# Reasons in Favor of a Hubble-Lemaître-Slipher’s (HLS) Law

## Abstract

**:**

## 1. Introduction

^{th}Century, in particular of the non-Euclidean geometries, on the part of Friedrich Gauss (1777–1855), Nikolai Lobachevski (1792–1856), János Bolyai (1802–1860), and Bernhard Riemann (1826–1866), which allowed Einstein—with the inestimable collaboration, according to some historians, of his mathematical partner Marcel Grossmann and his wife Mileva Marić (1875–1948)—to formulate his theories of relativity, first the special and then the general one. We must not forget the important contributions of other great scientists, such as Henri Poincaré (1854–1912), David Hilbert (1862–1943), and Hendrik Lorentz (1853–1928), to mention only three of them. In short, all modern cosmology is based on Einstein’s field equations, which he formulated in 1915, corresponding to his theory of general relativity (for interesting recent overviews, see, e.g., [1,2]). This gives rise to many authors to place, with precision, the origin of modern cosmology in 1917, in which Einstein used his equations, for the first time, to build a model with which to describe our universe. The universe, at that epoch, was believed to be static, without origin or end in time, and was very small because everyone was convinced that everything discovered was within the Milky Way. Since a static universe was not a solution to his field equations, Einstein introduced into them an additional term, the now famous cosmological constant, which with the right sign, provided a kind of repulsive force that counteracted the attraction of gravity.

^{th}General Assembly of the International Astronomical Union (IAU), celebrated in Vienna (20–31 August 2018), five resolutions were proposed for approval [3]. The fifth of them, Resolution B4, addressed a suggested renaming of the Hubble law, recommending that from now on, this law on the expansion of the universe be referred to as the “Hubble–Lemaître law”. The basic point in favor of the resolution being

that the Belgian astronomer Georges Lemaître, in 1927 published (in French) the paper entitled ‘Un Univers homogene de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques’ [4]. In this, he first rediscovers Friedmann’s dynamic solution to Einstein’s General Relativity equations that describes an expanding universe. He also derives that the expansion of the universe implies the spectra of distant galaxies are redshifted by an amount proportional to their distance. Finally he uses published data on the velocities and photometric distances of galaxies to derive the rate of expansion of the universe (assuming the linear relation he had found on theoretical grounds).

About my contribution of 1927, I do not want to discuss if I was a professional astronomer. I was, in any event, an IAU member (Cambridge, 1925), and I had studied astronomy for two years, a year with Eddington and another year in the U.S. observatories. I visited Slipher and Hubble and heard him in Washington, in 1925, making his memorable communication about the distance [to] the Andromeda nebula. While my Mathematics bibliography was seriously in default since I did not know the work of Friedmann, it is perfectly up to date from the astronomical point of view; I calculate [in my contribution] the coefficient of expansion (575 km per sec per megaparsec, 625 with a questionable statistical correction). Of course, before the discovery and study of clusters of nebulae, there was no point to establish the Hubble law, but only to calculate its coefficient. The title of my note leaves no doubt on my intentions: A Universe with a constant mass and increasing radius as an explanation of the radial velocity of extra-galactic nebulae.

## 2. Vesto Melvin Slipher

^{th}Century (see, e.g., M.J. Way [22]), with contributions by, among others, Swedenborg (1734), Wright (1750), Kant (1755), and Lambert (1761) [23,24,25,26]. William Herschel (1785) [27] was also convinced for a time that spiral nebulae were outside the Milky Way, but changed his mind later [28].

“This might suggest that the spiral nebulae are scattering but their distribution on the sky is not in accord with this since they are inclined to cluster.”

“... our whole stellar system moves and carries us with it. It has for a long time been suggested that the spiral nebulae are stellar systems seen at great distances ... This theory, it seems to me, gains favor in the present observations.”

and John Peacock adds to that [34]“probably made more fundamental discoveries than any other observational astronomer of the twentieth century.”

“Slipher was indeed a great pioneer; not simply through his instrumental virtuosity in achieving reliable velocities where others had failed, but through the clarity of reasoning he applied. Slipher in 1917 lacked the theoretical prior of a predicted linear distance-redshift relation, which de Sitter only published the same year. Slipher was simply looking for a message that emerged directly from the data, and it is therefore all the more impressive that he was able to reach in 1917 his beautiful conclusions concerning the motion of the Milky Way and the nature of spiral nebulae as similar stellar systems. Slipher’s other main legacy to modern cosmology remains as relevant as ever. The peculiar velocity field that he discovered has become one of the centerpieces of modern efforts to measure the nature of gravity on cosmological scales.”

## 3. Hubble on Slipher

in a Letter of E.P. Hubble to V.M. Slipher, March 6, 1953 (Biographical Memoirs, Vol 52, National Academy of Sciences (U.S.)). This actually occurred, as Marcia Bartusiak explains [42,46], as follows: In 1953, as Hubble was preparing a talk, he wrote Slipher asking for some slides of his first 1912 spectrum of the Andromeda Nebula, and in this letter, he, at last, gave the Lowell Observatory astronomer due credit for his initial breakthrough, writing:“your velocities and my distances”,

“I regard such first steps as by far the most important of all. Once the field is opened, others can follow.”

“emerged from a combination of radial velocities measured by Slipher at Flagstaff with distances derived at Mount Wilson.”

“... the first steps in a new field are the most difficult and the most significant. Once the barrier is forced further development is relatively simple.”

## 4. The Expanding Universe

“the Universe may expand since General Relativity equations admit dynamical solutions.”

“it is difficult to believe that the velocities are real; that all matter is actually scattering away from our region of space. It is easier to suppose that the light waves are lengthened and the lines of the spectra are shifted to the red, as though the objects were receding, by some property of space or by forces acting on the light during its journey to the Earth” [56,58].

“the 200-inch telescope will definitely answer the question of the interpretation of red-shifts, whether or not they represent actual motions, and if they do represent motions ‘if the universe is expanding’ the 200-inch may indicate the particular type of expansion” [47].

## 5. Discussion and Conclusions

- In all the discussion, the IAU text of the resolution, and followups (as [62], for one), a very important issue has been systematically neglected: the very crucial role of the astronomer Vesto Slipher in the derivation of Hubble’s law. To obtain the law, you need to compare two tables: one of radial velocities and one of distances to the extragalactic objects.
- While there is no doubt that Hubble produced the table of distances (he was a master in this respect, systematically using Henrietta Leavitt’s law), the table of velocities was due to Vesto Slipher.
- Hubble himself was the first to recognize (albeit too late) the very important role of Slipher, talking of “your velocities and my distances”, in a Letter of E.P. Hubble to V.M. Slipher, 6 March 1953 (Biographical Memoirs, Vol 52, National Academy of Sciences (U.S.)), and writing in his famous book E.P. Hubble, “The realm of the nebulae” [47], while referring to Slipher, that “... the first steps in a new field are the most difficult and the most significant. Once the barrier is forced further development is relatively simple.” This is an explicit recognition of the seminal role of Slipher in the conception of the expansion law.
- Why did Hubble eventually say that? Although Slipher did not calculate the distances to the objects, his results on the redshifts, which he started to obtain in 1912, where so astonishing, pointing in some cases to such enormously high recession speeds, that he was undoubtedly the first astronomer to recognize that something weird and incredibly unusual was happening in the universe: how could it be static at all if those objects were around, receding at such speeds? When he presented his results at the 1914 meeting of the American Astronomical Society he received a long, standing ovation. The community of astronomers (Hubble included) realized immediately that an important discovery was on the making.
- It may seem contradictory that in Lemaître’s 1927 paper (now being vindicated), there is no mention to the table of redshifts by Vesto Slipher (which, by the way, adds reasons to his having been neglected). This may seem very strange, since Lemaître perfectly knew about Slipher’s results, from his visit to the Lowell observatory in Arizona during the period of his MIT thesis. Instead, in deriving Hubble’s law, Lemaître takes his radial velocities from a table due to G. Strömberg [63]. However, alas, you need only read the first page, even just the first two lines of Strömberg’s paper, to realize that all of it is, again, an extraordinary tribute to Slipher: “the great majority of the determinations being by Slipher.”, obtained “through the perseverance of Professor M. Slipher.”, and so on.

- I consider the role of Slipher in the derivation of Hubble’s law to be of paramount importance, as recognized (implicitly and explicitly), to begin with, by the two other actors of this drama, and subsequently by an increasing number of reputed specialists. His role was invaluable, both in inspiring the whole development (Hubble’s dixit) and in providing one of the two tables that were absolutely necessary for the formulation of the law, both by Hubble and Lemaître (which nobody can oppose).
- I therefore propose to the community of cosmologists that we make the effort to re-name the Hubble law as the Hubble–Lemaître–Slipher (HLS) law. With this naming of the law of the universe expansion, we can de-facto improve the IAU original idea and give due credit to the three main actors of this play.
- I am absolutely sure that both Edwin Hubble and Georges Lemaître would had been very happy with this decision.
- Further, I am also sure that, if the three brilliant cosmologists were alive now, under the standard criteria of the Nobel Academy, they would be most perfect candidates for a shared Nobel Prize, for their work that led to the discovery of the universe expansion law.

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Elizalde, E.
Reasons in Favor of a Hubble-Lemaître-Slipher’s (HLS) Law. *Symmetry* **2019**, *11*, 35.
https://doi.org/10.3390/sym11010035

**AMA Style**

Elizalde E.
Reasons in Favor of a Hubble-Lemaître-Slipher’s (HLS) Law. *Symmetry*. 2019; 11(1):35.
https://doi.org/10.3390/sym11010035

**Chicago/Turabian Style**

Elizalde, Emilio.
2019. "Reasons in Favor of a Hubble-Lemaître-Slipher’s (HLS) Law" *Symmetry* 11, no. 1: 35.
https://doi.org/10.3390/sym11010035