Investigating the legend of Einstein’s “biggest blunder”

In 1956, the year after Albert Einstein’s death, physicist George Gamow wrote a Scientific American article on the Big Bang model that included a tantalizing historical tidbit: “Einstein remarked to me many years ago that the cosmic repulsion idea was the biggest blunder he had made in his entire life.”¹ Gamow repeated the claim in his 1970 autobiography,² and the story became one of the great legends of 20th-century physics. The story only got juicier with the 1998 discovery that the rate of cosmic expansion is increasing, an observation that cast Einstein’s “biggest blunder” in a new light.

But did Einstein really use those words? A recent analysis³ by astrophysicist Mario Livio concluded that Einstein probably never made the statement (see Physics Today, August 2013, page 48). Indeed, references to Einstein’s “biggest blunder” are nowadays usually accompanied by a disclaimer to the effect that the statement may be an invention on the part of Gamow.

After reviewing the literature, my research group has concluded that Gamow may stand unjustly accused. We find it very likely that Einstein called the cosmological constant his biggest blunder, and that he did so in front of several people.

Adopting and abandoning the cosmological constant

The story of the cosmological constant began just over a century ago, when Einstein decided to investigate what general relativity—his newly minted theory of gravity, space, and time—had to say about the universe as a whole. He soon found a curious problem: Assuming a static, uniform distribution of matter, the field equations of relativity $G_{\mu \nu }=-\kappa \left(T_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }T\right)$ gave a null solution for the case of the universe at large. (Here G_μν is a four-dimensional tensor representing the curvature of spacetime with elements g_μν; T_μν is a tensor representing energy and momentum; T is a scalar; and $\kappa$ is the Einstein constant.)

Einstein’s answer to the conundrum was to modify the field equations by adding a new term according to $G_{\mu \nu }-\lambda g_{\mu \nu }=-\kappa \left(T_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }T\right)$, where λ was a universal constant that became known as the cosmological constant. The modified field equations gave what appeared to be a satisfactory solution that predicted a static universe of radius R inversely related to the average density of matter $\rho$ it contained,⁴ given by $1/R^2=\kappa \rho /2=\lambda$. In his correspondence around this time, Einstein even attempted a rough estimate of the size of the universe (and thus the value of the cosmological constant) from estimates of the density of matter in the Milky Way, although he later realized that such calculations were unreliable.⁵

In 1929, American astronomer Edwin Hubble published the first tentative evidence of a linear relation between the redshifts of the spiral nebulae and their radial distance.⁶ Interpreting the phenomenon as evidence of an expansion of space on the largest scales, many theorists turned their attention to nonstatic relativistic models of the universe that had been proposed in the 1920s by Alexander Friedman and Georges Lemaître.^7,8

Einstein himself lost little time in abandoning his static cosmology, publishing in early 1931 a model of the expanding universe similar to that of Friedman.⁹ However, unlike Friedman and Lemaître, Einstein also abandoned the cosmological constant term, declaring the entity both unsatisfactory (it gave an unstable static solution) and redundant (relativity could describe the expanding universe without the term). A year later, Einstein suggested an even simpler model of the cosmos, once again without a cosmological constant term.¹⁰

Some other physicists argued against abandoning the cosmological constant. They noted that without a cosmological constant term, models would predict a universe with an age younger than the oldest stars. However, Einstein was not swayed by such concerns, and he never reinstated the term (see the article by Steven Weinberg, Physics Today, November 2005, page 31). As he remarked in one of his last reviews of relativistic cosmology: “If Hubble’s expansion had been discovered at the time of the creation of the general theory of relativity, the cosmologic 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.”¹¹

Evaluating the claim

In light of Einstein’s published statements, Gamow’s report that Einstein once described the cosmological constant as his “biggest blunder” seems reasonable. However, over the years Gamow’s claim has become the subject of increasing skepticism. Initial suspicion took the form of mild doubts expressed by the occasional physicist or historian. More recently, the study by Livio concluded that Einstein probably never made the statement.

One reason for the skepticism of Livio and others is that no record of Einstein’s famous comment has been found in his scientific works, personal papers, letters, or books. Historians make a clear distinction between primary and secondary sources, and the lack of a primary source for Einstein’s remark certainly raises doubts. Another issue concerns the reliability of the secondary source. Gamow had a deserved reputation as an irreverent physicist with a well-developed sense of humor, given to hyperbole; an acknowledged drinker and bon viveur, he struggled with alcoholism later in life. More specifically, Livio cites Stephen Brunauer, a US Navy lieutenant who recruited both Einstein and Gamow as consultants for the Navy during World War II. In a little-known 1986 article, Brunauer suggests that Gamow may have overstated his interactions with Einstein.³

On the other hand, the research of my own group leads us to conclude that Einstein probably did make the “biggest blunder” remark. First, the remark is highly compatible with Einstein’s science—from 1931 onward, he emphatically dismissed the cosmological constant in all of his writings on cosmology. None of those papers includes the blunder remark, but that’s not surprising, as it is unlikely that Einstein would have included such an informal comment in any of his formal scientific papers. It is true that the comment is not to be found in Einstein’s private papers, either, but very little of his correspondence in his later years was concerned with cosmology. In addition, we find Brunauer’s report somewhat misleading, as it pertains to Navy matters only. A study of the correspondence between Gamow and Einstein suggests that they had many interactions after the war that had nothing to do with the US military.

Finally, and perhaps most important, it turns out that Gamow is not the only physicist to have reported Einstein’s “biggest blunder” remark. In the 2000 book Exploring Black Holes: Introduction to General Relativity, the famous theorist John Archibald Wheeler (1911–2008) states the following: “Going into the doorway of the Institute for Advanced Study’s Fuld Hall with Einstein and George Gamow, I heard Einstein say to Gamow about the cosmological constant, ‘That was my biggest blunder of my life.’”¹² Similarly, Ralph Alpher (1921–2007), a close colleague of Gamow’s, recalled on an online message board a conversation with Einstein at Princeton about problems concerning the apparent time span of cosmic expansion: “A way to fix this was to reactivate the cosmological constant. Einstein did not like this very much and, as I recall, said his introduction of the concept in his early work was a blunder.”¹³

It is possible that both Wheeler and Alpher were influenced by Gamow’s writings; however, it seems a stretch to accuse three different scientists of invention. A more likely explanation is that all three reports pertain to the same occasion at Princeton. There is little doubt that Einstein came to dislike the cosmological constant, and given the arguments above, we find it very plausible that he spoke of the term as his “biggest blunder” on at least one occasion.

Implications for today’s cosmology

It is sometimes argued that Einstein’s real blunder was not the introduction of the cosmological constant in 1917 but rather his banishment of the term 14 years later. After all, modern measurements of cosmic expansion and of the cosmic microwave background suggest the presence of a significant component of cosmic energy known as dark energy, a phenomenon that can be described within the context of general relativity by including a cosmological constant term in the field equations.

However, Einstein’s cosmology was focused on the attempt to describe the observed universe as simply as possible, at a time when the discovery of dark energy lay in the distant future. Einstein’s clear distrust of the term as a complication of the field equations gives pause for thought: Is it possible we are once again adjusting the general theory of relativity in an ad hoc manner to account for a cosmological puzzle that may one day be described without recourse to such changes? If nothing else, Einstein’s “biggest blunder” remark prompts us to not dismiss out of hand those cosmologists who seek to describe the observed universe without resorting to a cosmological constant term.

References

1. G. Gamow, Sci. Am. 195, 136 (1956).
2. G. Gamow, My World Line: An Informal Autobiography, Viking Press (1970).
3. M. Livio, Brilliant Blunders: From Darwin to Einstein, Simon & Schuster (2013).
4. A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 142 (1917).
5. C. O’Raifeartaigh et al., Eur. Phys. J. H 42, 431 (2017).
6. E. Hubble, Proc. Natl. Acad. Sci. 15, 168 (1929).
7. A. Friedman, Z. Phys. 10, 377 (1922).
8. G. Lemaȋtre, Ann. Soc. Sci. Brux. A47, 49 (1927).
9. A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 235 (1931).
10. A. Einstein, W. de Sitter, Proc. Natl. Acad. Sci. 18, 213 (1932).
11. A. Einstein, The Meaning of Relativity, Princeton University Press (1945).
12. E. F. Taylor, J. A. Wheeler, Exploring Black Holes: Introduction to General Relativity, Addison Wesley (2000).
13. R. A. Alpher, Electronic posting on the online message board of the History of Astronomy Discussion Group (HASTRO), 2 April 1998.

Cormac O’Raifeartaigh lectures in physics at Waterford Institute of Technology in Ireland and is a Fellow of the UK Institute of Physics. A longer version of this article, cowritten with Simon Mitton, has been accepted for publication in the journal Physics in Perspective. A preprint can be found on arXiv.