# When Einstein Met Lemaître

Editor’s note: Discovery Institute Press is delighted to announce the publication of The Big Bang Revolutionaries: The Untold Story of Three Scientists Who Reenchanted Cosmology, by Jean-Pierre Luminet. The book has received rave reviews including from three Nobel Prize winners. The following is an excerpt from Chapter 12.

Georges Lemaître’s work is notable for providing the first interpretation of cosmological redshifts as a natural effect of the expansion of the universe within the framework of general relativity, instead of attributing it to the real motion of galaxies. As it is given in equation 23 — R/R = v/cr — space is constantly expanding and consequently increases the apparent separations between galaxies. This idea would prove to be one of the most profound discoveries of our time.

The proportional relation between the recession velocity v and the distance r is an approximation valid at not too large distances which can be used, he writes, “within the limits of the visible spectrum.” Then, using the available astronomical data, Lemaître calculates the relation in equation 24, with a factor 625 or 575 km/s/Mpc (which means that galaxies that are 1 megaparsec away have a recession speed of 625 or 575 km/sec). Depending on the choice of observations, this presented an enormous scatter:

Using the 42 extra-galactic nebulae in the Hubble and Strömberg lists, and taking into account the Sun’s own speed, we find an average distance of 0.95 million parsecs and a radial velocity of 600 km/s, or 625 km/s at 10parsecs. We will therefore adopt R’/R = v/rc = 0.68´ 10-27 cm-1 (equation 24).

For this the Belgian scientist uses a list of forty-two radial velocities compiled by Gustav Strömberg, a Swedish astronomer at the Mount Wilson Observatory, and deduces the distance of the corresponding extra-galactic nebulae from an empirical formula relating the distance and the absolute magnitude provided by Hubble, who himself took the magnitudes from Hopmann. This was the first calculation of the so-called Hubble law and the Hubble constant, to be recognized only much later.

## Mostly Unnoticed

The significance of Lemaître’s work remained mostly unnoticed for three years. A reason commonly given is that it was published not in one of the prestigious astronomical journals of the time but in French and in a journal that has been characterized as obscure and inaccessible. There is a grain of truth in this explanation, but as D. Lambert has rightly pointed out, the journal in question, Annales de la Société Scientifique de Bruxelles, published some articles in English, was of an excellent scientific level, and therefore was included in a large number of academic libraries and observatories around the world. Moreover, a much larger scientific audience then than today could read French. Rather, the main obstacle to a larger diffusion of Lemaître’s article was that most of the physicists of the time, such as Einstein and Hubble, could not accept the idea of a non-static universe. This was not the case with Eddington. Unfortunately, his former mentor, to whom Lemaître had sent a copy, either forgot to read it in time, or failed to understand its importance.

## The Fifth Solvay Conference

From October 24–29, 1927, the Fifth Solvay Conference in Physics took place in Brussels, one of the great meetings of world science. The Solvay Conference was devoted to the new discipline of quantum mechanics, whose problems disturbed many physicists. Among them was Einstein. For Lemaître, it was the opportunity to meet and talk with the father of general relativity. He later reported on this meeting:

While walking in the alleys of the Parc Léopold, [Einstein] spoke to me about an article, little noticed, which I had written the previous year on the expansion of the universe and which a friend had made him read. After some favorable technical remarks, he concluded by saying that from the physical point of view that appeared completely abominable to him. As I sought to prolong the conversation, Auguste Piccard, who accompanied him, invited me to go up by taxi with Einstein, who was to visit his laboratory at the University of Brussels. In the taxi, I spoke about the speeds of nebulae and I had the impression that Einstein was hardly aware of the astronomical facts.

André Deprit, a former student of Lemaître, gave a more picturesque and slightly different version of this encounter:

Einstein had been invited to discuss his deterministic conception of the world with the young pioneers of quantum mechanics; Lemaître was pacing up and down in front of the Institute, hoping to hook him on the way. While it’s true that Professor Piccard, who was escorting Einstein that afternoon, picked Lemaître up in the taxi, the fact remains that Lemaître felt spurned. Yes, Einstein had read the note that had just appeared in the Annales de la Société Scientifique; the mathematics were correct, but the physics of the article, what an abomination! Need one say more? To defend himself, Lemaître mumbled a discreet allusion to Hubble’s observations in English, which he withdrew immediately so as not to embarrass Professor Piccard, as he understood that Einstein was not aware of them. The conversation stopped for a moment, and Piccard resumed it with Einstein, but in German: Lemaître, who knew no German, had no choice but to remain silent.

Einstein’s response to Lemaître shows the same unwillingness to change his position that characterized his former response to Friedmann: he accepted the mathematics, but not a physically expanding universe. According to D. Lambert, this reaction came from the fact that Einstein’s implicit philosophy was inspired by Spinoza. For the Dutch philosopher, “God” (Deus) was identified with “Nature” (Natura): “Deus sive Natura.” Consequently, due to the immutability of God, one could not accept any motion or evolution of Nature itself. Einstein thus rejected the idea of an evolving universe, i.e., a world with a real history. This “theological” prejudice led him also to criticize strongly the idea of expanding (and contracting) universes put forward by Friedmann and Lemaître.

In July 1928, Lemaître went to Leiden, where de Sitter presided over the third assembly of the International Astronomical Union, but did not meet him. The hour of the Big Bang had obviously not yet come.

## The Hour Approaches

The same year H. P. Robertson published an article seeking to replace de Sitter’s metric with a “mathematically equivalent [metric] in which many of the apparent paradoxes inherent in [de Sitter’s solution] were eliminated.” He got the formula v = cd/R where d is the distance of the nebula and R the radius of curvature of the universe, but in the framework of a static solution. Robertson used the same set of observations that Lemaître used (though he did not know of Lemaître’s articles of 1925 and 1927) and that Hubble would later use. From this he calculated R = 2 ´ 1027 cm and a proportionality constant of 464 km/s/Mpc. In a trailblazing article the following year, Robertson related his detailed search for all the mathematical models satisfying a spatially homogeneous and isotropic universe and that also imply strong symmetries in the solutions to Einstein’s equations.

In 1929, Hubble used the experimental data on the Doppler redshifts, mostly given by Slipher, and found a linear velocity-distance relation v = Hr with = 465 ± 50 km/s/Mpc for twenty-four objects and 513 ± 60 km/s/Mpc for nine groups. The law was strictly identical to Lemaître’s equation 24, with almost the same proportionality factor.

However, Hubble did not take the crucial step to expanding-universe models. He stated, “The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect.” In the introduction to his 1936 book, The Realm of Nebulae, Hubble discussed the interface between observation and theory, and honestly stated, “The author of this book is primarily an observer.” In fact, out of the 202 pages in the book, he discusses the theoretical interpretation of his observations only on page 198, in a last paragraph entitled “Theories of Cosmology.” He makes no mention of the work of Lemaître, but quotes Friedmann, Robertson, and Arthur Milne (who attempted a Newtonian explanation with his theory of “kinematic relativity”). Moreover, Hubble makes the mistake of considering the spectral shift as a pure Doppler effect (due to the galaxies’ own recession velocity) and not as an expansion effect (increase of the space scale radius over time).

## Life as a Skeptic

And all during his life he would remain skeptical about the general relativistic interpretation of his observations. As his biographer G. Christianson has pointed out, Hubble was chary of “all theories of cosmic expansion long after most astronomers and physicists had been won over. When queried about the matter as late as 1937, he sounded like an incredulous schoolboy: ‘Well, perhaps the nebulae are all receding in this peculiar manner. But the notion is rather startling.’”

Indeed, the idea that the expansion of the universe was discovered by Hubble is a myth that was first propagated by his collaborator Milton Humason as early as 1931 and by Hubble himself. Fiercely territorial, Hubble wrote in a letter to de Sitter, dated August 21, 1930: “I consider the velocity-distance relation, its formulation, testing and confirmation, as a Mount Wilson contribution and I am deeply concerned in its recognition as such.”