An example of the failure of Plasma Cosmology

[Hans Blaster]

If you read the hysterical response to your post at EU central you might to want change your assessment from "stubborn refusal to comprehend the paradox" to "incapable of comprehending the paradox."

He literally does not understand the statement he quoted. I suppose that's what happens when you're in a fog bank so thick that there are water droplets in every direction.

I think I'd rather go back to talking about scattering...

 

[SelfSim]

Is Olber's still gumming up their works over there???

For goodness sake, we went through all that > 2 years ago (after 18 pages and 340 posts, and beyond here .. and also on the Supernova 1a/static universe topic here which even went across multiple sites, IIRC) .. and yet not a single thing has changed!?

Sorry to see Hans copping a traditional nasty serving over at E-lusions Anonymous!

(I wouldn't hold out for any better treatment when it comes to the scattering topic either!?)

 

[Hans Blaster]

Is Olber's still gumming up their works over there???

For goodness sake, we went through all that > 2 years ago (after 18 pages and 340 posts, and beyond here .. and also on the Supernova 1a/static universe topic here which even went across multiple sites, IIRC) .. and yet not a single thing has changed!?

Sorry to see Hans copping a traditional nasty serving over at E-lusions Anonymous!

(I wouldn't hold out for any better treatment when it comes to the scattering topic either!?)

I can handle it, I'm a big boy. I only read their site for my amusement. They are so silly. They had a link to that SN Ia thread a week ago or so, and looked through it then. I spent several hours deconstructing the paper that triggered the OP in the thread, but it all got buried by a stupid discussion of Olbers' paradox. Sigh.

Olbers' paradox is something that gets covered in 5-15 minutes in a lecture on the early attempts to apply rigor to cosmology. It's a *very* simple exercise.

 

[sjastro]

I can handle it, I'm a big boy. I only read their site for my amusement. They are so silly. They had a link to that SN Ia thread a week ago or so, and looked through it then. I spent several hours deconstructing the paper that triggered the OP in the thread, but it all got buried by a stupid discussion of Olbers' paradox. Sigh.

Olbers' paradox is something that gets covered in 5-15 minutes in a lecture on the early attempts to apply rigor to cosmology. It's a *very* simple exercise.

I recall doing cosmology as an extension of general relativity as a unit in applied mathematics.
Olbers' paradox was briefly covered from a historical perspective, very simple maths and easy to grasp.

 

[sjastro]

I’ve updated the summary table for this thread to include Olbers’ paradox.
Since both mainstream and PC predict the surface brightness is constant in a static universe instead of the histrionic nonsense thrown up at EU central the table reflects this.

 

[Hans Blaster]

Can we "fake" redshift with scattering?

OK, I said I'd get back to this...

There is a notion among some pseudoscience communities that scattering can cause a redshift. (The other major "alternative theory" is something called tired light, where I guess photons just wear down and drop in energy as they propagate or some such nonsense.)

Before we get to that we have to be sure to clarify the difference between...

Reddening versus redshift:

Both are things change the shape and apparent "color" of the spectrum, but they are fundamentally different.

Reddening occurs when blue (or bluer, or higher energy) photons are preferentially scattered out of the light beam or absorbed relative to redder (lower energy photons). For example interstellar dust absorbs light more readily at shorter wavelengths than longer wavelengths so a star behind some dust looks redder as well as generally dimmer than an identical star at the same distance not behind some dust. Reddening changes the shape of the continuum, but does not shift the wavelengths of the spectral lines *at all*.

This is different than redshift, which doesn't change the shape of the continuum or the relative positions of the lines within that continuum, but the *position* of the spectrum is shifted to the red for the continuum and lines in the same fashion by changing the apparent wavelengths.

Next: What is scattering?

 

[sjastro]

The “Theory of Everything” serves as an example of another failure in Plasma Cosmology which is unable to explain the production of protons and neutrons in the universe by examining a preliminary process, the electroweak interaction or force highlighted in the diagram.

The electroweak force is the unification of the electromagnetic and weak forces.
This was experimentally confirmed in particle accelerators in the 1980s.
To gain an understanding of how these forces unify is to consider the opposite case, how the unified force splits into its constituent forces.

The potential of a scalar field is defined by considering the simplest case; Newtonian gravity.
The gravitational scalar potential ϕ is defined as ϕ = -Gm/r.
The gravitational potential is the amount of work required to move a point mass m from infinity to some point r in the gravitational field.
The potential energy V is the value of ϕ at r and is defined as V = mϕ.
Hence V = V(ϕ), the potential energy is a function of the potential ϕ.

In general however fields are much more complicated and are of the form V(ϕ, T….) = -(1/2)m²ϕ² + (1/4)λϕ⁴ + (1/8)λT²ϕ² +……. where T is the temperature of the universe and λ is a constant.
Furthermore these fields can exist in a state of unstable equilibrium like balancing a chair on one leg where the slightest disturbance can cause the chair to move to a more stable equilibrium by balancing on all four legs.

The electroweak field existed in an unstable equilibrium in the early universe and while the maths is complicated and beyond the scope of this thread it can be explained by the Mexican hat potential defined by the formula;
V(ϕ) = -10|ϕ²| + |ϕ⁴|

The scalar potential field of the electroweak force can be visualized by a ball precariously balanced on top of a Mexican hat.

Since the ball is on the central axis of the hat the system is in a symmetrical state.
A perturbation applied to the Mexican hat will cause the ball to drop from a higher to a lower potential into the brim of the hat.
Individually the ball and Mexican hat are still in a symmetrical state but the ball plus Mexican hat is not.
The Mexican hat analogy suggests a geometrical interpretation of symmetry but the mathematics or physics definition of symmetry is when a property remains invariant under a transformation.
For example the electric field around a charge remains the same if the field is rotated at any angle around any axis of rotation.
In this case the electric field is said to have a U(1) symmetry.

The electroweak force of U(1) X SU(2) symmetry is said to have undergone spontaneous symmetry breaking into the separate electromagnetic and weak forces which have a U(1) and SU(2) symmetry respectively.
The number of bosons or force carriers depends on the the number of elements in the U(n) or SU(n) matrix and is defined as U(n) = n² and SU(n) = n² - 1
U(1) = 1 is the photon γ for the electromagnetic force and SU(2) = 3 are W⁺, W⁻ and Z⁰ bosons for the weak force.
The weak force interacts with the Higgs field and gives the W⁺, W⁻ and Z⁰ bosons their masses; the electromagnetic force on the other hand does not interact with the Higgs field and γ is a boson of zero mass.

The perturbation can be a change in temperature.
At energies below E ≈ 1 TeV the temperature becomes low enough for symmetry breaking of the electroweak force.
This is known as a phase transition and is analogous to the phase transition when steam bubbles are formed in water at a given temperature.
The phase transition of the electroweak force is a preliminary step to the production of protons and neutrons as the universe becomes cooler, which on further cooling leads to the production of the primordial elements hydrogen, helium and lithium via nucleosynthesis.

While GUT symmetry breaking is well beyond the energy range of particle accelerators to be tested, the discovery of electroweak symmetry breaking supports Big Bang cosmology.
In Plasma cosmology phase transitions are impossible as the universe can never attain the high temperatures for the transitions to occur once the universe begins to cool.
Plasma cosmology offers no explanation for proton and neutron production.

 

[sjastro]

Here is another example where Plasma cosmology is contradicted by particle physics involving magnetic monopoles.
Magnetic monopoles provide the link between electromagnetism, GUT and Big Bang cosmology.

While classical physics forbids the existence of magnetic monopoles (Gauss’s law for magnetism, Maxwell’s equations), the development of quantum mechanics has changed this.
Dirac (who proposed the existence of antimatter) in the early days of Quantum Field Theory suggested the quantization of electric charge could be due to the existence of a magnetic monopole with magnetic charge gₘ = 0.5hcn/e ≈ 68.5en where h is Planck’s constant, c the speed of light, e the electric charge and n is an unspecified integer.
This would modify Maxwell’s equations rendering them symmetrical with respect to both electric and magnetic source terms.
A single monopole in the universe would result in electric charge being quantized but the converse is not necessarily true.

A motivating factor for the development of GUTs is the standard model of particle physics cannot answer a fundamental question; why is the magnitude of the charge for protons and electrons equal?
The electroweak interaction is a unification of the electromagnetic and weak forces and has been confirmed in experiments; GUT’s are the unification of the strong and electroweak forces.

Modern day consensus indicates an increasing acceptance of magnetic monopoles among particle physicists given most GUTs predict their existence as illustrated in this model.

The structure of a magnetic monopole according to GUT is a core populated by X and Y leptoquark bosons which are surrounded by a layer of W and Z bosons at a radius of about 10⁻¹⁶cm.​

Beyond this is a confinement region based on an unusual property of the confinement of quarks.
Whereas the strength of the electromagnetic force and weak force (at short distances only since the W and Z bosons have short lifetimes) follows an inverse square law, the strong force between quarks and gluons (g bosons) remains constant with increasing distance.
This is due to the separation energy instead of pulling quarks and gluons apart is converted to create quark/antiquark pairs.
This has been confirmed in particle accelerator tests where individual quarks are not observed but jets of mesons which are bosons and contain a quark/antiquark pair.

The existence of magnetic monopoles poses serious problems for particle physics, astrophysics and cosmology.
Magnetic monopoles are extremely massive with a lower mass limit of around 9 GeV/c² which would require particle accelerators of at least 10¹⁶ GeV centre of mass energy to be created.
The most powerful particle accelerator currently available is the LHC with a centre of mass energy of 14 x 10³ GeV.
In non mainstream theories involving a higher number of dimensions such as the Kaluza-Klein or superstring theory, lighter magnetic monopole masses are predicted and should be created in current particle accelerators.
The other option is to detect magnetic monopoles.
If magnetic monopoles exist then Maxwell’s equations become symmetrical in which case a magnetic monopole passing through a wire coil unlike a dipole should be able to induce a current.
These should be detectable in superconducting loops where the current is long lived.
In astrophysics superheavy magnetic monopoles should accumulate in the cores of stars where they can collide with protons.
Some protons may penetrate the W and Z boson layer and collide with an X virtual leptoquark boson which converts the d quark in the proton according to the reaction.
d + X → e+ where e+ is a positron.
Hence magnetic monopoles would destroy hadronic (protons and neutrons) matter at a faster rate than its natural decay and change the time scale for the evolution of the Universe.
From a cosmological perspective at the time of the GUT epoch when the strong and electroweak forces were unified and magnetic monopoles formed, the Universe had a particle horizon volume of ≈(2 x 10⁻²⁹m)³.
Even if there was only 1 magnetic monopole per 10 particle horizon volumes at the GUT epoch, the density of magnetic monopoles today assuming the Universe expanded at a linear rate is 0.1 x ((2 x 10⁻²⁹m) x (4.4 x 10²⁷))⁻³ ≈ 150m⁻³
The current density parameter for mass is Ωₘ = 0.27; including the magnetic monopole number density of 150m⁻³ with an average mass of 9 GeV/c² results in Ωₘ ≈ 2.8 x 10¹⁷.
This enormous value would not only negate the effects of expansion but cause the Universe to collapse under gravity in the ridiculously small time scale t = π/2H₀ Ωₘ ≈ 40 years where H₀ is Hubble’s constant.

Particle physicists who have made the transition to cosmology such as Alan Guth and Andre Linde have applied quantum field theory in the form of an Inflaton field where a false vacuum state in the field decays to a lower state through quantum tunnelling driving inflation and resulting in an exponential expansion of the early Universe.
With the discovery of the Higgs boson some theorists have speculated the Inflaton field is the Higgs field.
This exponential expansion resulted in a single magnetic monopole occupying a considerably larger particle horizon volume and negligible current monopole number densities too low to be detected or impact on stellar formation and the current value of Ωₘ.
Not only did inflation resolve the problems in particle physics, astrophysics and cosmology, but also the flatness and horizon problems in Big Bang cosmology.

As shown in my previous post Plasma cosmology is incompatible with particle physics as temperatures are too low for particle physics processes such as the unification of the electromagnetic and weak forces to naturally occur.
If magnetic monopoles exist the situation is even worse as the lack of space-time expansion exacerbates the problems in particle physics, astrophysics and cosmology as mentioned previously.

 

[sjastro]

In a previous post it was shown Plasma Cosmology is incompatible with nuclear physics as it cannot explain the existence of cosmic chronometers in an infinitely old universe.
Similarly it incompatible at the smaller time scales of particle physics such as being unable to explain how free neutrons which have a half life of 15 minutes have “enough time” to form nuclei.
As a result Plasma Cosmology offers no explanation for the evolution of elements in the universe.

Big Bang Cosmology has no such compatibility issues with particle physics as the important link between the two is the reaction rate of any particle physics process Γ must be greater than the Hubble expansion rate H.
Γ/H > 1
Using the half life of the neutron as an example; if the Hubble expansion rate is higher, the cosmological time t is greater in which case the bulk of neutrons have already decayed before the formation of deuteron (deuterium nuclei) with protons.
The reaction rate Γ depends on temperature T which in turn depends on expansion of the universe which cools the universe down.
In the radiation era of the early Big Bang illustrated in the table below when neutrons first formed the temperature scales as T².
Depending on how the particle physics process temperature scales determines the temperature range when the process can occur in the universe.
For example the electroweak interaction which ultimately leads to the creation of neutrons as illustrated in post #107 scales as T⁵.
Since Γ/H > 1
T⁵/T² = T³
Hence Γ > T³H is the condition for which the electroweak interaction can occur in the universe.

Since Plasma Cosmology is a static model there is no temperature scaling with expansion and as demonstrated in post #107 the temperature is too low for the interaction to occur.

 

[sjastro]

The problems Plasma cosmology has with the CMB (Cosmic Microwave Background) have been covered in earlier posts.
The Alfven-Klein model doesn’t predict it, the Eddington version is not a blackbody, Robitaille’s version is pure nonsense and Lerner’s model predicts circular polarization of CMB photons which is not observed.
The CMB is an almost perfect blackbody but exhibits very slight anisotropy due to temperature fluctuations of around ΔT = 18 μK.
These temperature fluctuations are due to regions of over and under density of the CMB.
Lerner’s model is the nearest to something that resembles a CMB but fails to predict these small scale temperature variations which are shown as mottled regions in the Planck satellite image.
The red central region is our galaxy.

The CMB is analogous to “background noise”.
In this case the “background noise” is a combination of signals at various frequencies.
Mathematically this can be shown by decomposing the signal intensity amplitudes in the time domain to amplitudes in the frequency domain using Fourier analysis.
The data is expressed as a function sₙ(x) which is a linear combination of sinusoidal functions at their respective frequencies and is of the form;

The CMB data is projected onto a celestial sphere in which case the anisotropic structure can be decomposed into separate images using spherical harmonics and multipole expansion.
Multipole expansion of the function f(θ,φ) involves expressing the CMB data as a sum of spherical harmonic functions involving the mode number l which defines the angular scale where the smaller the number the larger the angular scale.
The function f(θ,φ) is of the form;

Cₗͫ are coefficients where Cₒ⁰ is a monopole, C⁻¹ₗ, C⁰ₗ, C¹ₗ, are the dipoles and Y(θ,φ)ₗͫ is the harmonic function.
For the l = 0 monopole, the angular scale is 360⁰ which corresponds to the average temperature of the CMB of T = 2.73 K which produces a featureless image.

​

The l = 1 dipole the angular scale is 180⁰ and is caused by the motion of our galaxy relative to the CMB.
In the direction of motion the CMB is Doppler shifted to the blue and slightly warmer, in the opposite 180⁰ direction the CMB is redshifted and slightly colder.
The temperature difference ΔT = 3.35 mK.

​

The l = 2 quadrupole reveals the temperature fluctuations at smaller scales where ΔT = 18 μK.

For l ≥ 2 the equation relating angular scale θ to l is given by the equation.
θ ≈ 60⁰/l
Plotting the multipole number for l ≥ 2 and angular scale θ against the temperature fluctuations produces a power spectrum.

The major peak near 1º and the two smaller peaks are acoustic peaks which cannot be explained by any Plasma cosmology model.

The acoustic peaks represent regions of over density of the CMB where there is a concentration of baryonic and dark matter.
The CMB photons are coupled to the baryonic matter as they are in thermal equilibrium due to Compton (Thomson) scattering of photons by electrons.
The scattering interaction rate is;
Γ = nₑσₑc
Where nₑ is the electron number density, σₑ is the scattering cross section and represents the probability of scattering; c is the speed of light.
As long as Γ > H where H is the Hubble expansion rate of the universe, the photons remain coupled.
Since photons of wavelength λ carry momentum p according to the equation p = h/λ they can exchange momentum when scattered by electrons and as a result can exert radiation pressure.
Over density regions will try to collapse under gravity but are prevented by the radiation pressure which causes an overshoot before trying to collapse again.

This results in an acoustic oscillation as shown in the diagram where the photons are represented as springs and the potential wells are regions of stronger gravity where the in falling baryonic matter represented as balls overshoot due to the radiation pressure.
Dark matter which does not interact with photons is unaffected by radiation pressure.

These acoustic oscillations can be heard by converting and amplifying the CMB signal and gradually stop when the condition Γ = H is met when the photons start to decouple during the reioinization era.

Needless to say Plasma cosmology cannot explain these sounds.

​

 

[sjastro]

Redshifting of gravitational waves is another issue that contradicts Plasma Cosmology.

Redshift calculations are straightforward for electromagnetic radiation; one measures the photon wavelength in the observer’s frame of reference λ₀ such as the Hα line in the spectrum of a distant galaxy.
The next step is to measure the photon wavelength value of the Hα line λ (=656.3nm) in its rest frame such as in the Balmer series of the laboratory hydrogen spectrum.
λ₀ = (1+z)λ where z is the cosmological redshift.

Determining the cosmological redshift of a gravitational wave is anything but straightforward.
Firstly we don’t have the benefit of a catalogue of gravitational wave laboratory spectra that serves as our rest frame.
The inability of determining the frequencies of the gravitational waves in a rest frame is due to a degeneracy issue which will be made clear a little later on.
We need to define the effective mass of a binary system to understand how the redshift of a gravitational wave is calculated.
Intuitively one might think this is simply the sum of the masses of the neutron stars or black holes making up the binary system but it is somewhat more complicated.
We are interested in the mass-energy of the binary system which also includes the energy contribution from the gravitational waves.

The effective mass or “chirp mass” Ϻ for a binary system is the equation;

m₁ and m₂ are the masses of the neutron stars or black holes, f and f(dot) is the gravitational wave frequency and the rate of change of the frequency respectively.
Since Ϻ is a function of frequency, Ϻ can be redshifted to a value Ϻ₀ according to the formula.
Ϻ₀ = (1+z)Ϻ
Note the similarity of the equation to that involving photon wavelength.

The gravitational wave frequency data from LIGO and VIRGO should allow us to calculate z.
Here lies the problem; while Ϻ₀ is measured from the data, Ϻ is unknown and z cannot be calculated.
This problem is known as the M, Z degeneracy.

For neutron star mergers, the solution to finding Ϻ involves using physics similar to what describes ocean tides.
The neutron stars orbit around a centre of mass, the gravitational pull is greater on each component on the side that is closest to the centre of mass.
This tidal field deforms each component and affects the gravitational waveform in the high frequency range.
The tidal field deformation is specifically a property of Ϻ.
Hence from the gravitational waveform, Ϻ can be calculated using the high frequency components during the inspiral stage as illustrated in the diagram.
While the diagram is for black hole mergers, the inspiral stage for neutron star mergers is similar.

If you want to subject yourself to a full blown assault on the subject here is the paper.
https://arxiv.org/pdf/1312.1862.pdf

The opportunity of comparing the redshift of a gravitational wave with the redshift of a hydrogen line came with the detection of the multimessanger event GW170817 which was the merger of two neutron stars.
Unlike black hole mergers, neutron star mergers produce short gamma ray bursts which allow the merger to be accurately pinpointed.
In this case the gamma ray burst emanated from the galaxy NGC 4993 the redshift of which is already known.
The redshift of the gravitational wave and NGC 4993 should roughly be the same.

Unfortunately the discovery came during the O2 run before the gravitational wave detectors were upgraded for improved sensitivity.
GW170817 did not resolve the degeneracy issue as the detectors at this stage were not sufficiently sensitive to accurately measure the frequency components due to the high noise levels.

At this stage Christopher Berry from LIGO chipped in with some valuable advice.
In the above equation for chirp mass Ϻ, the neutron star masses m₁, m₂ are constrained to a narrow range and I could use Ϻ as an approximation by using the average neutron star mass value for the calculation of z including the peculiar velocity or Doppler shift of the binary for a more accurate calculation.
From PRL paper on GW170817 Ϻ₀= 1.1977 solar masses from the data and the approximate value of Ϻ = 1.188 solar masses.
Using the formula Ϻ₀ = (1+z)Ϻ and substituting in these values, the redshift for GW170817 is found to be z=0.0082 without taking Doppler shift into account.
From the SIMBAD astronomical database NGC 4993 has a redshift z=0.009787.

The succeeding run O3 utilizing more sensitive detectors have allowed the high frequency components to be directly measured resulting in more refined values for the gravitational wave redshift.

How does Plasma Cosmology compare?
In a static Universe Ϻ₀ and Ϻ have the same value which results in z = 0 for every case.
Furthermore gravitational waves do not interact directly with matter hence their redshift cannot be explained by scattering which is yet another (indirect) reason why a tired light mechanism doesn’t work.

 

[sjastro]

From my previous post;

The neutron stars orbit around a centre of mass, the gravitational pull is greater on each component on the side that is closest to the centre of mass.
This tidal field deforms each component and affects the gravitational waveform in the high frequency range.

To expand on this comment GR predicts gravitational waves which have a quadrupole symmetry as explained here.
They are not produced by spinning objects which have a spherical symmetry.
A sphere spinning on its axis cannot produce gravitational waves where as the same spinning sphere when squashed does as it has a quadrupole symmetry.

When binary spinning neutron stars orbit around a centre of gravity in the early inspiral stage they are a sufficient distance apart to have spherical symmetry.
At this stage the gravitational waves are only produced through the loss of orbital energy as the neutron stars spiral into each other.
When the neutron stars get closer tidal forces distort the neutron stars prior to merging.
The spinning neutron stars which are no longer spherically symmetrical also contribute to gravitational waves.

The process is illustrated in this video.

In the late inspiral stage the gravitational waveform for neutron star mergers should be slightly different to the waveform of “rigid” objects such as spinning black hole binaries.

This difference would be detected in the O3 run.
Christopher Berry has sent me a message stating this was unduly optimistic.
So I stand corrected which shows the advantages of having a direct contact at LIGO.
While the noise levels have been reduced and the S/N ratio increased, the detectors were still not sufficiently sensitive to pick up the differences in the only definite neutron binary merger discovery for the O3 run GW190425.
According to Chris the low number of gravitational wave announcements involving neutron star mergers during the uncompleted O3 run was consistent with the theoretical detection rate.

Theoretical detection rate per year.

BNS- Binary neutron stars; NSBH:- Neutron star black hole; BBH:- Binary black holes.
H:- LIGO Hanford; L:- LIGO Livingston; V:- Virgo; K:-Kagra.

We will have to wait until the O4 run to see if further improvements in detector sensitivity will hopefully detect the effect of tidal forces.

So at this stage the redshift of gravitational waves is still based on theoretical values rather than direct measurement.