Latest revision 31-10-2022

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

## Let there be light

We shall continue now with the review of the paper that has been our main source in Support by Hoyle.
[ ... ] 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 Radius and Spacing are associated with Empty Space: Length Contraction is not applicable to the vacuum. According to Van Flandern this redshift is associated with a Hubble volume which is larger than the observable universe of the Big Bang theory. Which does not represent a problem, though, for a cosmos that is infinite in space and (atomic) time: $$D = \ln(1090)\;c_0/H_i \approx 7 \times \mbox{ Hubble radius}$$ A Cosmology Group tells us much more: there is a Tired Light section in the webpage. The Tired Light hypothesis seems to give rise to the same formulas as the Hypothesis by Arp. However, that is just at first sight. One crucial difference lies in the fact that light does not carry any rest mass; a Varying elementary Particle rest Mass (VPM) does not exist for light; Halton Arp's theory is not applicable to photons. And the Tired Light hypothesis is is not applicable to matter. Actually, the two phenomena are each other's opposites:
• Larger Intrinsic redshift corresponds with younger matter
• Larger TiredLight redshift corresponds with older photons
A second difference may be even more important, though. Photons may become redshifted at the source, due to Halton Arp's intrinsic redshift. But after this, they become redshifted even further by Tired Light, before reaching the eye of an observer on earth. Both redshift are being employed, separately, as an explanation of the Hubble process. Maybe they should be used in combination instead. In Narlikar's Law the following formula was encountered for the Total redshift: $$(1+z)=(1+z_{expansion})(1+z_{intrinsic})$$ We have decided to (ab)use this Ansatz for our own purpose as: $$(1+z_{\,Total})=(1+z_{\,Intrinsic})(1+z_{\,TiredLight})(1+z_{\,Classical})$$ Total redshift is conjectured to be the product of classical Redshifts such as (relativistic) Doppler, gravitational - but definitely NOT cosmological - and intrinsic / tired light redshift. If we stick to the latter two, then we have, with accompanying Hubble parameters according to Van Flandern: $$1+z = (1+z_i)(1+z_t) = e^{H_i D/c_0}\,e^{H_t D/c_0} = e^{(H_i+H_t) D/c_0} = e^{H_0 D/c_0} \\ \hieruit H_0 = H_i + H_t$$ The Hubble parameter as 0bserved could be the sum of an intrinsic and a tired light component.

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:

### And God said: "Let there be light", and there was light.

As simple as that! According to a literal interpretation of the Bible: in the beginning photons were created, out of nothing. Just created, and if you wish: without a Creator.
This is even consistent with modern science, as expressed in the book by [Fahr 2016] at page 157: Ein weiteres Mysterium bei der konventionellen Erklärung des CMB-Hintergrundes verbirgt sich in dem heute damit verbundenen Zahlenverhältnis von CMB-Photonen zu Baryonen (Protonen). Die Zahl der CMB-Photonen ist nämlich erheblich viel größer als die Zahl der Protonen, obwohl die Ersteren aus den Letzteren und ihren Antiteilchen dereinst einmal duch Annihilationsprozesse herforgegangen sein wollen.[ .. ] With help of Google translate: Another mystery in the conventional explanation of the CMB background is hidden in the numerical ratio of CMB photons to baryons (protons) associated with it today. The number of CMB photons is considerably larger than the number of protons, although the former are claimed to have emerged from the latter and their antiparticles through annihilation processes.

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
Let intrinsic redshift be assumed all over the place. Then the age is calculated from the Hubble according to a simple formula in Van Flandern, namely: age $= 2/H_i$. Hence we see that the CMBR is older than the stars. Apart from those billion years, at least the order of occurrence is in agreement with the Biblical account: photons first, protons, neutrons and electrons (i.e. star building material) afterwards.

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 := 265.0801755

So 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 only the sum of the intrinsic and tired light Hubble parameters $\,H_i+H_t = H_0\,$ is (supposed to be) known.
Orbital. Suppose that it is nevertheless admissable to (ab)use a formula from Van Flandern, namely $\,H_i(T_0-A)=2\,$. Then derivation proceeds with Milne's Formula, assuming that the latter is allowed for $\,H_0\,$ as well - as Milne himself would have agreed with. $$H_i(t-t_0) = \ln\left(\frac{x\,k_B\,\Theta_0}{m_0\,c_0^2}\right) = H_i(T_0-A)\ln\left(\frac{T-A}{T_0-A}\right) = \ln\left[\left(\frac{T-A}{T_0-A}\right)^2\right] \\ \hieruit \frac{T-A}{T_0-A} = \sqrt{\frac{x\,k_B\,\Theta_0}{m_0\,c_0^2}}$$
orbital := 2/H_0*sqrt(x*k_B*Theta_0/(m_0*c_0^2));
orbital/31556926;
7
0.1272665015 10

Creation of electrons in orbital time should have taken place say one million years after some big or little "Bang" at Alpha.
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 10

Our 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).