Archived project

# A Simpler Cosmology: Milne's Model

Goal: In 1935 Edward Arthur Milne published "Relativity, Gravitation, and World Structure" In the front cover of this book, you can see in plain language that he has predicted "A background of finite intensity." i.e. the Cosmic Background Radiation.

For whatever reason, though, modern cosmologists dismiss his model as a toy, or claim that it models an empty universe.

For the last few years, I have been trying to defend Milne's model. However, I've found that at least some moderated sites do not allow discussion of Milne's model, and will delete any post related to the topic as "Original Research".

My hope is that Researchgate does allow such discussion. I suppose I'll soon find out.

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## Project log

Cosmological General Relativity invokes Newton's Shell Theorem about a point of asymmetric contributions to Gravitational field in order to obtain an "observer dependent" gravitational field at every point in the universe. This paper shows the derivation of Newton's Shell Theorem and attempts to explain why, in an infinite distribution, a point of symmetry should be chosen where ρ/L²=ρ/R² is a function of R alone. The point of symmetry chosen must be the point where the gravitational field is actually being calculated. Furthermore, I present another calculation of the gravitational field using cartesian coordinates, but this method comes to g=(0,0,0), when a point of symmetry about the origin is selected.
The introduction of this text includes links to a number of demonstrations related to the Special Theory of Relativity created on "desmos calculator". There are also links to demonstrations of the cosmological distributions that are solutions to differential equations presented in Susskind's Cosmology Lecture 2. I have been posting this text as attachments in ResearchGate threads, but I decided to put it up as a "presentation" so that it can be found more easily.
This paper discusses why Milne's Model is not "empty" as many claim, but rather, has a negligible Gravitational Potential when compared to its Kinetic Energy content. There are two 1+1 spacetime diagram of the universe. The first imagines several phase transitions of the universe. In regards to the CMBR, the most important of these is the phase change from "Blackbody Spectrum" hydrogen to transparent hydrogen. An exaggerated diagram shows how the dipole anisotropy in the CMBR arises. Section 5 discuss how this model can account for the presence of redshift z=11 galaxies at 40 billion light-years away by using the concept of "peel-off-layers." Section 6 addresses potential concerns that peel-off-layers might be Lorentz variant.
https://en.wikipedia.org/wiki/Shape_of_the_universe discounts Milne's model, saying it is " It is incompatible with observations that definitely rule out such a large negative spatial curvature." What the article fails to acknowledge, though, is that the "negative spatial curvature" term in Friedmann Equations resolves to the equation "Distance = Velocity * Time". This statement is equivalent to the beginning of Newton's First Law: "An object in motion remains in motion at a constant speed". This law can only be made "large" or "small" in reference to phenomena that cause objects to accelerate (Gravitational Potential: Omega_M type phenomena), or cause distance to appear between objects due to some other effect other than velocity (deSitter; Omega_\Lambda type phenomena). However, recent observations of distant quasar groups have led to calculations of densities much greater than those predicted by the Lambda-CDM model. I posit that the most important feature, lacking in the Lambda-CDM model is acknowledgment that the primary cause of redshift is, in fact, neither gravitational, nor deSitter stretching of space, but the effect of an equipartition of radial rapidity, and the effect that equipartition has on densities of objects obeying "distance = velocity * time" which contemporary cosmologists inexplicably call "negative curvature"
Two exact solutions to the Friedmann equations are frequently mentioned. One is called a matter-dominated universe, where pressure = 0 which resolves to a(t) ∝ t ^2/3. I In the radiation dominated universe, p = 1 3 ρc^ 2 , and this resolves to a(t) ∝ t 1/2. I would like to introduce a third solution, which has the universe dominated by Kinetic Energy. In particular, what do we need to plug into the Friedmann equations for ρ, Λ and p to represent a universe where Kinetic Energy dominates, and the gravitational potential energy is relatively negligible?
I have been arguing for some time that cosmological inflation can be explained easily via Special Relativity. Just yesterday, it occurred to me how to estimate exactly what temperatures were needed to account for it. In this paper I imagine the end of the primordial universe, as the primordial gas reaches an age of 370,000 years, in a universe with a 25 billion light year radius. The time dilation factor is 68,000, and this can be achieved by a gas at a temperature of 1570 trillion Kelvin.
In my question on the transparency of diatomic hydrogen in the universe,
I was directed by George Dishman on May 6, toward a text by Farahjabeen Islam.
On reading some of the relevant sections, I found myself puzzled about
where some of the numbers were coming from. The text cited Dyson and Williams
"The Physics of Interstellar Medium" but upon closer look at the source, I found
that the content was describing the formation of a "typical molecule" rather than
the formation, specifically of diatomic hydrogen. Furthermore, there was no
information given about where the numbers were coming from in the
text by Dyson and Williams.
Most of the ideas presented in Dyson and Williams text were, I think, meant to
focus more on the process of what-needs-to-be-figured in order to establish
whether a diatomic molecule can survive in interstellar space. Although exact
values of several parameters are given, I don't think the authors intended for
those values to be taken literally.
One value given, was the flux of ultraviolet radiation, at 10 billion ultraviolet
photons per second, per square meter, per nanometer. At first I thought this
sounded like a lot, but on further calculation, it turned out, that 10 billion
ultraviolet photons at each nanometer of wavelength from 120 to 190 nanometers
would only result in about 10 microWatts of energy per square meter.
I found, assuming the total radiation flux from the sun at earth, is 1370 Watts
then the ultraviolet radiation at wavelengths less that 190 nanometers is
about 1.26 Watts per square meter.
With a inverse distance squared law, I calculated that to have the intensity
of radiation given by Dyson and Williams, one would need to be 369 Astronomical
Units from the Sun, which is well within the minimum radius usually given
for the Oort Cloud.
The minimum radius often offered for the oort cloud, being about 5000 AU, is where
one ought to calculate the maximum amount of ultraviolet radiation which diatomic
hydrogen in the interstellar medium is exposed. (Since this is the region where diatomic
hydrogen would ordinarily form.)
With a value of 5000 AU from the sun, I found that we should expect the amount of
one percent of the mean flux of ultraviolet radiation expected by Dyson and Williams.
I have posted a video that shows some of my concerns and goes through the
calculations in more detail.
Thanks,
Jonathan Doolin

I'm thinking that the canonical partition function would
be a good tool to estimate the relative concentration
of diatomic, monatomic, and ionized hydrogen, in any system
where you have a gas/plasma in thermal equilibrium
Calculations could be made for a gas at 1 million Kelvin,
such as the conditions in the corona of the sun,
or at 5800 Kelvin
such as the conditions in the photosphere of the sun.
The following was originally posted at:
====================
The use of the canonical partition function gives an estimate, of the proportions.
In the corona, we can get a very rough estimate by pretending there are two species
(1) Free electrons and protons, with chemical potential 0 per e/p pair (2) Ground state monatomic hydrogen with chemical potential     of -13.6 eV per e/p pair
The partition function is
Z = \Sigma e^-(\mu/(k_b T))
where \mu is the chemical potential of each species.
k_b is boltzmann's constant = 1.38x10^-23 Joules per Kelvin = 8.63x10^-5 eV/mol Kelvin.  So when T = 1,000,000 Kelvin, k_b T = 86.3 eV.
Z = e^-(-13.6/86.3) + e^(0)   = 1.17 + 1 = 2.17
In this case the proportions of diatomic to P(monatomic hydrogen) = 1.17/2.17 = 53.9% P(ionized hydrogen) = 1/2.17 = 46.1%
If we wanted to account for diatomic hydrogen as well, I'd say (1) Free electrons and protons, with chemical potention of 0 per e/p pairs. (2) Ground state monatomic hydrogen with chemical potential of -13.6 eV per e/p pair (3) (half portions of) Ground state diatomic hydrogen with chemical potential of -13.6 eV - 1/2 (4.74 eV) = 16 eV
Z = e^(16/86.3)+e^(13.6/86.3) + e^(0)
= 1.20 + 1.17 + 1 = 3.37 Portion by mass (diatomic hydrogen) = 1.2/3.37 = 35.6% Portion by mass (monatomic hydrogen) = 1.17/3.37 = 34.7% Portion by mass (ionised electron/proton pairs) = 29.7%
===============================
This should give a rough prediction of how much diatomic hydrogen
should be present in the part of the corona which is 1 million Kelvin.
Many other issues would affect this, though, such as how much
hydrogen becomes attached to other elements in the photosphere,
and how many particles of the photosphere are traveling through
on convection currents, which are not part of a system
in thermal equilibrium.