I don't think such an explanation would work. We have a clear temperature maximum at around 2.725 K, corresponding to a redshift of z=1089. This means that the original temperature was 1089 times higher, which would indeed be the surface temperature of some smaller stars. But where have they gone? A star with a surface temperature of about 3000 K has a lifetime well beyond that of the current age of the universe.

So what would the hypothesis require? It would require that we had a massive collection of stars at the correct distance and that that collection would have disappeared after. (As we do not see them anymore.) Moreover, the density of stars closer to us would have to be much lower than the density that created the cosmic microwave background. For we do not see a contiuous background at higher temperatures, i.e. from stars closer to us and with lower redshift. What would be the explanation of such an inhomogenous distribution of stars?

There have been attempts to explain the cosmic microwave background in other cosmological models, such as the steady-state universe. These explanations (e.g. absorption by cosmic dust, iron needles) all had quantitative difficulties in the end. The idea that explains the observations best in quantitative terms (even though it was published before observation of the CMB) is that of the big bang, leading to a radiation-dominated phase of the universe, long before any stars could form, of which we see the remnants today.

It should also be pointed out that Mach's ideas most likely were incorrect. Our current theory of gravitation, general relativity, is a local theory, although it has some Machian effects. (But it has a clear notion of rotation in empty space, which Mach would deny.)

I don't think such an explanation would work. We have a clear temperature maximum at around 2.725 K, corresponding to a redshift of z=1089. This means that the original temperature was 1089 times higher, which would indeed be the surface temperature of some smaller stars. But where have they gone? A star with a surface temperature of about 3000 K has a lifetime well beyond that of the current age of the universe.

So what would the hypothesis require? It would require that we had a massive collection of stars at the correct distance and that that collection would have disappeared after. (As we do not see them anymore.) Moreover, the density of stars closer to us would have to be much lower than the density that created the cosmic microwave background. For we do not see a contiuous background at higher temperatures, i.e. from stars closer to us and with lower redshift. What would be the explanation of such an inhomogenous distribution of stars?

There have been attempts to explain the cosmic microwave background in other cosmological models, such as the steady-state universe. These explanations (e.g. absorption by cosmic dust, iron needles) all had quantitative difficulties in the end. The idea that explains the observations best in quantitative terms (even though it was published before observation of the CMB) is that of the big bang, leading to a radiation-dominated phase of the universe, long before any stars could form, of which we see the remnants today.

It should also be pointed out that Mach's ideas most likely were incorrect. Our current theory of gravitation, general relativity, is a local theory, although it has some Machian effects. (But it has a clear notion of rotation in empty space, which Mach would deny.)

The spectrum of the CMB is the Planck curve to within less than 10 parts per million. No individual star achieves that, and stars have different temperatures. The average stellar spectrum can be seen in the spectra of galaxies. The attached illustration shows how a range of stellar spectra contribute to the nearly flat curve seen in typical galaxies, the CMB would have the shape of just one of those component lines.

Dear Johan,

No, the starlight is not related with cosmic microwave background (CMB).

The CMB was the most important discovery made for sustain the present cosmology. Its origin was due to decoupling between matter and radiation which has allowed the atomic formation. This happens around 100.000 years later the Big Bang starting and was hypothesised by Gamow in 1948 for first time. Penzias and Wilson measured it in 1964 for earning the Nobel Prize of Physics in 1978 for it.

In 1992 the NASA obtained interesting data of the CMB showing its anisotropy which has been related with the formation of the Galaxies and other structures for the first time ( the team awarded the Nobel Prize of Physics in 2006 for such discovery)

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 397, no. 2, p. 420-429.

Finally the CMB fits perfectly within the General Relativity for the solution associated to FLRW metric in one expansive model following the Hubble's law.

K. Kassner: "Moreover, the density of stars closer to us would have to be much lower than the density that created the cosmic microwave background."

Dear K.,

I understand H. W. Olbers on the basis of homogeneous (!) star density expected by far the largest contribution of sky illumination from the most distant stars, see reference below, but he erroneously expected them to appear similarly bright as our sun. He couldn't know some 200 years ago that those remote stars due to redshift appear dimmer to such extent that they cannot be perceived by our eyes.

https://en.wikipedia.org/wiki/Olbers%27_paradox

GD: "The average stellar spectrum can be seen in the spectra of galaxies."

Dear George,

your above statement doesn't fit to the current discussion. Continued: You don't consider that in the Olbers model the largest contribution comes from redshifted light of more distant galaxies. The contribution increases with increasing distance. The task will be to integrate redshifted contributions over very large distances and volumes, and compare resulting profile with Planck curve.

DB: "The CMB was the most important discovery made for sustain the present cosmology."

Dear Daniel,

thanks for reviewing current theories on cosmology and related Nobel awards.

No, redshifted starlight won't work. First, you have to realize that "starlight" is itself a whole spectrum of radiation that would be smeared out rather than confinable to a single "temperature" as was the primordial fireball radiation. Starlight is neither homogeneous nor isotropic and would produce greater departures from the mean than observed of the CMB. The CMB is locatable in time whereas starlight is not.

Dear Johan,

One thing is to keep an electromagnetic radiation in a cavity, as Olbers thought in a finite static Universe, where the radiation of stars is obviously important and another very different is to have a remaining radiation no coupled to matter (CMB). Among other things the stars radiation ( not only starlight)works only since the stars were formed, which obviously depends strongly of what model of Universe you use. Nowadays is not easy to denied the explanations of the Big Bang theory, although there are many admirable theories trying to supplant it, but I all that I know there are a relevant (or less) importance for the matter distribution effects on local rotation as Mach principle says. How do you relate the CMB with Mach?

DB: "How do you relate the CMB with Mach?"

Dear Daniel,

I understand Mach recognized remote masses rather than nearby ones as most relevant for local appearance of inertia, and similarly did James C. Keith with his high-speed rotor experiment. I recently suggested that even luminal speed c might be related to remote masses, see reference below. Apparently, the Olbers model also points to the predominant significance of remote sources.

In present physics discussion possible local influences from remote sources are obviously neglected in favour of the Big Bang hypothesis.

https://www.researchgate.net/post/Is_speed_of_light_basically_limited_by_local_cumulative_gravitational_potential_originating_from_remote_masses_of_the_universe?

Hi Johan,

JKF: your above statement doesn't fit to the current discussion.

It is highly pertinent, you cannot assume that all stars have exactly the same spectrum, they vary widely in temperature.

JKF: You don't consider that in the Olbers model the largest contribution comes from redshifted light of more distant galaxies.

In a universe which is infinitely old and infinite in spatial extent but also includes cosmological redshift (such as from tired light), then what we would see would be the typical galaxy spectrum nearby marged with redshifted versions of that for more distant sources.

JKF: The contribution increases with increasing distance.

The number of galaxies in a thin shell at radius r is proportional to r2, but the luminosity is proportional to r-2 so the total contribution per shell would be constant excluding "relativistic beaming". Including the latter, more distant sources would contribute less to the total flux. In addition, although galaxies are mostly empty, there will be some shadowing of distant by nearby but that is a small effect. It would add an exponential term to the integral but over immense distances.

JKF: The task will be to integrate redshifted contributions over very large distances and volumes,

Take the galaxy curve and extend it towards the infra red end. You would get an almost perfect flat line with a slow fall at the low end.

JKF: and compare resulting profile with Planck curve.

The spectrum for even a single galaxy is far too flat and integrating it flattens it farther. The only way to get the Planck curve (which is shown several time on the graphic I posted) would be if every star in the universe had exactly the same temperature and there was no redshift to smear it out, but then all stars would have to be at 2.725K and that is obviously wrong.

Dear Johan,

I don't see the relationship between CMB and Mach principle. Let me go step by step

J> I understand Mach recognized remote masses rather than nearby ones as most relevant for local appearance of inertia, and similarly did James C. Keith with his high-speed rotor experiment

Yes, Mach was trying to explain the origin of the inertial mass as the outcome of the gravitational interaction of the rest of bodies of the Universe. However, as even Einstein recognizes soon after its formulation of General Relativity, Mach’s principle is not followed by his theory and all the rest of gravational theories have failed to do it too. Amongst those Brans Dicke theory and Hoyle Narlikar theory are most notable, but no mention know about James C. Keith for showing anything respect to these Mach's theories. And less to the CMB issue.

J> I recently suggested that even luminal speed c might be related to remote masses, see reference below. Apparently, the Olbers model also points to the predominant significance of remote sources

It is clear that the Olbers "model" is not necessary at all in an expanding Universe as the Big Bang one and the relationship between light transport associated to the gravitational potential (if I have understood it well) is clearly wrong. The gravitational potential depends with the inverse of the distance and therefore the very far bodies haven't any importance and on other hand, from this approach, gravitation follows Gauss law which screens the rest of sourrounding massas action provided we have spherical symmetries as it is assumed in Cosmology.

GD: "The number of galaxies in a thin shell at radius r is proportional to r2, but the luminosity is proportional to r-2 so the total contribution per shell would be constant"

Dear George,

please note that the number of shells may increase ad infinitum with increasing distance, edit: and every additional shell will contribute to filling the remaining illumination gaps.

GD: "what we would see would be the typical galaxy spectrum nearby marged with redshifted versions of that for more distant sources."

When distant galaxies contribute by far the predominant fraction of background illumination then I rather think the latter should appear predominantly redshifted with marginal components of typical nearby galaxy spectra.

It will be essential to compare integral illumination profile according to the Olbers theorem with the Planck curve profile.

DB: "as even Einstein recognizes soon after its formulation of General Relativity, Mach’s principle is not followed by his theory and all the rest of gravational theories have failed to do it too."

Dear Daniel,

I understand Einstein's and related theories are confined to local spacetime geometry and associated interaction while remote masses as not contributing to local spacetime curvature are not considered at all.

DB: "It is clear that the Olbers "model" is not necessary at all in an expanding Universe as the Big Bang one ..."

Of course it is not, as Big Bang is based in all aspects on a central event which doesn't take into account any influence from remote sources.

Dear Johan,

Perhaps I didn't understand you properly, sorry, what kind of gravitation are you then thinking about? One which doesn't depends of the distance between the masses? Are you assuming that this interaction can go faster than the velocity of the light? How do you introduce the nonlocal information in this theory?

DB: "what kind of gravitation are you then thinking about?"

Dear Daniel,

I think Newton and Heaviside are doing well on short as well as on large distances, and also do not preclude limited propagation speed.

DB: "How do you introduce the nonlocal information in this theory?"

Via gravitational potential and supplements: associated local dynamic phenomena like inertia, rotational drag (Keith) and maybe some sort of "aether".

Ok Johan, Ok

We were speaking about very different things. Nowadays it is quite difficult to assume that any physical interaction can be at higher velocity than light. It that were true then we'll enter in very difficult problems and never could understand results as the gravitational waves and so on.

Dear Daniel,

I agree, waves will only build up at finite propagation speed. Keith's experiment, in particular, focuses on gravitational force retardation.

JKF: "every additional shell will contribute to filling the remaining illumination gaps."

When a given gap is to be filled by illumination from sources at ten times the distance then this part of the sky will shine at colours with ten times as much redshift. This should apply independently of the "true" colour of sources. When background illuminution with increasing coverage is increasingly supplied from sources with increasing redshift then spectral density of overall sky illumination should increase at increasing rate towards lower frequencies until intensity at still lower frequencies drops down when illumination approaches full coverage. The resulting intensity-vs-frequency characteristic thus might well resemble the Planck curve characteristic.

August 20, 2018

A lot of other possibilities were considered and discarded before CMB was concluded to be a relic of early universe radiation.

Hi Johan,

GD: "The number of galaxies in a thin shell at radius r is proportional to r2, but the luminosity is proportional to r-2 so the total contribution per shell would be constant"

JKF: please note that the number of shells may increase ad infinitum with increasing distance, edit: and every additional shell will contribute to filling the remaining illumination gaps.

Yes, we are saying the same thing, but because the luminosity of any individual galaxy falls as the inverse square of the radius while the number of galaxies in a shell of thickness dr increases as the square, the total flux from each shell is the same.

GD: "what we would see would be the typical galaxy spectrum nearby marged with redshifted versions of that for more distant sources."

JKF: When distant galaxies contribute by far the predominant fraction of background illumination then I rather think the latter should appear predominantly redshifted with marginal components of typical nearby galaxy spectra.

Yes, the total spectrum includes shells out to infinite redshift but that just makes the problem worse. It extends the combined spectrum to ever lower frequencies. To match the CMB you would need a single shell of stars covering the whole sky with no breaks, all at exactly the same distance with none closer, and all at exactly the same temperature.

JKF: It will be essential to compare integral illumination profile according to the Olbers theorem with the Planck curve profile.

That is trivial though, the fact that stars have different temperatures alone means they cannot match, the integration only extends the red end making the problem worse. The diagram I posted as the second reply in this thread illustrates why it cannot work. If you doubt me, just do the integral.

P.S. in regard to your second comment:

JKF: "every additional shell will contribute to filling the remaining illumination gaps."

JKF: When a given gap is to be filled by illumination from sources at ten times the distance then this part of the sky will shine at colours with ten times as much redshift.

It's not necessarily linear but the redshift would increase.

JKF: This should apply independently of the "true" colour of sources.

The redshift is a multiplicative factor so what is seen depends on both the original frequency and the redshift.

JKF: When background illuminution with increasing coverage is increasingly supplied from sources with increasing redshift then spectral density of overall sky illumination should increase at increasing rate towards lower frequencies until intensity at still lower frequencies drops down when illumination approaches full coverage.

No, you are forgetting that a candle seen twice as far away gives illumination that is a quarter of nearer candle. The same is true of stars. In addition, the Hubble law says they are moving away which further reduces the light coming towards us, that is the basis of the "Tolman Test", but just the simple inverse square effect is enough to cancel out the greater number of sources per shell.

JKF: The resulting intensity-vs-frequency characteristic thus might well resemble the Planck curve characteristic.

No, that is not possible. Relative to the peak, the Planck curve has the minimum possible width. If you blend two stars, the result is wider than one and every extra star you add increases the width. Integrating to infinite completely removes the low frequency end, the width becomes nearly infinite.

JD: "CMB was concluded to be a relic of early universe radiation."

Dear Jerry,

"CMB was concluded to be" something free of doubt ?? I understand CMB is good for Big Bang theory while Big Bang theory is good for CMB. Such kind of circula reasoning reminds me of current discussion on the existence of gravitational waves which relies on the existence of binary black hole mergers, while the existence of binary black hole mergers depends on the existence of gravitational waves and capability of LIGO type detectors to prove them.

GD: "the total flux from each shell is the same."

Dear George,

fully agreed, but every new shell will illuminate additional parts of black sky thus contributing to full sky illumination. The misunderstanding of Olbers and resulting "dark night sky paradox" is that sky illumination was expected at typical star temperatures rather than from redshifted ones.

GD: "the simple inverse square effect is enough to cancel out the greater number of sources per shell."

That's apparently the same argument as the above one.

GD: "If you blend two stars, the result is wider than one and every extra star you add increases the width."

Even by superposition of quasi continuous spectra such as you have sketched previously the blue ends will appear increasingly redshifted and accumulated with increasing sky coverage up to a maximum close to full coverage at the red end. I'll try to prepare a suitable sketch for visualization.

August 22, 2018

Dear Johan,

JKF: fully agreed, but every new shell will illuminate additional parts of black sky thus contributing to full sky illumination. The misunderstanding of Olbers and resulting "dark night sky paradox" is that sky illumination was expected at typical star temperatures rather than from redshifted ones.

Yes, that is what causes the problem.

GD: "the simple inverse square effect is enough to cancel out the greater number of sources per shell."

JKF: That's apparently the same argument as the above one.

It means the integral is roughly flat rather than increasing towards the red end as your previous comment suggested.

GD: "If you blend two stars, the result is wider than one and every extra star you add increases the width."

JKF: Even by superposition of quasi continuous spectra such as you have sketched previously the blue ends will appear increasingly redshifted and accumulated with increasing sky coverage up to a maximum close to full coverage at the red end.

The blue end of distant sources is redshifted but closer sources replenish it. The problem is that the result has to be wider than a single star but the CMB exactly matches a single source temperature, not a spread.

JKF: I'll try to prepare a suitable sketch for visualization.

That would help.

SEG: "Download all the papers with CMB in the title and I suppose you have no questions any more."

Dear Sydney,

thanks for information on CMB literature, I just requested copy of annexed paper.

Article Ruth Durrer: The cosmic microwave background

GD: "It means the integral is roughly flat rather than increasing towards the red end as your previous comment suggested."

Dear George,

when largest part of the sky is illuminated by nothing else but redshifted light then the the sky should appear red colored rather than "white".

GD: "The blue end of distant sources is redshifted but closer sources replenish it."

How can closer sources replenish the overwhelming fraction of distant ones when covering only a negligible fraction of the sky ?

When 3K background radiation is perfectly Planck type shouldn't we also consider average thermal energy of interstellar gas as a possible source ?

Hi Johan,

JKF: How can closer sources replenish the overwhelming fraction of distant ones when covering only a negligible fraction of the sky ?

They are closer hence appear brighter. That compensates for the greater number of dimmer distant sources.

JKF: When 3K background radiation is perfectly Planck type shouldn't we also consider average thermal energy of interstellar gas as a possible source ?

If there were no expansion and no redshift, that would be valid, it would all have to be at exactly the same temperature to give a Planck curve. However, in reality, the thermal emissions from distant gas must be redshifted which again broadens the spectrum.

Taking redshift into account, to get the Planck curve without expansion would require that Earth is uniquely at the coldest place in the universe and the temperature of the gas elsewhere is higher by exactly the right amount to cancel the effect of redshift.

The standard model works that way in part, the plasma was expanding and therefore cooling around the time the CMB was released so the deeper we look into the source, the higher the temperature but also the higher the redshift so what we see looks like a single temperature curve.

JKF: "How can closer sources replenish the overwhelming fraction of distant ones when covering only a negligible fraction of the sky ?"

GD: "They are closer hence appear brighter. That compensates for the greater number of dimmer distant sources."

Dear George,

I don't think so. Lets go on stepwise and take, for instance, the Adromeda galaxy which covers a sky area of about 3x10-4 with 1012 stars covering a total area of about 3x10-15. All stars of Adromeda thus cover no more than about 10-11 of the background sky area behind Andromeda. I presently don't know how to adequately visualize the situation. Redshifted background stars even at similar brightness appear dimmer, of course, since our eyes are less sensitive to infrared than within the visual range.

August 25, 2018

JKF: “All stars of Adromeda thus cover no more than about 10-11 of the background sky area behind Andromeda.“

Revised paragraph: According to the above estimate Adromeda should appear 12 orders of magnitude dimmer than our sun in fair agreement with the actual difference of 30 star magnitudes.

We now can extrapolate on the basis of above data to more distant sources. Andromeda is located at about 1 Mpc distance from earth. Taking into consideration a volume radius of 10 Mpc, the equivalent number of stars would increase by 103 and – due to quadratic loss of visual cross section with distance – visual luminosity by a factor 10. By extrapolation to larger distances we can work out the annexed table* showing that the largest area of background sky is illuminated from stars at ~ 10 Gpc distance and redshift z ~ 10. Refinement of the above procedure I think may qualitatively lead to a luminosity-vs-wavelength characteristic similar to the observed CMB profile.

* Values for z according to dH plot at z=10 in https://en.wikipedia.org/wiki/Redshift#/media/File:Distance_compared_to_z.png

August 26, 2018

Please note minor changes to my previous contribution.

August 27, 2018

"The Cosmic Microwave Background: The history of its experimental investigation and its significance for cosmology" [Ruth Durrer; 2015]

Dear Sydney,

thanks for providing direct link to above publication which, however, fully relies on the Big Bang theory, and so doesn't allow for alternative interpretation of CMB.

If the LISA experiment (although some years away) proves a direct interaction between gravity and light, then the explanation for the red-shift will necessarily change from expansion of the universe to 'reduced energy levels' in the photonic energy.

At that point  the foundations of physics will change.

• No longer will we argue against a static universe
• It is entirely possible that we will change the assumption that light travels at a fixed speed. And as we can see x-ray events long before we see similar optical evidence, I see this as a probability rather than a possibility.
• We will probably see extensions to the argument that light (meaning the entire EM spectrum) and gravity are different aspects of some more fundamental force and this more fundamental force will be related to the formation or changes (of whatever sort) in mass.

Ian

Johan, your table is not correct. The number of sources in a shell at radius r depends on r2, not r3. You are probably thinking of the enclosed volume but you will be integrating over r which means you need to think of the surface area instead.

You also need to remember that photon energy decreases with redshift which reduces the flux by an extra factor of 1+z.

JKF: * Values for z according to dH plot at z=10 in https://en.wikipedia.org/wiki/Redshift#/media/File:Distance_compared_to_z.png

JKF: thanks for providing direct link to above publication which, however, fully relies on the Big Bang theory, and so doesn't allow for alternative interpretation of CMB.

The plot you have used is also from the Lambda-CDM model so your comment appears inconsistent. If you are using an alternative to the standard cosmology, the distance vs. redshift relation will change. For example a non-expanding Tired light model would predict exponential decay of photon energy with distance (because z is independent of frequency).

GD: "The number of sources in a shell at radius r"

Dear George,

please note that I'm not considering shells but volumes. When viewing a certain sky sector with homogeneous star density, the number of stars within that sector increases with r3.

GD: "You also need to remember that photon energy decreases with redshift which reduces the flux by an extra factor of 1+z."

GD: "For example a non-expanding Tired light model would predict exponential decay of photon energy with distance"

I think in the present discussion on fractional sky coverage by more or less distant light sources we should better consider photon rates rather than energy flux.

Continued:

GD: "The plot you have used is also from the Lambda-CDM model so your comment appears inconsistent."

I only picked the distance value at z=10 from the proportional section and linearly interpolated to lower values.

@George Dishman

"a non-expanding Tired light model would predict exponential decay of photon energy with distance"

Could you explain your reasoning here please? I would have expected the opposite, that it light at a further distance would lose its energy more slowly as it feels the drag of gravity so much less as distance from the mass increases.

I am of course bearing in mind the assumption that the light will pass more and more matter as it travels, but discounting this for the sake of the point.

Ian

IP: "If the LISA experiment (although some years away) proves ..."

Dear Ian,

I'm afraid LISA similar to LIGO might preferably adapt experimntal results to main stream theory rather than the opposite direction.

Dear Johan,

JKF: please note that I'm not considering shells but volumes.

Your table lists shells.

JKF: When viewing a certain sky sector with homogeneous star density, the number of stars within that sector increases with r3.

It does but those stars have different redshifts. To calculate what we see as a spectrum you have to integrate over r and take account of change of redshift as a function of r (which you are doing), but to get the r3 total, you integrate r2.dr over r. In your table, you have numbers against radii so again you need to use r2 and it then becomes apparent that each shell contributes an equal photon count which is diminishing energy with increasing redshift.

JKF: I think in the present discussion on fractional sky coverage by more or less distant light sources we should better consider photon rates rather than energy flux.

The Plank curve is a plot of energy flux versus frequency (or wavelength), not photon count. If you want to do a comparison, it has to be like-for-like.

JKF: I only picked the distance value at z=10 from the proportional section and linearly interpolated to lower values.

The coverage in any shell is a small fraction, you will have to go to much higher redshifts though of course the contribution becomes smaller.

Hi Ian,

Let me take your second point first:

IP: I would have expected the opposite, that it light at a further distance would lose its energy more slowly ...

That is correct, the frequency falls as fr=fse-D/L where fr is the frequency received, fs is the frequency at the source, D is the distance travelled and L is some characteristic length.

GD: "a non-expanding Tired light model would predict exponential decay of photon energy with distance"

IP: Could you explain your reasoning here please?

A signal at f1 travels some distance d and is reduced to f2 where it passes another source. That source emits a second also at f1 locally and after they have travelled a farther distance d, it must be reduced to f2 if the Copernican Principle holds. Redshift is observed to be independent of frequency so if the second signal has been reduced by a factor of f2/f1, so must the first which must now be (f2/f1)*f2. The exponential form follows.

Note this is a Tired Light prediction and quite different from conventional cosmology. Of course Tired Light is ruled out by observation but if Johan is looking for an alternative cosmology, I think it's appropriate to discuss it.

Good morning.

This is a very interesting topic and it is in part related to this RG-Question >>> https://www.researchgate.net/post/Black_Holes_out_of_a_galaxy_do_they_exist

I am very interested in your point of view.

Thank you for the attention

--s.v.--

Johan K. Fremerey

The cynic in me continues to suggest that LISA, like LIGO and the CERN discovery of Higgs Boson, will produce whatever results the politicians want to see, immediately after those same politicians have threatened to pull the funding.

However, 2030 is a long time away and in the absence of real results speculation is our friend.

LIGO told the world where to look for GW170817 and it took another 12 hours for the optical observatories to find it. After that, there has been no doubt that LIGO is working as advertised.

LISA was cancelled by the politicians years ago, eLISA has a long way to go as you say.

The Higgs particle has nothing to do with either but I agree we have some serious discoveries to make beyond the present standard particle model.

GD: “To calculate what we see as a spectrum you have to integrate over r and take account of change of redshift as a function of r.“

Dear George,

That‘s ok. In a first step we will have to integrate sky coverage by star disks as a function of distance r. For low coverage integration in fact complies with what the above table says: Relative coverage (not illumination) increases proportional with r. In view of Olbers and related paradoxon I have set coverage equal to illumination which due to reduced energy flux from remote sources of course does not apply. But reduced energy flux from remote sources apparently is the actual reason for darkness of sky at night and the Olbers paradoxon. This idea, in fact, was a major motivation of my introductory question.

At large distance relative coverage of background sky by star discs will asymptotically end at full coverage. When suspecting distance rfull to be somehow related to CMB radiation profile, rfull should be somehow related to corresponding redshift at z = 1,100. According to above table this would lead to rfull = 1,100 Gpc which appears rather unlikely when compared with the “established“ radius of the universe. Number of stars N = 1024 as extrapolated in above table for r = 10 Gpc, however, appears reasonable in view of established data. On the other hand, shouldn‘t GMB radiation require some sort of bodies or particles to come from?

Dear Johan,

GD: “To calculate what we see as a spectrum you have to integrate over r and take account of change of redshift as a function of r.“

JKF: That‘s ok. In a first step we will have to integrate sky coverage by star disks as a function of distance r.

Yes, that's right but that means you need to work with the number of stars per shell so it is the surface area, not the volume that goes into the integral and your second column should go with r2. The fourth column has a different relationship (see below), the illumination per star goes as 1/(1+z) and the total flux (third column) follows from the fractional coverage (see below).

JKF: For low coverage integration in fact complies with what the above table says: Relative coverage (not illumination) increases proportional with r.

At low coverage you can approximate it as proportional but as the number of shells increases, more star disks in each shell are hidden by closer star disks. So for example if 2% of the sky is covered by the first shell, by the time the total is 50%, the next shell only adds 1%, the other 1% in the shell is behind closer stars. The total coverage is therefore again an exponential and never reaches total coverage, it is asymptotic as you say.

JKF: rfull should be somehow related to corresponding redshift at z = 1,100. According to above table this would lead to rfull = 1,100 Gpc which appears rather unlikely

You are forgetting that the proportionality is only valid for low redshift, beyond z=1.6 in standard cosmology, r decreases as z increases. As I warned, you need to have a different rule if you want an alternative cosmology. However, you are right because the coverage by stars in general is very small in standard cosmology, if that were not the case, we would not be able to see the CMB from between the stars.

JKF: On the other hand, shouldn‘t GMB radiation require some sort of bodies or particles to come from?

Yes, in standard cosmology it is the hydrogen/helium plasma that filled the universe at uniform density. If you could have been there 400k years after everything started, it would have looked like the surface of the Sun in every direction, just a shade cooler. It turned transparent at ~380k years and the first stars formed perhaps 100 million years later.

In Olber's universe it would have been the surface of stars out to much greater distances than can be seen in the standard version because there was no plasma phase.

GD: "you need to work with the number of stars per shell"

Dear George,

(amendments in bold) on integrating visual star coverage (R2π/r2)*ρn*4πr2*dr from within a differential shell of volume 4πr2*dr at variable distance r, with constant star radius R and number density ρn, where R2π/r2 denotes the visual disk cross section of a single star at distance r, we get the simple result that visual sky coverage increases proportional to distance r.

GD: “as the number of shells increases, more star disks in each shell are hidden by closer star disks.“

This will become significant only at very large distances. As demonstrated above, stars within the Andromda galaxy at 1 Mpc distance overlap by an insignificant rate of 10-11. At 10 Gpc distance the total coverage will still amount to a negligible order of 10-7. This in fact suggests that background coverage by stars up to z ~ 103 and beyond might be responsible for the observed CMB radiation.

August 29, 2018

I think there is something wrong with my above calculations, I'll try to correct.

Dear Johan,

[edited a couple of "P.S." points

JKF: I think there is something wrong with my above calculations

They don't look too bad at first glance. However, remember when you come to do the integration, you need to be finding the flux in a small frequency (or wavelength) increment at the observer, so you integrate the emitted intensity at a frequency (1+z) times the observed frequency.

Just a couple of points:

JKF: This will become significant only at very large distances.

Yes but to get full coverage you will calculate the integral to infinity and it's not hard to include the exponential term.

JKF: At 10 Gpc distance the total coverage will still amount to a negligible order of 10-7

I think that's roughly the figure I saw many years ago when discussing this on Usenet. It means you need to integrate to perhaps 1019 GPc to get to ~90% coverage, a really enormous distance! However, it's usually easier to integrate to infinity anyway.

JKF: ... background coverage by stars up to z ~ 103 and beyond might be responsible for the observed CMB radiation.

No, that is not possible, it would require that

a) each star has a perfect Planck curve

which they don't due to 'limb darkening' and spectral lines, plus either

b1) all stars have identical temperatures and

b2) there is no redshift

or

c) every star has a temperature proportional to (1+z) as viewed from Earth

and either (b) or (c) would result in the whole sky having the same temperature as the surface of a star at z~0, Olber's Paradox.

If star temperatures are independent of distance but redshift exists, even if (a) and (b1) applied, the integral would spread the spectrum making it impossible to match the CMB.

JKF: “I think there is something wrong with my above calculations, I'll try to correct.“

In fact, errors are not realy dramatic: There is missing a factor 4π in the above formula of shell coverage which correctly should read (R2π/4πr2)*ρn*4πr2*dr = R2π*ρn*dr. A total sky coverage by visual star disks of the order 10-13 instead of previously stated 10-11 will result on integration up to r = 10 Gpc, which even more suggests almost perfect transparency.

GD: “If star temperatures are independent of distance but redshift exists, even if (a) and (b1) applied, the integral would spread the spectrum making it impossible to match the CMB.“

This statement appears quite reasonable and apparently rules out my original suggestion that CMB may result from direct star light.

On the other hand, when direct star light due to insignificant sky coverage by star disks practically doesn‘t contribute at all to CMB radiation, the latter should rather be attributed to interstellar matter. If interstellar matter preferably consist of gas molecules thermally excited by radiation from embedded stars, then a perfect Planck curve may quite well be expected for thermal emission from interstellar gas.

August 31, 2018

Dear Johan,

JKF: This statement appears quite reasonable and apparently rules out my original suggestion that CMB may result from direct star light.

Thank you, that was my original point.

JKF: On the other hand, when direct star light due to insignificant sky coverage by star disks practically doesn‘t contribute at all to CMB radiation, the latter should rather be attributed to interstellar matter. If interstellar matter preferably consist of gas molecules thermally excited by radiation from embedded stars, ...

It doesn't consist of molecules or even atoms, hydrogen atoms absorb at the Lyman Alpha spectral line which makes it a powerful tool in astronomy. Do a Google search for the terms "Lyman Alpha Forest" and "Gunn Peterson Trough" and you'll see the consequence.

JKF: then a perfect Planck curve may quite well be expected for thermal emission from interstellar gas.

No, you get a fine line in the ultraviolet from monatomic hydrogen. To get thermal emission, you need dense material at a uniform temperature.

GD: "To get thermal emission, you need dense material at a uniform temperature."

Dear George,

this apparently may apply for gas masses as well, see references below.

http://www2.ipp.mpg.de/~bds/astro/thermal-radiation.html

http://www.oxfordscholarship.com/view/10.1093/oso/9780199662104.001.0001/oso-9780199662104-chapter-3

Jerry Decker: "A lot of other possibilities were considered and discarded before CMB was concluded to be a relic of early universe radiation."

Dear Jerry,

can we definitely rule out the possibility that CMB via thermal equilibrium of interstellar gas is caused as well by present universe radiation ?

JKF: "(R2π/4πr2)*ρn*4πr2*dr = R2π*ρn*dr. A total sky coverage by visual star disks of the order 10-13 instead of previously stated 10-11 will result on integration up to r = 10 Gpc, which even more suggests almost perfect transparency."

When applying the same procedure to free intergalactic hydrogen on the basis of (ρn)H = 10/m3 sky coverage turns out many orders of magnitude larger for free hydrogen atoms than for star disks. On recalculating the above term R2π*ρn I come to 5x10-14/Gpc in case of star coverage, and 10+6/Gpc with hydrogen. This even under consideration of overlap would imply full sky coverage by hydrogen atoms already at distances r of the order 10 kpc.

So I conclude that on night sky we are looking into a tight cloud of atomic hydrogen which due to optical transparency enables us to make visual observations, and CMB is the black body radiation emitted under local thermodynamic equilibrium (LTE) conditions from that cloud.

September 1, 2018

JKF: can we definitely rule out the possibility that CMB via thermal equilibrium of interstellar gas is caused as well by present universe radiation ?

Yes because the CMB matches the intensity of the Planck curve, not just its shape. Thin local gas could give the right shape but if it was say 90% transparent, the intensity would be just 10% of the Planck curve. To give the observed intensity, a shell round our galaxy for example would be totally opaque and it would be impossible to see any other galaxies.

For that reason, the CMB must be generated beyond the most distant visible galaxies, currently around z=11.

GD: “Thin local gas could give the right shape but if it was say 90% transparent, the intensity would be just 10% of the Planck curve.“

Dear George,

that‘s a good point. We know that earth atmosphere is transparent at least up to distances of several 100 km. Number density of atmospheric gas at normal pressure is 3x1019 per cm3 or 3x1025/m3. When comparing this figure with (ρn)H = 103/m3 as previously assumed for intergalactic hydrogen then distance of view in space should be estimated 3x1022 times larger than 10 kpc as calculated above. Thus, blackbody radiation intensity from intergalactic hydrogen should be regarded insignificant up to distances comparable to the dimensions of our “known“ universe. But what should we expect in case of an infinite universe?

I tend to next conjectures:

As for the question:

• Frankly I don't know!

Dear Demetris,

All of your assertions in your comment above are correct. Big Bang, Machism, Inflation, Expansion et. ad nausem (the frenzy of official cosmology) have no meaning in an infinite, eternal and ever-changing universe – a philosophical conclusion of dialectics since Epicurus.

An alternative to the view of a finite, God created universe and ALL the associated Fairy- Tales of official cosmology does indeed exists, Please see the following article as a representative of the dialectical view: Article Ambartsumian, Arp and the Breeding Galaxies*

As for CMB and the “Face of God” of George Smoot of COBE fame, the following is what Halton (Chip) Arp (known to some as the Galileo of modern times) had to say in a personal letter “The intergalactic medium has to have some temperature. Eddington calculated about 2.7 deg. in 1926. In the 1940’s Max Born calculated 2.7 deg. on the basis of tired light. Gamow calculated 50 deg. before Pezias and Wilson measured 2.73 deg. But a Canadian astronomer, McKellar had already measured it from the excitation of the inter-stellar CN molecule.

The ultimate irony is that it is a primary reference frame, which violates Einstein’s assumption about no preferred reference frames.”

Dear Johan,

JKF: that‘s a good point.

Thanks, a lot of people trying to come up with alternatives miss that.

JKF: Thus, blackbody radiation intensity from intergalactic hydrogen should be regarded insignificant up to distances comparable to the dimensions of our “known“ universe. But what should we expect in case of an infinite universe?

There are three points to consider related to redshift. First, again, if the origin is spread over a range of distance in an alternative cosmology in which the material had the same temperature everywhere, you would get a mix of observed temperature and non-Planck spectrum due to redshift alone. The variation in the CMB is around 10 parts per million so if the source were say 10 billion light years away, it would be no thicker than 10,000 light years thick.

Second, the temperature would be a lot higher, that's probably not a problem though.

Third, you would expect the temperature as seen at some distance from us and at some time in the past to be the same as we see now. However, studies have examined thin isolated sources some billions of light years away and their temperature is higher because the CMB was hotter in the past by an amount that matches what is expected from expansion.

DC: "As for the question: Frankly I don't know!"

Dear Demetris,

the current discussion has lead us to the insight that direct star light due to low sky coverage by star disks should be negligible compared to radiation from intergalactic gas.

GD: "if the source were say 10 billion light years away, it would be no thicker than 10,000 light years"

Dear George,

according to my previous post we are meanwhile considering distances of view up to the order 3x1022 x 10 kpc = 3x1017 Gpc.

GD: "you would expect the temperature as seen at some distance from us and at some time in the past to be the same as we see now."

Yes, because I think that background radiation mainly originates from background gas at distances much larger than those of observable objects.

DC> "space time as it is defined in relativity does not exist, except from our dashboards"

Very well said! Please see the following: "The Philosophy of Space-Time: Whence Cometh Matter and Motion?"

https://www.amazon.com/Philosophy-Space-Time-Whence-Cometh-Matter/dp/984041884X

Hi Johan,

JKF: according to my previous post we are meanwhile considering distances of view up to the order 3x1022 x 10 kpc = 3x1017 Gpc.

Yes, my numbers were only to illustrate the relative thickness. The minimum as I said is that any material has to be beyond z=11 which is ~32 billion light years in conventional cosmology.

Anyway, I think you have followed all the technical points we've discussed. As you can see, finding an alternative to the conventional view is surprisingly difficult given nothing more than the intensity and shape of the CMB.

Dear Johan,

As far as I study I tend to concern that we are blind arrogant beings who think that have explained the whole of the world and have not given answers to less broad questions like yours.

Personally I am waiting for other, non light kind of radiations to be discovered.

Otherwise we'll continue to wonder why the sky is so black...

(Although it is full of stars and intergalactic gas)

DC> "Otherwise we'll continue to wonder why the sky is so black..."

Dear Demetris,

The Olber's paradox does not arise in the dialectical view of an infinite, eternal and ever-changing universe. Because as the great Heraclitus (may be naively but essentually correctly) said "Everything in the world comes into being in their own specific way and goes out of existence, due to inner conflict".

This view posited the brilliant germ of dialectics; which others subsequently contributed to fluorish. I have tried to interpret this "coming into being and passing out of existence" in terms of Hegel's (ontological triad - "Being-Nothing-Becoming") and the Virtual Particles of the quantum vacuum. Existing "real" quantum particles of the universe are not here for ever to lead to Olber's paradox!

A real particle can become "virtual" and vice versa through quantum tunnelling, or some other yet unknown processes, such that there is a dynamic equilibrium between the real and virtual worlds. A virtual particle of the quantum vacuum can also become real if the mass equivalent of energy is available.And as the Uncertainty Principle and "Being-Nothing" of dialectics asserts, there must always be some finite (real) matter/antimatter in the universe. Dialectics forbids only "Being" or only "Nothing"; both must be together in a dialectical contradiction of the "unity of the opposites"!

Any existence is therefore a contradiction. Since reason cannot rest in a contradiction this contradiction must be resolved. But this resolution only leads to another existance (evolution, development, change") or contradiction of higher or lower forms and continues for ever without coming to an end; leading either way to the primary contradiction of "Being-Nothing". The universe is a process of change as Heraclitus correctly viewed.

I have tried to extend materialist dialectics to the quantum phenomena; in other words interpret quantum electrodynamics in terms of dialectics; in my few books and journal articles on cosmology and QED. Please see my comments in various RG forums, particularly the most recent and ongoing one: https://www.researchgate.net/post/Is_physics_necessarily_empiricist

Dear Abdul,

I didn't mean such like that.

I only meant that due to our blindness we are not able to "see" the fllood of existing non light radiations and particles...

Dear Demetris,

If by "the fllod (flood?) of existing non light radiations and particles..." you mean Dark (matter/energy), then I would say that it is an inference from inadequate theory (of gravitation), unlimited extention of idealized mathematics, spurious and subjective observation based on contrived, insensitive or poor measurements etc., that is very unlikely to reflect the reality. In one word this whole cosmology of official science is wrong and only inspired by theology. There is little "scientific" about it; even though we see the proud display of the highest level of technology, the highest of brainy scientists from the greatest universities and research projects manned by thousands of the brighest scientists of the world, in this whole enterprise - these are meant to justify an "a priori" premise, hence a tautology. Observational (telescopic, spectroscopic etc.) evidences are interpreted to fit a priori premise. Contrary interpretations are rejected outright!

My evaluation/judgement is based on a considered materialist dialectical world view and in opposition to the official view based on causality. This whole edifice of cosmology has defect at the very conceptual, philosophical and foundational level. Please see my article on the question of gravity: Article THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR...

Dear Abdul,

By the term flood (thanks for correction!) I mean what we cannot see because of our relativistic orthodox view and that is not the "dark matter" which is a pure relativistic entity...

Can you explain in a few words your "materialist dialectical world "?

Thank you

JKF: "Number density of atmospheric gas at normal pressure is 3x1019 per cm3 or 3x1025/m3. When comparing this figure with (ρn)H = 103/m3 as previously assumed for intergalactic hydrogen then distance of view in space should be estimated 3x1022 times larger ..."

Number density in fact was previously assumed at (ρn)H = 10/m3 (not 103) which would make distance of view larger by another two orders of magnitude.

On this occasion I would like to comment on intergalactic hydrogen density figures in general: When assuming total mass and radius of the universe at 1053 kg and 14 Gpc, respectively, as according to Wikipedia*, and further assume all that mass would exist in form of equidistributed atomic hydrogen, this would lead us to a mean density number [(ρn)H]universe = [nH]universe / Vuniverse = 6x1079 / (3x1080 m3) = 0.2/m3 which is two orders of magnitude less than the above figure.

Does anyone here have a reasonable value for the number density of intergalactic hydrogen? If it were much larger than 0.2/m3, would intergalactic hydrogen then constitute what is being searched for as "Dark Matter" ?

* Starting from Average Density 4.5x10−31 g/cm3 as quoted by Wikipedia we get to about 0.3 hydrogen atom masses per m3.

https://en.wikipedia.org/wiki/Universe

DC> Can you explain in a few words your "materialist dialectical world "?

Dear Demetris,

You are asking me to do something that is impossible to do and even if I "explain in a few words" it would be of no use to you. I have expressed my dialectical materialist world view in some published journal articles, books, and discussed in various forums including in RG.

The shortest and probably quick way for you to know about my views (that comes to my mind) would be the following two:

!. A new (started 10 days ago) and short RG forum, "Is physics necessarily empiricist?" : If you read only few of my comments (in response to others' comment), you may have some idea about my world view. You may join that discussion if you want: https://www.researchgate.net/post/Is_physics_necessarily_empiricist

2. A review of two of my books (it was brought to my attention recently) in a website run by some leftist group in America. I do not fully agree with the reviewer, but generally it is a fair reflection of my materialist dialectical world outlook:

http://maydaybookstore.blogspot.com/2017/12/thephilosophy-of-space-time-whence-come.html

Regards.

JKF: "Starting from Average Density 4.5x10−31 g/cm3 as quoted by Wikipedia we get to about 0.3 hydrogen atom masses per m3."

The above figures apply for the “known“ universe as a whole. In order to avoid discussion on hydrogen as constituting an essential fraction of “Dark Matter“ let us assume an upper limit of the order 0.1 free hydrogen atoms per m3. This is two orders of magnitude less than (ρn)H = 10/m3 as we started from in our above estimates on sky coverage and visual distance. The latter should increase by another two orders of magnitude, i.e. up to about 3x1019 Gpc on the basis of our above estimates and (ρn)H = 0.1/m3.

In view of negligible sky coverage, as derived on the basis of our above estimates, it in fact appears rather unlikely that compact matter and/or free hydrogen will contribute in any straight manner to CMB radiation.

The geometric model of CMB in non expanding universe is given in our work in Journal of Modern Physics , special issue on Cosmology Gravitation and Astrophysics. It gives all of the observable properties , isotropy , homogeneity and spectrum. Model applies to the universe as whole. See also on this site.

J. G. von Brzeski

Thanks a lot for drawing our attention to your remarkable paper "CMB — A Geometric, Lorentz Invariant Model in Non-Expanding Lobachevskian Universe with a Black Body Spectral Distribution Function", from where I just cite the following conclusion: **

"It follows that both phenomena, the CMB and the cosmological redshift, are inherently interconnected as two features having a common root — Lobachevskian geometry."

** I got a PDF copy of your paper from your publication list.

J. G. von Brzeski:

I just read your exciting article "Topological Intensity Shifts of Electro-Magnetic Field in Lobachevskian Spaces. Olbers Paradox Solved, Deep Space Communication, and the New Electromagnetic Method of Gravitational Wave Detection" from 2003, see reference below.

May I ask you to kindly summarize reactions of the science community, in particular main stream "Big Bang" representatives, to your own and related findings of previous investigators you refer to ?

http://www.jpier.org/PIER/pier.php?paper=0303271

Dear Johan,

Reaction of the "Big Bang club " is hostile and in a view,( from money side ) how science is working you have to expect that. Our universities here in US and also those in Europe ( which I know from personal experience) are still in a feudal mode of operations. Grants ($$$) are only available to those who belongs to the "club" or follows those charlatans who have grip on funds. To see that feudal structure clearly , recall that a few years ago a Ph.D. student in department of mathematics in Stanford University ,California, killed with hammer his doctoral supervisor because that professor kept him for 6 years as a personal slave not moving him up or down. All that was in a media. In UC Berkeley , California I witnessed the same practices however with no such tragic finale. Another example from astrophysics: Halton Arp a prominent US astrophysicist was removed from telescopes in the USA because he had an alternative view on some phenomena related to quasars. Banned from work in the USA , Arp emigrated to Germany where he worked at Max Planck Institute . There are more and more examples like those above . Rules which govern so called "scientific community" are very similar to those practiced in feudalism , Hitler's Germany and Stalin"s Soviet Union. And that seems to be for a long, long time.

Dear Georg,

when both, cosmological redshift and background radiation are related to some certain hyperbolic curvature of space geometry on large scales I imagine that respective observational data, i.e. Hubble constant and 3K background temperature should be closely related. Do you think this can be shown in a comprehensible manner ?

Hi Johan K. Fremerey,

The Hubble constant is primarily a scaling factor and the temperature depends on the density so they are related but not as directly as you might think. Curvature is measured using several other indicators including the apparent spatial size of the hot/cold variations of the CMB, its polarisation and separate evidence from "Baryon Acoustic Oscillations" or BAO as they are known.

Back in July, the Planck mission released its final report.

https://www.cosmos.esa.int/web/planck

The measured curvature is very small, the latest value is ΩK = 0.0007±0.0019.

https://arxiv.org/pdf/1807.06209.pdf

The topic is covered in section 7.3 (page 40) and the result above which includes the BAO evidence is given in equation 47b.

Johan, the way the cosmological parameters are calculated involves finding the best fit to many different features so it is quite a complex subject. Skimming through that Planck paper may not explain it "in a comprehensible manner" but is as thorough as most people will understand.

Dear Johan,

your question about the nature of CMBR is very important for the true physical cosmology.

Actually in the frame of the Standard Cosmological Model (LCDM in Friedmann's expanding space) there is NO PHYSICAL REASONABLE explanation of the CMBR.

I have explained in our preceding discussions with George Dishman that in expanding Friedmann's space the cooling of the hot primordial photon gas is due to VIOLATION of the energy-momentum conservation law in any local volume (it is an exact mathematical consequence of the Friedmann's equations, photons energy disappear nowhere) - see:

Harrison, E. R., Cosmology: the science of the universe, Cambridge University

Press, 2nd edition (2000), and

Baryshev, Yu. V. Paradoxes of the Cosmological Physics in the Beginning of

the 21-st Century, invited report at XXX-th International Workshop on High

Energy Physics - Particle and Astroparticle Physics, Gravitation and Cosmology -

Predictions, Observations and New Projects, June 23-27, 2014, Protvino, Moscow

region, Russia (2015), (arXiv:1501.01919).

Cosmology is an application of gravitation theory and the expanding space model is a strict mathematical consequence of the geometrical general relativity, so violation of energy - momentum is inherent problem of LCDM model.

Photons produced by stars can be the source of CMBR, as it was suggested by Hoyle in 60th - energy generated by nuclear reactions in all stars during the life of the Universe (Hubble time) is equal to the CMBR energy.

Termalization of this photon gas can be achieved in a static universe where large-scale fractal structure emerges during evolution of primordial matter, so the linear Hubble law (the global gravitational cosmological redshift) and CMBR are tightly related phenomena ( arXiv:0810.0162 and arXiv:1702.02020 ).

Dear George Dishman (my previous post in fact was addressed to J. Georg von Brzeski who didn't respond so far)

thanks a lot for providing extensive material from the Planck mission and related evaluation by N. Aghanim et al. I should admit that I feel unable to follow the reasoning of the latter manuscript in detail. It appears rather obvious, however, that their reasoning is strongly devoted to cosmological theories on the basis of GRT including Big Bang, Dark Matter, etc., as represented by the current main stream society, with no room for alternative views as proposed, in particular, by J. Georg von Brzeski, see his above contributions. Did you already have a look at his papers?

"Photons produced by stars can be the source of CMBR"

"Termalization of this photon gas can be achieved in a static universe where large-scale fractal structure emerges during evolution of primordial matter"

Dear Yurij,

thanks for your instructive comments. Do you think your idea of fractal structure might be compatible with J.G. and V. von Brzeski's idea of hyperbolic space curvature?

Article CMB —A Geometric, Lorentz Invariant Model in Non-Expanding L...

Dear Johan,

unfortunately the paper by Brzeski on the Lobachevskian geometry interpretation of cosmological redshift and CMBR is actually an exercise in geometry which is completely outside physics. It has very naive and non-professional view on physical phenomena ... I think it is possible to find many mathematical models which can give such formulas as z = d and n = 1/(e^{v/t} - 1) , but it is not an alternative physical theory.

Cosmology as a physical science includes whole modern physics, and especially it is based on gravitation theory, which nowadays has at least two alternative ways - Einstein's geometrical gravity (GRT) and Feynman's material field in Minkowski space (FGT) (see arXiv: 1702.02020). In the frame of FGT there is possibility to construct cosmological model of evolving matter in static Minkowski space, where large-scale fractal structure originates together with global gravitational redshift and CMBR (see arXiv:0810.0162 and arXiv:1702.02020 ).

Dear Johan,

JKF: (my previous post in fact was addressed to J. Georg von Brzeski who didn't respond so far) ... Did you already have a look at his papers?

I looked back and showed "previous replies" as far as a month back but a page search for "Georg" didn't find his name. I assumed you had just mistyped my name. Now that you've added his surname, it seems you were referring to "J. G. von Brzeski" which is why the search didn't find him.

JKF: thanks a lot for providing extensive material from the Planck mission and related evaluation by N. Aghanim et al.

I always feel that discussions are best conducted based on actual measurements rather than philosophical preferences or personal opinions so raw data should always be welcome. I'm glad you found it useful.

JKF: I should admit that I feel unable to follow the reasoning of the latter manuscript in detail.

The degeneracies between parameters are complex and the way they are broken by, for example, BAO is equally hard to follow. In simple terms, BAO are like spheres of concentrations of galaxies. They exist nearby and also far away and haven't changed in size since they were formed. Curvature of space would act like a lens making them appear bigger or smaller so we can use them to check how flat it is.

JKF: It appears rather obvious, however, that their reasoning is strongly devoted to cosmological theories on the basis of GRT including Big Bang, Dark Matter, etc., as represented by the current main stream society, with no room for alternative views as proposed, in particular, by J. Georg von Brzeski, see his above contributions.

From what I've seen, he is only suggesting an alternative value for one of the parameters of standard cosmology, a value that is in conflict with the measurements. The standard model doesn't say there is no curvature but observations do place quite tight limits on the value.

"see arXiv:0810.0162 and arXiv:1702.02020"

Dear Yurij,

thanks a lot for drawing our attention to your fascinating view on cosmology via fractal distribution of baryonic matter with D=2 and resulting explanation of both, Hubble law and CMBR.

Even though I feel unable to follow your mathematical reasoning in detail, the outcome apparently fits to my intuitive view that apparently limited radius of the universe might just be due to limited sight within an infinite universe. In particular, I‘m happy to see confirmed 2GM/Rc2 ~ 1 which apparently is a basis for the existence of a 1/c3 proportional drag on small size high speed rotors due to interaction with background masses of the universe as proposed by James C. Keith, see reference below. I was notified via RG that last week you had a look at our detailed report on related experiments. Do you think the results might be relevant in support of your theory?

"From what I've seen, he is only suggesting an alternative value for one of the parameters of standard cosmology"

Dear George Dishman,

thanks for valuable hints including the above one. I would have expected something comparable to what Yurij gets out from his theory, in particular, relationship between redshift and CMBR.

Dear Johan,

JKF: I would have expected something comparable to what Yurij gets out from his theory, in particular, relationship between redshift and CMBR.

I had a look at the paper and the only mention of the CMB is where Yuri writes:

• The cosmic microwave background radiation
• According to the classical argument by Hoyle (1982, 1991) the CBR could be a remnant of the evolution of stars, which energy density equal s to the energy released by the nuclear reactions in stars of all generations. The optical photons radiated by stars could be thermalized by scattering and gravitational deflections by structures of different masses and scales.

As you know, you and I discussed the hypothesis of the CMB being distant starlight quite thoroughly and it doesn't work in any way. Hoyle worked on that for years and never solved the problem. Unless I missed something, Yuri's approach does not provide an explanation for the existence of the CMB at all, he merely references Hoyle's failed efforts.

On the other hand, the fractal dimension of the universe is still somewhat poorly defined at large scales, and I think we will continue to find structure at larger scales than the standard model suggests should be the maximum, but how far that goes is difficult to determine. There's a very basic summary here:

https://en.wikipedia.org/wiki/Fractal_cosmology#Fractals_in_observational_cosmology

GD: "you and I discussed the hypothesis of the CMB being distant starlight quite thoroughly and it doesn't work in any way."

Dear George,

that's right, but originally was thought of as direct star light, while I understand Yurij was talking about "thermalized" star light.

What's more important to me in view of the gravitational Keith effect is that 2GM/Rc2 ~ 1 may hold as well for an infinite universe, where R is to be regarded as distance of sight. Sometimes I'm inclined to think present cosmology on the basis of Big Bang theory is trapped at a stage we already have lived in when the earth was still considered a disc.

In order to answer the CMB related question, we need to solve an inverse problem of radiative transfer. It is well known that there is no single solution in this case and regularization, which is almost mandatory, will introduce uncertainties. Referring to the history of the inverse problems of science we often quote work of Lagrange, it is possible that Olbers was influenced by the same papers. His speculations on the distribution of the brightness of the sky were unfortunately based on an erroneous geometrical model.

Today, our measurements and our deep knowledge of the geometry of space-time allow for much more general speculations. I have attached a file with a presentation describing the history of CMB measurements and some discussions from the point of view of the theory of inverse problems. The most difficult remaining question is related to the topology of our Universe. The discussion of this problem is presented by Luminet in the review paper: The Status of Cosmic Topology after Planck Data (the paper is also attached). It is interesting tp note that Schwarzschild (1900), de Sitter (1917) and Friedmann (1924) presented the hypothesis of the multi-connected topology as a model of the Universe.

The multi connected space will definitely affect the solution of an inverse problem discussed in the context of CMB.

Reference (inverse problem)

http://123.physics.ucdavis.edu/week_10_files/microwave/microwave_notes.pdf

“The most difficult remaining question is related to the topology of our Universe.“

Dear Janusz,

that‘s quite a notable statement and apparently underlines the significance of Yurij‘s work. In J.P. Luminet‘s paper “The Status of Cosmic Topology after Planck Data“ you quoted above I read: “The observable universe is the interior of a sphere centered on the observer and whose radius is that of the cosmological horizon“ in agreement with my previous suggestion. Do you think the Poincaré Dodecahedral Space model as illustrated in Fig.2 of the same paper, or similar topological space model, might be related in some way to the repetitive observation of distant quasar images referred to by Thierry De Mees in a recent discussion, see reference below?

https://www.researchgate.net/post/Would_it_make_sense_to_assume_a_limited_age_in_case_of_a_static_universe

Dear Johan,

thanks for the reference to very interesting paper by Keith (1963).

Actually the Field Gravitation Theory (FGT) is a modern development of the paper

Birkhoff G.D, Flat space-time and gravitation, Proc. Nat. Acad. Sci. U.S. 30, 324 (1944), together with ideas Thirring (1961), Kalman (1961) and Feynman (1962) (see review in arXiv gr-qc: 9912003 , where the Birkhoff's error in the field equation was corrected). In my review arXiv:1702.02020 (B2017) I also refer the Birkhoff's paper and call the tensor potential Psi^{ik} = fi_Newton diag(1,1,1,1) - as the Birkhoff's potential (p.40, eq.83 in B2017).

J. Keith used Birkhoff's equations of test particles motion, which also must be corrected. The accurate equation of rotating body motion in FGT was derived in

Baryshev Yu.V., Translational motion of rotating bodies and tests of the equivalence principle, Gravitation & Cosmology, 8, 232 (gr-qc/0010056) (2002).

There is very important measurable effect in the free fall of rotating bodies which violate the equivalence principle at the level of additional acceleration

dg/g ~ ( v / c )^2 where v = r Omega is the linear velocity of rotation (see discussion in B2017 pp. 50 - 54 ) . I think that the Keith effect should be reanalyzed in the future.

"I think that the Keith effect should be reanalyzed in the future."

Dear Yurij,

thanks for valuable comments from your theoretical point of view. It appears worthwhile as well to repeat experimental investigation of the Keith effect at some closer pole distance than before in order to minimize Coriolis drag.

I regard it a challenging outcome of Keith's theoretical analysis that he gets one and the same drag formula (25) when considering local acceleration of mass points on the spinning rotor as he derives by considering interaction of the same mass points with remote masses of the universe. This strongly suggests reconsidering the validity of Mach's principle. Do you see any hints along this direction on the basis of your theory?

Dear George,

the fractal dimension D = 2 of the observed large-scale spatial distribution of galaxies at the Local Volume with radius ~ 100 Mpc around our Galaxy is the firm observational fact as demonstrated by 2MRS data, see our analysis in

Tekhanovich D. I. & Baryshev Yu. V., Global Structure of the Local Universe

according to 2MRS Survey, Astrophys. Bulletin, Vol. 71, No. 2, p. 155 (2016)

(arXiv:1610.05206).

The severe paradox for the SCM is that the observed linear Hubble Law ( the distance - redshift relation (not velocity, which is a theoretical interpretation)) exits starting just from 1 Mpc, i.e. deeply inside the fractal structure. However, according to SCM the linear velocity - distance law is a strict consequence of the homogeneity of matter distribution, so which contradicts the reality.

It means that the most important observations should be related to the study of the spherical Local Volume and its further extension.

Dear Johan,

yes, in the frame of FGT the Mach's principle is fulfilled and inertial mass can be understund as the gravitational interaction with all masses of the Universe, which gives the potential fi ~ c^2 and the relation GM/Rc^2 ~ 1 (M is the Hubble mass and R is the Hubble radius).

Dear Johan,

“Do you think the Poincaré Dodecahedral Space model as illustrated in Fig.2 of the same paper, or similar topological space model, might be related in some way to the repetitive observation of distant quasar images referred to by Thierry De Mees in a recent discussion....”

The repetitive appearance of the same object is the first effect of the non-trivial topology of space. In-depth discussion of the mechanisms of this phenomenon is presented in the Luminet articles. In light of his observations, I note that the statements in the related thread makes a lot of sense. This answer, however, is based on theoretical analysis, obtaining experimental evidence remains a major challenge.

While waiting for experimental data, we can try to improve the analysis of light propagation in the Universe by constructing a general mathematical / numerical model (assuming different topologies). Such a model will greatly facilitate the analysis of all experimental data using formal inverse methods.

"in the frame of FGT the Mach's principle is fulfilled"

Dear Yurij,

that sounds great, what is the reasoning of opponents to Mach's Principle ?

"the potential fi ~ c^2 and the relation GM/Rc^2 ~ 1"

This apparently fits to one of my recent questions here, see reference below.

https://www.researchgate.net/post/Is_rest_mass_of_a_body_equivalent_to_local_accumulated_gravitational_potential_originating_from_remote_masses_of_the_universe

Red shifted plasma temperature is more likely.

"Red shifted plasma temperature is more likely." ...

Dear Jerry,

... at least if you look at it from within the Big Bang trap.

I don't know if that could help but there was an article published in Scientific American (April 2011) by Paul J. Steinhardt : The Inflation Debate: Is the theory (he is referring to the Big Bang) at the heart of modern cosmology deeply flawed....For him and other physicists they are more and more talking about the deflating cosmology...they are reconsidering whether the universe really went through an intense growth spurt shortly after the Big Bang. (see page 36-43)

According to the PFO-CFO Theory of Solar System Formation and Transformation, the cosmic microwave background represents the result of oscillation of the eternal and endless mass/energy field of a low potential, which is the material for the Universe origination in a rather remote indeterminable past; the stars result from the interference of the oscillations and origination of gravity initiated by the deformation of space, the mass/energy transformation into matter proceeds in stars and their nearest surroundings, the conservation laws observe always, and no big bang and fantasies connected with it occured.

(see RG and our publications).

CMB is the space of horospherical electromagnetic wavefronts in static Lobachevskian geometry of the universe. The model has detailed mathematical as well as physical description in our paper " CMB Lorentz invariant model ..." published in Journal of Modern Physics. Potential reader must have some basic knowledge of Lobachevskian (hyperbolic) geometry in order to understand paper.

Accepting that CMBR redshift is due to dopler effect from recession, and that the earth is not at the center of the universe, should we not expect a polarization of the redshift intensity along the line of earth's motion along the expansion? Is this evident in the observed CMBR? Please refer to my illustration.