}{m} = 1+z_i = 1090 $$ However, Hoyle's theory is not ours. The reason is that his

- Larger Intrinsic redshift corresponds with
*younger matter* - Larger TiredLight redshift corresponds with
*older photons*

Now it is obvious that the Cosmic Microwave Background Radiation (CMBR) consists of photons only and has nothing to do with Arp's VPM.
According to *Origins of the CMB*: **young**
photons had much shorter wavelengths with high associated energy, corresponding to a temperature of about 3,000 K.
And with Wikipedia we observe that
the formula relating temperature to redshift is
extremely simple. Using it the other way around we get:
$$
\Theta = 2.725\cdot(1+z) \hieruit \Theta = 2.725 \times 1090 = 2,970.25 \approx 3,000 K
$$
Before going on, let us scrutinize the claim that it would be easy to calculate the current redshift
of the CMB. To me it has become obvious that there is sort of a circular reasoning in there.

When taking Occam's razor into account,
I find, for example, Genesis
far more convincing than the over-complicated story they tell us in even the
Brief History of the Universe, according to nowadays cosmology.
In verse 1:3 it reads:

This is even consistent with modern science, as expressed in the book by [Fahr 2016] at page 157:

A lot of questions may be raised. For example: what assumptions should be made about the original light? An important requirement may be that the light must have been seeable by us. Being observable by the human eye means that these photons should have had wavelengths in the order of, say, light that is emitted by a common light bulb: An electric current heats the filament to typically 2,000 to 3,300 K [ .. ]. Meaning that the abovementioned value of $\Theta \approx 3,000 K$ is quite a reasonable one. Furthermore, it's easily explained now why the CMBR shows such a precise black-body radiation spectrum. No other elementary particles were involved in the beginning than just photons. So what else could the spectrum have been? Imagine the primordial radiation as emanating into a tiny "hole" (eye pupil) from an infinitely large and empty "cavity" i.e. the whole universe.

There is a more rigorous argument, though. According to
Planck's law (Wikipedia)
the spectral radiance of a body for frequency $\,\nu\,$ at absolute temperature $\,\Theta\,$ is given by
$$
B(\nu,\Theta) = \frac{2h\nu^3}{c_0^2}\frac{1}{\exp\left(\frac{h\nu}{k_B\Theta}\right)-1}
$$
where $\,k_B\,$ is the Boltzmann constant, $\,h\,$ is the Planck constant, and $\,c_0\,$ is the speed of light in vacuum.
With varying elementary particle (rest) mass, frequency and temperature are subject to change as explained in our
Support by Hoyle. The other quantities remain constant.
$$
\frac{\nu}{\nu_0} = \frac{\Theta}{\Theta_0} = \frac{m}{m_0} \hieruit \frac{B}{B_0} = \left(\frac{m}{m_0}\right)^3 = (1+z_i)^{-3}
$$
Leading to the important conclusion that *black body radiation is invariant* for varying elementary particle (rest) mass.
More precisely: the magnitude of the spectral radiance may be different, but the shape of its distribution does not change.
Very much the same is expressed by Wien's displacement law ($\lambda=$ wavelength) which turns out to be invariant as well.
$$
x \equiv \frac{h\,c_0}{\lambda_{peak}\,k_B\,\Theta}
\quad \mbox{with } \,x\, \mbox{ as the (dimensionless) solution of} \quad (x-5)\,e^x+5=0 \\ \hieruit
\frac{h\,c_0}{\lambda_{peak}} = x\,k_B\,\Theta \quad \mbox{with} \quad x = 4.965114231744276304
$$
This result is consistent with above text fragments where the CMBR temperature is calculated:
$$
\frac{\Theta_0}{\Theta} = \frac{\lambda}{\lambda_0} = 1+z_i
$$
There is another physical argument, confirming that photons have been created first and stars afterwards. This argument comes
with the fact that a Cosmic clash over Hubble constant shows no sign of abating. Grossly speaking, there are two main competing methods for
determining the Hubble constant. And the two give different outcomes, as has been explored earlier in Hubble tension.

- With help of the CMBR: $H_i = 66.9 \pm 0.6 \; km / s / Mpc$ , giving an age of $29.25$ billion years
- With help of the stars : $H_i = 74.0 \pm 1.4 \; km / s / Mpc$ , giving an age of $26.45$ billion years

From an email: In Narlikar's model, an electron is created with a null mass which increases with its age.
It's easy to see, however, that elementary **rest mass** such as the rest mass of an electron **cannot be zero**. Because,
according to Length Contraction that would result in an infinitely large Bohr radius or electron radius.
Just one hydrogen atom or one elementary particle would fill up the whole universe (so to speak) ! With other words, Narlikar's model
is *singular* for any zero rest mass. And we should know that singularities are impossible in physics - and in mathematics too:
Infinitum **Actu** Non Datur.
Now the only particles *without* a zero rest mass are photons. Therefore it must be concluded that only photons are candidates
for being created in the beginning. And there must have been sort of a *phase transition* for converting photons into the more
"heavy" elementary particles.

That being said, is it indeed possible - in principle - *to create* for example *young electrons from young photons alone*?
The Wikipedia page about Matter creation says: **yes!**
According to the Big Bang theory, in the early universe, mass-less photons and massive fermions would inter-convert freely.
A known physical mechanism for accomplishing this eventually is particle Pair production, maybe a Breit-Wheeler process.
Where a persisting problem is in the *Pair*. No physical mechanism is known yet by which one can make an electron without
its antiparticle the positron. But we are not going to solve every problem that comes on our path instantly. We shall proceed
with small and certain steps that we can take here and now. Let's only check if it is possible *energetically* that one
young electron with mass $\,m_0\,$ here and now may be created from one young photon at wavelength $\,\lambda_{peak}\,$ and
Cosmic Microwave Background Radiation temperature $\,\Theta_0\,$ here and now. An order of magnitude should be sufficient.
With intrinsic redshift and tired light combined then we might have this, with $\,H_i,H_t\,$ as the Hubble parameters for
intrinsic and tired light redshift respectively, $\,t=$ creation time (atomic), $\,t_0=$ here and now timestamp.
Light matter = out of = heavy light:
$$
e^{-H_i(t_0-t)}m_0\,c_0^2 = e^{H_t(t_0-t)}\frac{h\,c_0}{\lambda_{peak}} \hieruit
e^{(H_i+H_t)(t_0-t)} = e^{H_0(t_0-t)} = \frac{m_0\,c_0^2}{x\,k_B\,\Theta_0} \\ \hieruit
t_0-t = \ln\left(\frac{m_0\,c_0^2}{x\,k_B\,\Theta_0}\right)/H_0
$$
Plug in the numbers and calculate with Maple 8:

# 1 megaParsec Mpc := 3.08567758*10^22; # Hubble parameter (2022-02-08) H_0 := 73.4*1000/Mpc; x := 4.965114231744276304; k_B := 1.380649*10^(-23); Theta_0 := 2.725; c_0 := 299792458; m_0 := 9.1093837*10^(-31); ago := ln(m_0*c_0^2/(x*k_B*Theta_0))/H_0; # How long ago in billion years (atomic time) years := ago/31556926/10^9; years := 265.0801755So creation of light electrons out of powerful light might have happened $\approx 265$ billion years ago. Unfortunately, it is not possible to calculate the temperature of the radiation and the mass of an electron at that time, at least not with our theory so far. The reason is that

orbital := 2/H_0*sqrt(x*k_B*Theta_0/(m_0*c_0^2)); orbital/31556926; 7 0.1272665015 10Creation of electrons

We are not finished yet. From C-decay Theories we have $\,m\,c^2=m_0c_0^2\,$ and so: $$ x\,k_B\,\Theta_0 \left(\frac{T_0-A}{T-A}\right)^2 = m\,c^2 \hieruit \Theta = \frac{m_0\,c_0^2}{x\,k_B} $$

Theta := m_0*c_0^2/(x*k_B); 10 Theta := 0.1194312215 10Our primordial temperature should have been a billion Kelvin. In some Brief History of the Universe it is read that the Universe grows and cools until 100 seconds after the Big Bang. The temperature is 1 billion degrees, $10^9$ K. Electrons and positrons annihilate to make more photons [ .. ]. The nice thing about Cosmology Models is that you have so many to choose from (: Andrew S. Tanenbaum).