In science literature and online sources, the whole universe is often depicted in the shape of a cylinder.
In year 2018, I completed my first book (on the topic of big bang) but a perplexing issue remained outstanding which I could not solve till the publication of the book. The problem was that Friedmann (1922) was saying that Einstein’s depiction of universe was cylindrical whereas Einstein’s own paper (1917) had described universe as spherical.
In their well-known works on general cosmological questions, Einstein and de-Sitter arrive at two possible types of universe: Einstein obtains the so-called cylindrical world ……..
Whereas if we read Einstein (1917) paper, we find that Einstein was talking about spherical universe:
From our assumption as to the uniformity of distribution of the masses generating the field, it follows that the curvature of the required space must be constant. With this distribution of mass, therefore, the required finite continuum of the x1, x2, x3 with constant x4, will be a spherical space.
Here x1, x2 and x3 are coordinates of three dimensional space and 4th dimension x4 (time) is kept constant and the result is a spherical space.
So the issue remain unresolved till the publication of my book (2018) regarding why did Friedmann (1922) write that Einstein (1917) had obtained a cylindrical universe. However, now I get the clue of this apparent anomaly. It turned out that Friedmann (1922) had taken his understanding of Einstein (1917) from Arthur Eddington’s (1921) book i.e. a secondary source. Following is written in Eddington (1921) book:
It is with some such underlying idea that Einstein’s cylindrical space-time was suggested, since this cannot exist without matter to keep it stretched. Now we freely admit that our assumption of perfect flatness in the remote parts of space was arbitrary …..
Space, Time and Gravitation, An outline of the General Relativity (1921)
Now case is clear before the readers. Einstein (1917) was talking about three dimensional space as spherical while keeping 4th dimension (time) as constant. Eddington (1921) was talking about 4 dimensional space-time to be cylindrical in shape. Friedmann (1922) was talking about three dimensional space and calling it cylindrical on behalf of Einstein.
In a letter to Isaac Newton, David Gregory declared in 1694: “A continual miracle is needed to prevent the Sun and the fixed stars from rushing together through gravity.” Newton pondered the issue over the years starting around 1685 and concluded:
“The fixed stars being… at such vast distances from one another, can neither attract each other perceptibly, nor be attracted by our Sun.”
I. Newton, Principia (1728)
Newton reasoned that:
“if the matter of our sun and planets and all the matter in the universe were evenly scattered throughout all the heavens, and every particle had an innate gravity toward all the rest, and the whole space throughout which this matter was scattered was but finite; the matter on the outside of the space would, by its gravity, tend toward all the matter on the inside, and by consequence, fall down into the middle of the whole space and there compose one great spherical mass. But if the matter was evenly disposed throughout an infinite space, it could never convene into one mass; but some of it would convene into one mass and some into another, so as to make an infinite number of great masses, scattered at great distances from one to another throughout all that infinite space.
I. Newton, letter to theologian Richard Bentley (1692)
Therefore, if we assume that both Einstein and Newton were logically correct and differed only in the underlying assumption, then we see that concept of galaxies is a logical outcome of the assumption of an infinite universe. If we say that Einstein’s cosmological constant prevented the collapse of whole universe but did not prevent the collapse at smaller scale of individual galaxies (or clusters) … then still the point remains that up to the year 1924 i.e. when existence of galaxies was confirmed through observations, there were at least three solutions (i.e. Einstein (1917), de-Sitter (1917) and Friedmann (1922)) to the GR equations (as applied to whole universe) available and none of them was able to describe such collapses at smaller than whole universe scale. Therefore, if their logic was correct and they did not derive such localized collapses in their works then our conclusion is that cosmological constant also won’t help in the derivation of localized galactic structures within a finite universe. In other words, mere existence of galaxies is the proof that either this is an infinite universe or at least the universe is much larger in size than what standard model has to tell.
In my book “A Philosophical Rejection of The Big Bang Theory” (2018), I pointed out and explained that Friedmann (1922) had not actually reached to Hubble Law that was officially found in year 1929. In my (2018) book, I had quoted the stance of Wikipedia which clearly stated at that time that the law was first derived by Friedmann. Following was written in Wikipedia at that time and I had quoted the same in my (2018) book:
“Although widely attributed to Edwin Hubble, the law was first derived from the general relativity41equations, in 1922, by Alexander Friedmannwho published a set of equations …..”
Hubble Law article of Wikipedia in early 2018
After my book, Wikipedia has somewhat corrected this mistake. Now same portion of same Wikipedia article reads as follows:
Hubble Law article of Wikipedia … as on 18-06-2020.
So Wikipedia now does not insist that Hubble Law was first derived by Friedmann. However it still insists that “notion of expanding universe at a calculable rate” was first derived by Friedmann. I want to state here that this stance is also wrong. My claim is that Friedmann did not even say that galaxies are moving away. He did not even talk about galaxies. All he knew was that at cosmic scale, “stars” are static and not in motion.
According to ‘FLRW metric’ expansion of space is taking place all the time everywhere. If 1 mm distance is becoming 2 mm in 1 billion years then 2 mm is becoming 4 mm in same 1 billion year and so on. Every length of space has to become double in same 1 billion years.
So it is like Big Bang of creation of empty space taking place right now – everywhere. Nothing solid is being created by this everyday-everywhere happening Big Bang. However solid things are getting distant apart due to this all the time everywhere happening Big Bang.
And we are told that this is science. Failure to rightly explain cosmological redshifts has resulted in this non-sense Physics. This is really possible only in balloon surface like expansion where every point of surface keeps on expanding. But balloon is expanded due to continuous application of pumping action or force whereas in Big Bang Model, it is said that only the original one time pumping action is still doing its work. It cannot be argued that current expansion is the inertial motion generated by original one time Big Bang because it is not one time thing. This ‘Big Bang’ is taking place all the time – even now.
This type of Big Bang is all the time creating only ‘new empty space’. We should conclude that matter was never created by Big Bang. Matter existed already. Big Bang could only create ‘space’ and even now doing only the same. Given that Universe existed prior to Big Bang, the Big Bang only started ‘expansion’. Before start of Big Bang, it was a static universe. After stoppage of ongoing Big Bang, universe shall be again static.
Title of the paper is: “A relation between distance and radial velocity among extra-galactic nebulae.”
Here “radial velocity” means “redshift”.
From 1912 onwards, scientists had been noticing redshifts in far off galaxies (then thought of spiral nebulae). Naturally by that time those redshifts were interpreted in terms of Doppler’s Effect. Due to Doppler’s interpretation, those redshifts were also called “radial velocities”.
Here in the title of his paper, Hubble has used common term “radial velocity” for “redshift”.
But to determine what he actually wants to say, we must very carefully study the first paragraph of 1929 paper. Following is the first paragraph:
“Determinations of the motion of the sun with respect to the extra-galactic nebulae have involved a K term of several hundred kilometers which appears to be variable. Explanations of this paradox have been sought in a correlation between apparent radial velocities and distances, but so far the results have not been convincing. The present paper is a re-examination of the question, based on only those nebular distances which are believed to be fairly reliable.”
Here it is also true that he starts his paper with sentence “Determinations of the motion of the sun with respect to the extra-galactic nebulae”.
But … in the very first paragraph … he is pointing something perplexing for which he is using word ‘paradox’ and after pointing out this ‘paradox’, now he is using term apparentvelocities instead of velocities.
Following is relevant sentence in the first paragraph:
“Explanations of this paradox have been sought in a correlation between apparent radial velocities and distances, but so far the results have not been convincing.”
Here is the point. In Doppler’s Shift, there is no redshift-distance relationship but what Hubble was observing was a redshift-distance relationship. Therefore with this paper, he was seeking explanations for this ‘paradox’.
From whom he was seeking explanation?
He wrote this question in a public paper so he asked it from wise community. But he asked for this explanation from particular people of his choice also. Furthermore, he has skeptically concluded this paper with following words:
“In the de Sitter cosmology, displacements of the spectra arise from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter. The latter involves an acceleration and hence introduces the element of time. The relative importance of these two effects should determine the form of the relation between distances and observed velocities; and in this connection it may be emphasized that the linear relation found in the present discussion is a first approximation representing a restricted range in distance.”
In the letter to de-Sitter, he writes:
“Mr. Humason and I are both deeply sensible of your gracious appreciation of the papers on velocities and distances of nebulae. We use the term ‘apparent’ velocities to emphasize the empirical features of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.[i]”
Thus ‘apparently’ redshifts seemed like velocities but for Hubble, the actual interpretation of redshifts was unresolved question. With this, he actually rightly recognized the fact that redshift involved in extra galactic nebulae was of a different kind than to the usual Doppler’s Shift.
With his 1929 paper, Hubble not only did not suggest ‘expansion of universe’, he also almost denied that meaning of ‘redshifts’ was ‘velocities’. He used term ‘apparent velocities’ and he even looked for such reasons of redshift as apparent slowing down of atomic vibrations and a general tendency of material particles to scatter.
The usage of term ‘apparent’ for velocities and then looking for explanation of redshifts in such reasons as apparent slowing down of atomic vibrations and a general tendency of material particles to scatter indicates that for Edwin Hubble, ‘velocities’ was not the final meaning for redshifts. The term ‘apparent’ points to the determination of meaning of redshifts as indeterminate.
But soon Robertson and Walker were going to give him an undue gift of literal meaning of ‘apparent velocities’. FLRW metric (Friedmann-Lemaître-Robertson-Walker) was declared to be the only possible interpretation of cosmological redshifts. In this so-called metric, ‘apparent velocities’ of galaxies literally became ‘apparent velocities’ such that there was no actual velocity but ‘space’ was expanding thus galaxies were ‘apparently’ receding away from our solar system.
Whatever FLRW metric says but point of this blog post is only to show that Edwin Hubble himself did not suggest expansion of universe and neither did he took redshifts of galaxies as actual receding velocities of those galaxies.
After having seen what Hubble exactly told us in year 1929, now we should guess the level of misinformation in general public about Hubble’s finding when NASA itself is also gravely misinformed. Following is a quote from NASA website:
“The Big Bang model was a natural outcome of Einstein’s General Relativity as applied to a homogeneous universe. However, in 1917, the idea that the universe was expanding was thought to be absurd. So Einstein invented the cosmological constant as a term in his General Relativity theory that allowed for a static universe. In 1929, Edwin Hubble announced that his observations of galaxies outside our own Milky Way showed that they were systematically moving away from us with a speed that was proportional to their distance from us. The more distant the galaxy, the faster it was receding from us. The universe was expanding after all, just as General Relativity originally predicted! Hubble observed that the light from a given galaxy was shifted further toward the red end of the light spectrum the further that galaxy was from our galaxy.”
For heaven’s sake NASA – Hubble DID NOT say that galaxies are ‘moving away’. At the most he said that galaxies are APPARENTLY moving away.
In year 1936, Edwin Hubble clearly stated following in his book “Realm of the Nebulae”:
And … he reached to final conclusion by the end of year 1941 where he clearly stated that observations are actually showing a static universe.