by Livio, Mario
After scrutinizing all the available documents, I first confirmed something that a few historians of science have already suspected: The tale of Einstein calling the cosmological constant his biggest blunder originated from a single source: the colorful George Gamow. Recall that Gamow was responsible for the idea of big bang nucleosynthesis, as well as for some of the early thinking about the genetic code. James Watson, the codiscoverer of the structure of DNA, once said about Gamow that he was “so very often a step ahead of everybody.” Gamow told the “biggest blunder” story in two places. In an article entitled “The Evolutionary Universe,” published in the September 1956 issue of Scientific American, Gamow wrote, “Einstein remarked to me many years ago that the cosmic repulsion idea was the biggest blunder he had made in his entire life.” He repeated the same story [and for some reason, most accounts of the history of the cosmological constant are aware only of this source] in his autobiographical book My World Line, which was published posthumously in 1970: “Thus, Einstein’s original gravity equation was correct, and changing it [to introduce the cosmological constant] was a mistake. Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life.”
Since Gamow was known, however, to embellish many of his anecdotes (his first wife said once, “In more than twenty years together, Geo has never been happier than when perpetuating a practical joke”), I decided to dig a bit deeper in an attempt to establish the authenticity of this account. My motivation to investigate this particular quote was enhanced by the fact that the recent resurrection of the cosmological constant has turned “biggest blunder” into one of Einstein’s most cited phrases. The last time I checked, there were more than a half million Google pages containing “Einstein” and “biggest blunder”!
I started by trying to ascertain whether Gamow was purporting to actually quote Einstein directly. Unfortunately, each of the two citations presented above appears insufficient, as it stands, to determine whether Gamow was claiming that Einstein himself had used the words “biggest blunder” that he ever made in his life, or whether Gamow was merely reporting the spirit of the conversation. However, in My World Line, Gamow continued to say, “But this ‘blunder,’ rejected by Einstein, is still sometimes used by cosmologists even today, and the cosmological constant denoted by the Greek letter ‘Λ’ rears its ugly head again and again.” The use of quotation marks around the word “blunder” seems at least to suggest that Gamow meant to imply an authentic quote. The fact that Gamow used precisely the same language twice also indicates that he was trying to give the impression, at least, that he was quoting Einstein directly. Note also that Gamow reveals here his own prejudice concerning the cosmological constant, through the phrase “its ugly head.”
Intriguingly, I discovered that Einstein did actually use the expression “I made one great mistake in my life,” but in an entirely different context. Linus Pauling spoke with Einstein (as one leading scientist and pacifist to another) at Princeton, on November 16, 1954. Immediately following the conversation, Pauling wrote in his diary that Einstein told him the following (figure 33 shows Pauling’s diary entry): “He had made one great mistake—when he signed the letter to President Roosevelt recommending that atom bombs be made; but that there was some justification—the danger that the Germans would make them.” Clearly, this fact in itself does not necessarily preclude the possibility that Einstein might have used “biggest blunder” also in a scientific context, although the language employed in the conversation with Pauling (“one great mistake”) does make you wonder.
The second question I wanted to try to settle was that of the circumstances; when might Einstein have used this expression with Gamow? In My World Line Gamow gives the impression that he and Einstein were very close friends. He describes how during World War II, the two of them served at the same time as consultants in the Division of High Explosives of the US Navy’s Bureau of Ordnance. Since Einstein was unable at the time to travel from Princeton to Washington, DC, Gamow recounts, Gamow was “selected,” in his words, by the navy to bring documents to Einstein “every other Friday,” since he “happened to have known Einstein earlier, on nonmilitary grounds.” Gamow goes on to depict a very warm and intimate bond between him and Einstein:
Figure 33
Einstein would meet me in his study at home, wearing one of his famous soft sweaters, and we would go through all the proposals, one by one . . . After the business part of the visit was over, we had lunch either at Einstein’s home or at the cafeteria of the Institute for Advanced Study, which was not far away, and the conversation would turn to the problems of astrophysics and cosmology . . . I will never forget these visits to Princeton, during which I came to know Einstein much better than I had known him before.
Taking this description as factual, physicist Gino Segrè naturally concluded in his book Ordinary Geniuses: Max Delbruck, George Gamow, and the Origins of Genomics and Big Bang Cosmology that Einstein made the “biggest blunder” remark during one of those “World War II Princeton talks.” Albrecht Fölsing, who wrote one of the most accurate biographies of Einstein, also assumed that Gamow’s account was authentic, and he repeated the alleged “biggest blunder” citation, as did many others. Unfortunately, as I have discovered, the reality was rather different.
Stephen Brunauer was already an accomplished surface scientist when he became, as a lieutenant, head of high explosives research and development for the US Navy during World War II. At one point, he inquired with the army and the civilian divisions whether Einstein was working for them. The answer was negative from both branches. They explained to Brunauer that Einstein was a pacifist, and, furthermore, he was “not interested in anything practical.” Unwilling to accept this characterization as definitive, Brunauer visited Einstein at Princeton on May 16, 1943, and he recruited him as a consultant to the navy for a fee of $25 per day. Brunauer was also the officer who recruited Gamow on September 20, 1943. (See his letter to Gamow, figure 34.) In an article published in 1986, entitled “Einstein and the Navy: . . . ‘an unbeatable combination,’ ” Brunauer described the entire episode in detail. He mentioned that in addition to himself, a few other scientists in the division occasionally made use of Einstein’s services, including physicists Raymond Seeger, John Bardeen (who went on to win two Nobel Prizes in physics), and George Gamow, as well as chemist Henry Eyring. When explaining Gamow’s precise role, Brunauer wrote, “Gamow, in later years, gave the impression that he was the Navy’s liaison man with Einstein, that he visited every two weeks, and the professor ‘listened’ but made no contribution—all false. The greatest frequency of visits was mine, and that was about every two months.”
Figure 34
This narrative clearly sheds a somewhat different light on the Einstein-Gamow interaction. Scrutiny of the few, quite formal letters exchanged between Gamow and Einstein only enhanced my sense that the two men were not close. In one of those, Gamow asked for Einstein’s opinion on the idea that the universe as a whole might have nonzero angular momentum (a measure of rotation). To another, Gamow attached his paper on the synthesis of the elements in the big bang. Einstein replied politely to Gamow’s letters, but nowhere did he mention the cosmological constant. Perhaps the most telling piece of information in the entire correspondence, however, is a comment Gamow added to Einstein’s letter of August 4, 1946. Einstein informed Gamow that he had read the manuscript on big bang nucleosynthesis and that he was “convinced that the abundance of elements as function of atomic weight is a highly important starting point for cosmogonic speculations.” Gamow wrote across the bottom of the letter (figure 35), “Of course, the old man agrees with almost anything nowaday.”
But if Einstein and Gamow were not close, isn’t it surprising that Einstein would use such strong language (“biggest blunder” in his “entire life”) concerning the cosmological constant with Gamow, and not with any other of his more
intimate friends and colleagues? To explore this point further, I perused Einstein’s papers, books, and personal correspondence written later than 1932, for any other mention of the cosmological constant. I used 1932 as the starting point because that was the year in which Einstein and de Sitter declared the cosmological constant unnecessary.
Einstein’s writings leave no doubt that following the discovery of the cosmic expansion, he was unhappy with having introduced the cosmological constant in the first place. For instance, in 1942 his assistant and collaborator physicist Peter Bergmann published a book entitled Introduction to the Theory of Relativity, which included a foreword by Einstein, who later reviewed the work. The book does not even mention the cosmological constant. However, in the second edition of his own book The Meaning of Relativity, Einstein added an appendix in which he did remark on the cosmological term:
The introduction of the “cosmological member” into the equations of gravity, though possible from the point of view of relativity, is to be rejected from the point of view of logical economy. As Friedman[n] was the first to show one can reconcile an everywhere finite density of matter with the original form of the equations of gravity if one admits the time variability of the metric distance of two mass points.
In other words, Einstein recognized that the principles of general relativity allowed the addition of the cosmological repulsion term to the equations, but since it was not needed, he invoked mathematical simplicity to reject it. He then supplemented this comment with a footnote:
Figure 35
If Hubble’s expansion had been discovered at the time of the creation of the general theory of relativity, the cosmological member would never have been introduced. It seems now so much less justified to introduce such a member into the field equations, since its introduction loses its sole original justification—that of lending to a natural solution of the cosmological problem.
In appendix 4 to his popular book Relativity: The Special and General Theory, Einstein also noted that the cosmological term “was not required by the theory as such nor did it seem natural from a theoretical point of view.” Similarly, the revised, 1958 edition of Nobel laureate Wolfgang Pauli’s book Theory of Relativity included a supplementary footnote referring to the fact that Einstein was fully aware of the Friedmann and Lemaître solutions and of Hubble’s discovery. According to the author, a member of Einstein’s inner circle, Einstein subsequently rejected the cosmological term as “superfluous and no longer justified.” Pauli commented further that he himself fully accepted Einstein’s new standpoint. Nowhere, however, is there any allusion to “biggest blunder.”
An analysis of Einstein’s entire record about the cosmological constant makes it absolutely clear that he denounced it on two grounds only: an aesthetically motivated simplicity, and the regret over the wrong motivation for its introduction. As I noted in chapter 2, simplicity in terms of the principles involved is considered one of the hallmarks of a beautiful theory. To Einstein, simplicity was more than that—it was almost a criterion of reality: “Our experience up to date justifies us in feeling sure that in nature is actualized the ideal of mathematical simplicity.” Einstein’s experience during the development of general relativity had only enhanced his trust in mathematical principles. When he tried to follow what he thought were the physical constraints, he got nowhere, whereas following the most natural equations from a mathematical perspective opened the door to a “theory of incomparable beauty,” in his words. Adding another constant (the cosmological constant) to the equations did not convey reductionistic beauty to Einstein, but he was willing to live with it for as long as it appeared to be imposed by what he perceived as a static reality. Once the cosmos was found to be dynamically expanding, Einstein was delighted to rid his theory of what he now regarded as excess baggage. He articulated his feelings in a letter he wrote to Georges Lemaître on September 26, 1947. This was a reply to a letter that the Belgian cosmologist had sent to Einstein on July 30 of the same year. In that letter (and in an article by Lemaître that followed), Lemaître did his best to persuade Einstein that the cosmological constant was actually necessary to explain a number of cosmic facts, including the age of the universe.
Einstein first admitted that “the introduction of the Λ term offers a possibility” to avoid contradiction with geological ages. Recall that the age of the universe implied by Hubble’s original observations was much shorter than the age of the Earth. Lemaître thought that he could resolve this conflict if the equations included the cosmological constant. However, Einstein repeated his reductionist arguments to justify his continuing reluctance to accept the cosmological constant. He wrote:
Since I have introduced this term I had always a bad conscience. But at that time I could see no other possibility to deal with the fact of the existence of a finite mean density of matter. I found it very ugly indeed that the field law of gravitation should be composed of two logically independent terms which are connected by addition. About the justification of such feelings concerning logical simplicity it is difficult to argue [emphasis added]. I cannot help to feel it strongly and I am unable to believe that such an ugly thing should be realized in nature.
In other words, the original motivation no longer existed, and Einstein felt that aesthetic simplicity was violated, so he did not believe that nature required a cosmological constant. Did he think then that this was his “biggest blunder”? Unlikely. Yes, he was uncomfortable with the concept, saying as early as 1919 that it was “gravely detrimental to the formal beauty of the theory.” But general relativity definitely allowed for the introduction of the cosmological term, without violating any of the fundamental principles on which the theory had been founded. In this sense, Einstein knew that this was not a blunder at all even before the more recent discoveries concerning the cosmological constant. The experience gained in theoretical physics since Einstein’s time has shown that any term allowed by the basic principles is likely to be necessary. Reductionism applies to the fundamentals, not to the specific form of the equations. The laws of physics thus resemble the rules in the Arthurian novel The Once and Future King by the English author T. H. White: “Everything that is not forbidden is compulsory.”
To conclude, it is virtually impossible to prove beyond any doubt that someone did not say something. Still, my best guess, based on the entire body of evidence, is that while Einstein may have had a “bad conscience” about the introduction of the cosmological constant, especially since he missed the chance to predict the cosmic expansion, he never actually called it “the biggest blunder” that he “had ever made.” That part was, in my humble opinion, almost certainly Gamow’s own hyperbole. Amusingly, in an article entitled “Einstein’s Greatest Blunder,” University of Manchester astronomer J. P. Leahy commented, “It is just as well that Einstein made his remark to Gamow, otherwise Gamow would have been severely tempted to make it up.” My conclusion is that Gamow probably did make it up!
You may wonder why this particular quip by Gamow has become one of the most memorable pieces of physics folklore. The answer, I believe, is threefold. First, people in general, and the media in particular, love superlatives. News in science is always more appealing when it involves “the fastest,” “the farthest,” “the biggest,” or “the first.” Einstein, being human, erred many times, but none of his other mistakes created such headlines as his so-called biggest one. Second, Einstein has become the embodiment of genius—the man who purely by his intellectual powers discovered the workings of the universe. He was the scientist who demonstrated that pure mathematics could discover what it creates and also create what it discovers. It has been said about the ancient Greeks that they found the universe a mystery and left it a polis (city-state). From the perspective of modern cosmology, this aphorism fits Einstein even better. (Figure 36 shows my favorite picture of Einstein.) The fact that even such a scientific powerhouse is fallible is both fascinating and a wonderful lesson in humility—and in how science truly progresse
s. Even the most impressive minds are not flawless; they merely pave the way for the next level of understanding. The third reason for the popularity of the cosmological constant, sometimes called the most famous fudge factor in the history of science, is that it has proven to be the ultimate diehard. Like drug dealer Pablo Escobar and Russian mystic Grigory Rasputin, the cosmological constant has been incredibly hard to kill, even though Einstein denounced it eighty years ago. What’s more, not only has this ostensible “blunder” refused to die, but in the past decade it has become the very center of attention. What was it that gave the cosmological constant its nine lives, and why was it thrown into the limelight again?
Figure 36
Hooked on Λ
Even during Einstein’s lifetime, there were a few scientists who did not want to give up on the cosmological constant. Physicist Richard C. Tolman, for instance, wrote to Einstein in 1931, “A definite assignment of Λ = 0, in the absence of experimental determination of its magnitude, seems arbitrary and not necessarily correct.” Lemaître, in addition to his general sentiment that Λ should not be rejected only because it had been introduced for the wrong reasons, had two other main motivations for wanting to keep the cosmological constant alive. First, it offered a potential solution to the discrepancy between the perceived young age of the universe (as Hubble’s observations seemed to imply) and geological timescales. In some of Lemaître’s models, a universe with a cosmological constant could linger for a long time in a coasting state, thus prolonging the age of the cosmos. Lemaître’s second reason for championing Λ had to do with his ideas about the formation of galaxies. He conjectured that regions of higher density would be amplified and grow into protogalaxies during that coasting phase. While this particular idea was shown not to work in the late 1960s, it did help to keep the cosmological constant on the back burner for a while.