## Preface

The analysis in this book is started with the confirmed fact that Alexander Friedmann’s 1922 work had no relation with Hubble’s Law that was yet to be found by Edwin Hubble in 1929. Official sources repeatedly tell us that Georges Lemaître had found similar to Friedmann’s solution in year 1927 so I thought that Lemaître’s work also should have no actual relation with Hubble’s Law. My analysis kept going with this assumption till section I.III where I realized that if unlike Friedmann, Lemaître had the data of Doppler’s Redshifts of various galaxies, then he also could have means to find the distance of those galaxies. Admittedly, this book up to section I.III is an analysis based on an incorrect assumption that by 1927, Lemaître should be unaware of Hubble Type redshift-distance relationship in light coming from far off galaxies. But that analysis forced me to download 1927 paper of Lemaître. Initially I found English Translation (1931) by the title: “A Homogeneous Universe of Constant Mass and Increasing Radius accounting for the Radial Velocity of Extra-galactic Nebulæ”. I was shocked to see that my analysis was wrong up to section I.III because apparently Lemaître had already derived Hubble type redshift-distance relationship solely from General Relativity (GR) Equations. But I was not wrong. **This was a manipulated translation; he had not derived that relationship from GR equations rather had derived from a method which he took directly from Hubble himself, detail thereof I have explained in this book.** Here in this book, original papers of Friedmann (1922), Lemaître (1927), Edwin Hubble (1929), Albert Einstein (1917) along with other important relevant papers have been analyzed and only the most fundamental aspects like expansion and CMBR of Big Bang Cosmology are covered. If these two aspects of Big Bang Cosmology are precisely refuted then there is nothing crucial left with the standard model.

Philosophy is not concerned with providing definite solutions to the problems. Therefore, alternatives suggested in this book should not literally be taken as definite alternatives. They however represent philosophically solid and justified positions and it is up to readers who should conclude the matter by applying their own critical judgment. This book will however expose the undue authoritative nature of FLRW metric and with this book, Big Bang Theory is set to become a story of past.

## Free Section I.IV.

## I.IV. In 1931, Lemaître Suppressed Crucial Facts by Publishing Manipulated Translation of his own 1927 Article

Parallel to the above narrated expectations, there were however surprising actual events. In 1927, Lemaître did present a redshift-distance relationship which is acknowledged by the mainstream science community of today but that was not acknowledged by Edwin Hubble himself. Yes, there is proportionality relationship between redshift and distance in the article titled “A Homogeneous Universe of Constant Mass and Increasing Radius accounting for the Radial Velocity of Extra-galactic Nebulæ” (English Translation: 1931)[i]. But why plain proportionality relation of redshift and distance could not satisfy Hubble? Pro-Lemaître sources[ii] directly blame Hubble that he never read actual paper of Lemaître that’s why he failed to appreciate the fact that Hubble type redshift-distance relation was already derived from equations by Lemaître.

Therefore it is important that we may analyze what actually Lemaître had proposed in year 1927. The source we have is the translation of 1927 article by Lemaître himself published in year 1931 and also the original French article published in 1927. My finding is that there is huge blunder in the translation of article that was published in year 1931. But before explaining the blunder of 1931 translation, let us first see what the case in favor of the Big Bang Theory is that exists today in year 2018. The whole case of the Big Bang Theory is that although exact redshift-distance relation was experimentally found by Hubble in year 1929, but at least Lemaître had already derived same relationship from a solution to relativity equations. Since equations rightly picked the underlying reality, therefore the only reason of redshift-distance relation that was found by Hubble was same equations. Therefore, we should forget that Cosmological Redshift (redshift-distance relation) is different from Doppler’s Redshift (redshift-speed relation) or that Cosmological Redshift, unlike Doppler’s Redshift, is not the physical proof of receding of anything. Since equations rightly described Cosmological Redshift and since same equations described an expanding universe, therefore there is no need of physical evidence that Cosmological Redshift is also the proof of receding of anything. Perhaps we can use both terms ‘Cosmological Redshift’ and ‘Doppler’s Redshift’ interchangeably which is actually being done in official papers and textbooks even today. It is exact this interchangeability of these two separate terms in official papers and science discussions that I call dodge that portrays Big Bang Theory as fully backed by experimental proof of ‘Doppler’s Effect’. In reality, we only have physical proof that yes Doppler’s Redshift actually indicates receding of anything but we do not have any experimental proof that Cosmological Redshift is also proof of receding of anything. We have only mathematics.

Anyhow, the whole case of the Big Bang Theory rests on a single fact that relativistic equations (Lemaître’s) predicted same Hubble type redshift-distance relationship almost two years before the actual experimental discovery of same relation by Hubble. But this single fact is a huge blunder. Yes 1927 French article had already ‘discovered’ that relationship (in less accurate form) but actually that relationship was not derived out of any equation. We have already seen in our previous analysis that given only the Doppler’s Redshifts data and relativistic equations, Hubble type redshift-distance relationship could not be derived. But after having written this analysis when I actually downloaded the 1931 English translation of article, I literally remained astonished and dumbfounded to see that almost same Hubble type redshift-distance relationship was already contained in that article. But before I also fell into believing the magic of mathematics, I read in another pro- Lemaître paper[iii] that there were certain discrepancies in original French article of 1927 and English Translation of 1931. Being pro- Lemaître, this paper at first projected Lemaître as a victim of those discrepancies that how whole para under equation 23 was replaced by a single sentence where redshift-distance was explained in details. The paper started first from blaming editor of journal and then Hubble or Eddington (teacher of Lemaître) but then concludes that recently it came to surface that Translation was written by Lemaître himself and modifications in translation were his own personal choices.

At that time, I did not read that paper in complete so could not realize that the paper also contains ‘right revised’ translation in Appendix at the end. I simply rushed to download original French article. Yes there was a complete paragraph under equation No.23 which was replaced by a single sentence in the English Translation. But since I could not read French article so I typed relevant para in notepad and sought google translation of para. And the resulting translation was depicting a gigantic blunder of Translation of 1931. The revised translation of original French explanation under equation No.23 includes following crucial sentences:

“Radial velocities of 43 extragalactic nebulæ are given by Str ̈omberg (6). The apparent magnitude m of these nebulæ can be found in the work of Hubble. It is possible to deduce their distance from it, because Hubble has shown that extragalactic nebulæ have approximately equal absolute magnitudes (magnitude = − 15. 2 at 10 parsecs, with individual variations ±2), the distance r expressed in parsecs is then given by the formula log r = 0,2m + 4,04.”

Actually, 1927 French article was published in an obscure journal and original article had failed to receive attention by scientific community. At that time, Lemaître had sent copy of article to his former teacher Arthur Eddington but he also did not respond and perhaps only had a cursory look of that article. According to para under equation No.23 of the original article, redshift-distance relation was not derived from any relativistic equation but was incorporated in the formulation of equations to get matching results with known observational data of redshift as well as distance. Essentially, redshift-distance relationship was formulated in exact same mode as later on Hubble would also formulate. The redshift-distance relationship had no mathematical derivation – it was simply derived from observational data. And Lemaître was the first to present that relationship but his original work did not reach to the right audience. So far there was no blunder. Only thing was that accompanying relativistic equations themselves never gave result of expansion but without proper experimental basis, Lemaître assigned meanings of ‘expansion’ to the whole new type of cosmological redshift which he discovered himself.

After two years, Edwin Hubble would find the same redshift-distance relationship in same (non-mathematical) observational data mode but he would not commit mistake of blindly assigning the meaning of expansion despite having no observational proof that redshift-distance actually had anything to do with receding of anything from observer. Rather, he would actively search for right person who could provide satisfactory theoretical justification for galactic redshift-distance relationship. However, everyone will listen to him only up to the statement that there is “(apparent) velocity-distance relationship” and everyone will automatically understand this statement in a modified form of “velocity-distance” relationship (i.e. automatic omission of word ‘apparent’). “Velocity-distance” would acquire the status of a confirmed scientific fact on authority of Edwin Hubble and discovery of expanding universe will be attributed to Hubble despite the fact that Hubble himself would remain skeptical to the idea of expansion and it is also possible that Hubble also sometime be using both terms “redshift-distance relationship” and “velocity-distance relationship” interchangeably.

Thus after 1929, “velocity-distance relationship” was known to everyone as newly found fact by Hubble. Eddington, former teacher of Lemaître, at that time was in an effort to account for observed ‘velocities’ of galaxies within the framework of relativistic equations[iv]. After knowing that Eddington was in search of kind of solution that he developed in year 1927, Lemaître again sent him copy of his paper and this time Eddington overwhelmingly acknowledged his article and also reported to de-Sitter, another prominent relevant mathematician of that time. Perhaps Eddington persuaded Lemaître to write English translation to be published in a reputed journal. Eddington even sponsored the translated article by himself writing a supportive article for same publication. Lemaître became a celebrated scientist in 1931 due to publication of translation of the original article. But there were blunders in translation.

If we read only translation, then it is a magically great article because without any reference to Hubble, there is derivation of a hard fact from equations such that hard fact was to be discovered by Hubble only two years after the publication of original French paper. The greatness of article (translated) was also greatly felt such that soon Lemaître would be invited to great conferences where he would propose as ridiculous ideas as ‘Primeval Atom’ (later became ‘Cosmic Egg’) for the whole of Universe and all the celebrated audience would accept like under trance.

But nothing was great up to the magical level. Lemaître had found a simple linear relation on the basis of observed data that he had. That relation was not derived from equations but equations were designed to remain consistent with observed data. No scientist would formulate equations without properly taking care of available observational data. If Lemaître had found that relationship purely out of equations then he should have explained this fact in the original French article. But in the original article, he simply writes that distance is found by applying simple deduction on observational data. And since he knew the redshift-distance relationship out of observational data, he was able to propose ‘radiation pressure’ as cause of expansion. We have already seen that idea of ‘radiation pressure’ was not derived from equations. He simply empirically knew the linear relationship between redshifts and distance and he only arbitrarily suggested cause of relationship to be the ‘radiation pressure’. After the publication of manipulated translation with the help of Eddington in 1931, he ‘abandoned’ the associated idea of ‘radiation pressure’ and did not pursue or develop it further.

In the capacity of a translator, it was his first duty to present only the original article in the translated language. But if any modification was indispensable, then he was duty bound to explain reasons for modification along with presenting translation of omitted portions in footnotes at least. The discrepancy in translation was perhaps never surfaced during his life time and even to-date the discrepancy is not widely known. There have been speculations regarding who omitted crucial parts of the article from translation. At first editor of journal; then Eddington and even Hubble is blamed for the omission. Lemaître has been projected as victim of the discrepancy as it deprived him of priority claim in finding Hubble law. Those who understand the meaning of French paragraph take it only from the point of view of who first time discovered expanding universe; Edwin Hubble or Georges Lemaître. The issue is largely overlooked from angle whether the relationship was derived from equations or equations were framed according to available observational data. However speculations regarding who omitted crucial paragraphs from translation have been resolved through special efforts of Mr. Mario Livio[v] who has found a letter written by Lemaître to the editor of journal where Lemaître is telling the editor that “I did not find advisable to reprint the provisional discussion of radial velocities which is clearly of no actual interest.” So it was someone’s advice to not include ‘provisional discussion’ of radial velocities which is of ‘no actual interest’. That someone should be Arthur Eddington, his former teacher who also happened to be at authoritative position of Royal Astronomical Society. The journal where translation was to be published was also under the administrative control of Royal Astronomical Society. Mario Livio takes above-mentioned words of Lemaître as his humbleness since he is not showing interest in a priority claim regarding discovery of expanding universe. Well, this could be humbleness or innocence of Lemaître that he was only being guided by his former teacher. Lemaître himself could be blank regarding what was the actual goal of Eddington but he should not be as simple as to call that crucial paragraph as having ‘no actual interest’. By all means that was a crucial and interesting paragraph. By choosing not to reprint ‘provisional discussion’, he did not abandon his priority claim. The linear relationship of redshift-distance was still present at the end of article where numerical results were presented in a table. After omission of ‘provisional discussion’ that was actually reference to Hubble as a source of that relationship, now the end part of article had become like a manifestation of magic that was showing how only the equations had already derived a hard fact two years before the actual discovery of that fact. Editor of journal raised no objection and published the modified translation. Eddington also wrote a sponsoring article in same issue of journal and while having published a sponsoring article in the same issue, the fact of modified translation could not be out of sight of Eddington.

Before moving on, one thing needs to be settled. Mario Livio writes that in 1927, Lemaître first derived Hubble law from equations and then went beyond mere theoretical calculations and attempted to find actual value of Hubble Constant. In the translation, he only omitted paragraph related to determination of value of Hubble Constant whereas linear relationship of ‘velocity-distance’ already had been derived from equations. My response is that once you have observational data of ‘velocities’ (redshifts) and you also know method of derivation of distance, then you can easily suggest linear relationship and there is no need of derivation of linear relationship from complex equations. In fact, Edwin Hubble would actually do the same within next two years. Likewise in 1927, Lemaître had the data of redshifts and he also knew the method of finding distance. He already had a rough sketch of linear relation between redshifts and distance and he simply developed mathematics that was consistent with the available sketch. The omitted paragraph was originally written after equation No.23 of the original French paper and this paragraph included calculation of radial velocity of 625 KM/sec/mega-parsec. This figure has come directly from observational data and it is not even consistent with equation No.23 because in equation No.23, as we shall see in coming paragraphs, * H* was not a constant term.

While yes, apparently there is resemblance between equation No.23 and the Hubble law which is ** V=HD** whereas equation No.23 is

**.**

*V/C=(R’/R)r*Here ** V/C** is redshift as Lemaître makes it clear under equation No.22 and also in a given table provided after equation No.31. In Hubble law, redshift is

**therefore LHS of Hubble law and equation No.23 of Lemaître is same. Furthermore,**

*V***and**

*D***of RHS of both equations are also same because both stand for ‘distance’.**

*r***is change in total radius of universe divided by original radius and this change of radius has occurred in time when light emitted from source (galaxy) has reached to observer. Now the question is whether**

*R’/R***and**

*R’/R**of both equations also same? Well, it is not clear but if we accept that equation No.23 is exactly equal to Hubble’s law then we should find the source of equation No.23 in Lemaître’s article whether it is derived from equation No.22 or from which of the earlier equations?*

**H**Apparently however this equation No.23 has come out of nowhere. In equation No.23, ** r** (distance) appears for the first time throughout the article and there is no back source of ‘distance’ in previous equations. The only source of

**(i.e. ‘distance’) is one sentence written just before equation No.23. The sentence is**

*r**“When the light source is near enough, we have the approximate formula.”*It means that Hubble type redshift-distance relationship was not really derived from equations but equation No.23 was formulated to remain consistent with later proceedings where actual data of redshifts and distances of various galaxies was going to be discussed.

Up to equation No.22, there is no reference to ‘distance’ of light emitting source. Since it is ‘Doppler’s Effect’ interpretation going on, distance is not even relevant because the relevant thing is ‘speed’. However, within Doppler’s interpretation, there is mention of time of emission of light from source (galaxy) and time when light is observed. With this information, we are obliged to give a remote margin that might be equation No.23 with ** ‘r’** was derived from equation No.22. But if it is the case then the linear relationship of equation No.23 resembled to Hubble’s linear relationship such that not

**, actually**

*H***was constant in that equation. The title of section 4 of the article (starting just before eq.22) is “Doppler Effect due to variation of the Radius of the Universe.” Even title of the article is “A Homogeneous Universe of Constant Mass and Increasing Radius accounting for the Radial Velocity of Extra-galactic Nebulae.” In this scheme of interpretation of redshifts, it is radius of whole Universe which is increasing due to which Doppler’s Effect is only ‘apparent’ i.e. extra-galactic nebulae are at fixed distance and they are not receding away from us.**

*D*In section 4 of the article, light is emitted from a coordinate **σ1** and slightly later another ray of light is emitted from same coordinate **σ1** and reached to observing coordinate **σ2**. Radius of whole Universe is increased during this slight duration but light emitting coordinate has remained the same. Equation No.22 describes a redshift and just after the equation the text states that * “it is ‘apparent’ Doppler’s Effect due to the variation of the radius of Universe.”* Then equation No.23 presents a Hubble type linear relationship with the crucial difference that instead of

**it is**

*H***which is constant and ‘distance’ comes into equations for the first time only out of an introducing sentence. Up to equation No.23,**

*D***(or**

*D***) is constant but afterwards**

*r***(or**

*H***) becomes constant. Therefore there are two distinct tracks within Lemaître’s article. Nice words here do not portray the reality as the fact is that two distinct parts of Lemaître’s article are inconsistent with one another.**

*R’/R*First part of the article is up to Equation No.23 where at the end, suddenly ** ‘r’** (distance) arrive in equation. This distance was constant as the only changing entity was radius of whole universe which is the radius of curvature of universe. The coordinate

**σ1**i.e. light emitting point remains the same but radius of universe changes and Doppler’s Shift was only

**apparent**as source of light was not moving – only radius of universe was expanding. Now it is crucial to point out that ‘FLRW’ metric has picked only Equation No.23 from first part of the article and that also in modified form.

The position of Equation No.23 that coordinate of light emitting source does not change is consistent with ‘FLRW’ metric where coordinates of receding galaxies also do not change as coordinates themselves recede away. If ‘FLRW’ principle is to be followed then coordinate of radius of universe also should not change. But within Lemaître’s equation, coordinates of radius of universe do change. Moreover, Lemaître is only talking about expansion of curvature of whole universe and he is not talking about ‘expansion of space’ within ‘FLRW’ type meanings. In fact, equation No.23, if written like Hubble’s law would be given as ** V=(R’/R)D** but ‘FLRW’ metric would make this equation into

**where**

*V=(S’/S)D***stands for ‘space’. But Lemaître had derived his own equations and not FLRW metric. Up to equation No.23, galaxies are not even moving away. Coordinates are also not moving within Lemaître’s article. Distance is perfectly constant for the light source. Doppler’s Effect is only apparent and it is due to expansion of whole universe. In other words, galaxies are not moving away but somehow gravitational hold of the whole universe is becoming weaker due to which spatial curvature of whole universe is getting straighter thus ‘apparent’ Doppler’s Effect is accounted for in this way.**

*S***If equations had derived anything then it was this something.**Top of all, he was able to derive equations merely because he had the data of ‘Doppler’s Effect’ of various extra-galactic ‘nebulae’ and he also knew how to deduce distance of those nebulae out of a method which he had learned from Hubble. Obviously he did not learn that method after having derived equation No.23. Given the fact that he already had sketchy idea of linear relationship of redshift and distance, why and how could he formulate structure of equations that should be devoid of this relationship? Evidently, his equations had to be consistent with sketchy idea of empirical facts which he had found himself.

After equation No.23, Lemaître joins a different track. Now he would do actual calculations of redshifts and distance purely out of observational data but this part would later on be omitted in the translated article. After presenting the table under equation No.31, he would first time say that not only radius of Universe but ** r** i.e. distance of galaxy and

**σ1**i.e. light emitting point (coordinates) are also proportional to Doppler’s Effect. This part of the article would therefore be inconsistent not only with first part of the same article, it will also be inconsistent with famous ‘FLRW’ metric because in second part of the article, galaxies are physically receding away and not within the meaning of ‘expansion of space’ since coordinates of light emitting sources are also changing.

Thus my response to Mario Livio is that before the omitted paragraph, Lemaître had not actually reached to Hubble’s law which means that GR equations alone failed to take him to the destination of Hubble’s law. He reached to Hubble’s law after equation No.23 only through the route of observational data and he also determined his original value of Hubble’s constant within the framework of observational data mode only.

But in year 1931, he deliberately presented modified translation. With translated article, he projected himself able to derive from equations a hard fact which he actually learnt from observational data and from a method of derivation of distance provided by Hubble. Clearly he was being guided by someone who could most probably be his former mentor – Arthur Eddington, who already had served the role of king-maker by authenticating Einstein’s General Relativity through his famous (may be notorious) experiment of confirming bending of light ray during solar eclipse in 1919. Role of Eddington makes sense because modification in translation was in his notice and he was the one who actually comprehended the desired consequences of omission of reference to observational data in the translated article. Eddington was fully aware that omission will highlight extraordinary power of equations that would be beneficial for himself and Lemaître both. The strategy worked. Lemaître never claimed priority in finding redshift-distance relationship. He only let people judge the matter in his favor. Equations received a recognized power in the topic. Einstein (old king) apologized to Lemaître (new king) for not previously accepting genuineness of his work. Expansion became real thing. Einstein also accepted that he had been playing around with fudge factors by abandoning ‘cosmological constant’[vi] and thus granted permission to the expansion to keep going on. Hubble could not openly challenge expansion regime because he had not received any plausible theoretical justification of Cosmological Redshifts. Not only that Lemaître never claimed priority in finding redshift-distance relation, he also preferred to remain silent on the issue of modified translation of original article. The modification was a mega blunder. If it was not a deliberate manipulation then a clarification should have come from Lemaître which never surfaced. Everyone was giving credit to equations for finding a hard fact yet to be discovered by Hubble but Lemaître never explained that he had learned path to discovery of that fact from Hubble himself. Clearly mathematical equations had no extraordinary power. They do have power only up to the extent of what can be logically deduced from given axioms and parameters. If redshift of Doppler’s effect has primary relation only with speed and not with distance and if gravity is concerned with attraction and not with expansion then equations based on these two parameters could not give, except in the way of error, the result of a kind of redshift that has direct relation with distance. It was possible only if equations were erroneously solved or at least one of the parameters already had direct relation of redshift with distance. The original French article duly acknowledged that parameter but the same crucial acknowledgement was unduly omitted from the Translation. Eddington was fully aware that mathematics does not really possess extraordinary magical powers. But he accepted all the benefits of confirming extraordinary powers of mathematics for the cases of Albert Einstein (1919 solar eclipse verification) and then Georges Lemaître (1931). Perhaps he was contented in serving the role of king-maker for these two persons. But at a later stage, he would not be comfortable in again serving the role of king-maker for the case of Chandrasekhar[vii] [viii] where he would argue that mathematics alone was not able to find realities of physics. … For further details, please see the book **“A Philosophical Rejection of The Big Bang Theory”**.

[i] https://academic.oup.com/mnras/article/91/5/483/985165

[ii] https://arxiv.org/pdf/1305.6470.pdf

[iii] https://arxiv.org/pdf/1305.6470.pdf

[iv] https://arxiv.org/pdf/1305.6470.pdf

[v] http://imgsrc.hubblesite.org/hvi/uploads/science_paper/file_attachment/69/pdf.pdf

[vi] He did not actually abandon cosmological constant. Only thing is that he adopted value assigned to it by Friedmann.

[vii] https://en.wikipedia.org/wiki/Arthur_Eddington

[viii] https://en.wikipedia.org/wiki/Subrahmanyan_Chandrasekhar