Einstein’s Lost Theory Describes a Universe Without a Big Bang

By Amir Aczel | March 7, 2014 10:32 am

Einstein with Edwin Hubble, in 1931, at the Mount Wilson Observatory in California, looking through the lens of the 100-inch telescope through which Hubble discovered the expansion of the universe in 1929. Courtesy of the Archives, Calif Inst of Technology.

In 1917, a year after Albert Einstein’s general theory of relativity was published—but still two years before he would become the international celebrity we know—Einstein chose to tackle the entire universe. For anyone else, this might seem an exceedingly ambitious task—but this was Einstein.

Einstein began by applying his field equations of gravitation to what he considered to be the entire universe. The field equations were the mathematical essence of his general theory of relativity, which extended Newton’s theory of gravity to realms where speeds approach that of light and masses are very large. But his math was better than he wanted to believe—his equations told him that the universe could not stay static: it had to either expand or contract. Einstein chose to ignore what his mathematics was telling him.

The story of Einstein’s solution to this problem—the maligned “cosmological constant” (also called lambda)—is well known in the history of science. But this story, it turns out, has a different ending than everyone thought: Einstein late in life returned to considering his disgraced lambda. And his conversion foretold lambda’s use in an unexpected new setting, with immense relevance to a key conundrum in modern physics and cosmology: dark energy.

The Static Universe Before Hubble

Einstein had what would have seemed a very good reason for ignoring what the math was telling him. Few people know that Einstein was not merely a superb theoretician, but also a physicist skilled in observations and experiments. In 1914, Einstein was wooing a young Scottish-German astronomer, Erwin Finlay Freundlich, to seek proof of relativity through shifts in apparent star locations during a total solar eclipse that was to take place in the Crimea (which ended badly because of the outbreak of World War I). Letters that Einstein wrote to Freundlich during 1913-4 reveal that Einstein had a burgeoning interest in astronomy and understood much about the field, including technical details of lenses and mirrors.* Ironically, his deep knowledge of astronomy would lead Einstein to make the greatest blunder of his entire career….Or not.

Astronomical knowledge of the time told Einstein that the universe was unchanging in its size. How could someone think that? Well, this was the second decade of the twentieth century, and telescopes were still relatively small and not very powerful. They were strong enough to allow astronomers to discover all the now-known planets in our solar system, to get good views of “cloudy patches” of the sky such as the Orion nebula, and to view several galaxies, including the Great Andromeda Galaxy—our nearest neighbor at 2.3 million light years’ distance.

But astronomers believed that all these fuzzy objects they were seeing were somehow part of our own Milky Way. (The great Eddington even believed at that time that the Sun was the center of this universe! And an idea about the distances to the most faraway stars only began to emerge through the work of Harlow Shapely on Cepheid variables, conducted at the Mount Wilson Observatory, in 1916.) Since astronomers could detect no expansion of stars or nebulas in the entire cosmos known to them, they assumed that the universe was static.

The Birth of the Cosmological Constant

To force his equations—which theoretically predicted the expansion of the universe—to remain still, Einstein invented the cosmological constant, λ. He multiplied the metric tensor in his equation, g, by the cosmological constant, leading to a term λg, which adjusted his metric tensor acting on space-time. This mathematical trick assured him that his equations would yield a universe that was prevented from expanding or contracting.

Unbeknownst to Einstein, at exactly the time he published his paper on the cosmological equations, across the world in California, the new 100-inch Hooker telescope was being fit in its place at the Mount Wilson Observatory. Within a little over a decade, Edwin Hubble, aided by Vesto Slipher and Milton Humason, would use this, the most powerful telescope on Earth, to study the redshift of distant galaxies and conclude from it definitively that our universe is expanding.

Einstein heard about these results, and in the early 1930s, he traveled to California and met with Hubble.  At the Mount Wilson Observatory he saw the massive data set on distant galaxies that had led to “Hubble’s law” describing the expansion of the universe and got angry at himself: had he not forced his equations to stay static with that cosmological-constant invention of his, he could have theoretically predicted Hubble’s findings! That would have been worth a second Nobel Prize for him (he deserved a few more, anyway)—in the same way, for example, that the CERN scientists’ 2012 experimental discovery of the Higgs boson recently won Peter Higgs the Nobel in 2013. In disgust, Einstein exclaimed after his Mount Wilson visit: “If there is no quasi-static world, then away with the cosmological term!” and never considered the cosmological constant again. Or so we thought until recently.

Dark Energy: Lambda Returns

When a genius such as Einstein makes a mistake, it tends to be a “good mistake.” (I am indebted to the mathematician Goro Shimura for this expression.) It can’t simply go away—there is too much thought that has gone into it. So, like a phoenix, Einstein’s cosmological constant made a remarkable comeback, very unexpectedly, in 1998.

That year, two groups of astronomers made an announcement that rocked the world of science. The “Supernova Cosmology Project,” based in California and headed by Saul Perlmutter, and the “High-Z SN Search” group at Harvard-Smithsonian and Australia, announced their results of the shifts of distant galaxies leading to a conclusion that nobody had expected: The universe, rather than slowing its expansion since the Big Bang, is actually accelerating its expansion!

And it turns out that the best theoretical way to explain the accelerating universe is to revive Einstein’s discarded lambda. The cosmological constant (acting differently from how it was designed, as a force stopping the expansion) is the best explanation we have for the mysterious “dark energy” seen to permeate space and push the universe ever outward at an accelerating rate. To most physicists today, lambda, cosmological constant, and dark energy are closely synonymous. But unfortunately Einstein was not there to witness the reversal of his “greatest blunder,” having died in 1955.

And it has been widely assumed that he died without ever reconsidering the cosmological constant. Until now.

Einstein’s Lost Manuscript

The Irish physicist Cormac O’Raifeartaigh was perusing documents at the Einstein Archives at the Hebrew University in Jerusalem in late 2013 when he discovered a handwritten manuscript by Einstein that scholars had never looked at carefully before. The paper, called “Zum kosmologischen Problem” (“About the Cosmological Problem”), had been erroneously filed as a draft of another paper, which Einstein published in 1931 in the annals of the Prussian Academy of Sciences. But it was not. It seems that even with Einstein, old notions die hard: This paper was his stubborn attempt to resurrect the cosmological constant he had vowed never to use again.

In a paper just filed on the electronic physics repository ArXiv, O’Raifeartaigh and colleagues show that in the early 1930s (the assumed date is 1931, but this is uncertain), Einstein was still trying to return to his 1917 analysis of a universe with a cosmological constant. Einstein wrote (the authors’ translation from the German):

“This difficulty [the inconsistency of the laws of gravity with a finite mean density of matter] also arises in the general theory of relativity. However, I have shown that this can be overcome through the introduction of the so-called “λ–term” to the field equations… I showed that these equations can be satisfied by a spherical space of constant radius over time, in which matter has a density ρ that is constant over space and time.”

But he was now aware of Hubble’s discovery of the expansion of the universe:

“On the other hand, Hubbel’s [sic**] exceedingly important investigations have shown that the extragalactic nebulae have the following two properties 1) Within the bounds of observational accuracy they are uniformly distributed in space 2) They possess a Doppler effect proportional to their distance”  (Quoted in O’Raifeartaigh, et al., 2014, p. 4)

And so Einstein proposed a revision of his model, still with a cosmological constant, but now the constant was responsible for the creation of new matter as the universe expanded (because Einstein believed that in an expanding universe, the overall density of matter had to still stay constant):

In what follows, I would like to draw attention to a solution to equation (1) that can account for Hubbel’s facts, and in which the density is constant over time.” And: “If one considers a physically bounded volume, particles of matter will be continually leaving it. For the density to remain constant, new particles of matter must be continually formed in the volume from space.”

Einstein achieves this property by the use of his old cosmological constant, λ:

“The conservation law is preserved in that by setting the λ-term, space itself is not empty of energy; as is well-known its validity is guaranteed by equations (1).” (Quoted in O’Raifeartaigh, et al., 2014, p. 7.)

So Einstein keeps on using his discarded lambda—despite the fact that he invented it for a non-expanding universe. If the universe expands as Hubble showed, Einstein seems to be saying, then I still need my lambda—now to keep the universe from becoming less dense as it expands in volume.

Almost two decades later, a similar “steady state” universe would be proposed by Fred Hoyle, Hermann Bondi, and Tommy Gold, in papers  published in 1949. But these models of the universe are not supported by modern theories. In fact, a tenet of modern cosmology is that as the universe will expand a great deal (after an unimaginably long period of time), it will become very thinly populated, rather than dense, with stray photons and electrons zipping alone through immense expanses of emptiness, all stars having by then died and disappeared.

Views of the Cosmos, Old and New

As for why Einstein was so intent on maintaining the use of his discarded lambda, the constant represents the energy of empty space—a powerful notion—and Einstein in this paper wanted to use this energy to create new particles as time goes on.

Today we view the same energy of the vacuum as the reason for the acceleration of the universe’s expansion. Einstein presciently understood that the energy of the vacuum, unleashed by his cosmological constant, was too important to let die.

Einstein was far from the only person to wonder about the universe and whether it has always existed or was born at some point in the past and would die at a future time. This question has been pondered by people ever since the dawn of civilization. The origin and ultimate fate of the universe are highly interlinked with its overall geometry—the actual shape of the space-time manifold. In a closed geometry, the universe was born and will someday recollapse on itself. In an open geometry, it was born and will expand forever, and the same happens in a flat (Euclidean) geometry. Based on modern theories supported by satellite observations of the microwave background radiation in space, space-time is nearly perfectly Euclidean, meaning that the universe was born in a Big Bang and will expand forever, becoming less dense with time. Eventually, matter may decay into few kinds of elementary particles and photons, the distances among them growing to infinity.

Cosmology in Context

Between 1917 and 1929—the year Hubble and his colleagues discovered the expansion of the universe, implying the possibility of a beginning for the cosmos—Einstein and most scientists held that the universe was “simply there” with no beginning or end. But it’s interesting to note that creation myths across cultures tell the opposite story. Traditions of Chinese, Indian, pre-Colombian, and African cultures, as well as the biblical book of Genesis, all describe (clearly in allegorical terms) a distinct beginning to the universe—whether it’s the “creation in six days” of Genesis or the “Cosmic Egg” of the ancient Indian text the Rig Veda.

This is an interesting example of scientists being dead wrong (for a time) and primitive ancient observers having an essentially correct intuition about nature. And with the present explosion of models of the universe and sometimes outrageous “scientific speculations” about its origin and future, some commentators are clearly overstating what science has done. One recent example is the book by the physicist Lawrence M. Krauss, A Universe From Nothing, which claims that science has shown that the universe somehow sprang out of sheer nothingness.***

A century ago, Einstein’s powerful field equations of gravitation showed the way forward. His uncanny intuition about the universe prevailed despite temporary reversals, and his decades-old insights are now at the cutting edge of modern physics and cosmology, helping us shed light on the greatest mysteries of all: the nature of matter, gravity, time, space, and the mysterious dark energy pushing it all outwards.


*I was fortunate to be the first scholar to examine these letters before they became accessible to the public, translated them from the German with the help of my father, and published some of the results.

**It’s interesting that Einstein repeatedly misspells the name of Edwin Hubble (“Hubbel”). Had he not yet met Hubble in person? We don’t know. The spelling error does hint at the fact that Hubble’s discovery was not yet so strongly established that his name would be well known by all scientists.

***I take strong issue with this approach, and expand on the topic of what is known by science about the birth and fate of the universe, in a forthcoming book.

CATEGORIZED UNDER: Space & Physics, Top Posts

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About Amir Aczel

Amir D. Aczel studied mathematics and physics at the University of California at Berkeley, where he was fortunate to meet quantum pioneer Werner Heisenberg. He also holds a Ph.D. in mathematical statistics. Aczel is a Guggenheim Fellow, a Sloan Foundation Fellow, and was a visiting scholar at Harvard in 2005-2007. He is the author of 18 critically acclaimed books on mathematics and science, several of which have been international bestsellers, including Fermat's Last Theorem, which was nominated for a Los Angeles Times Book Award in 1996 and translated into 31 languages. In his latest book, "Why Science Does Not Disprove God," Aczel takes issue with cosmologist Lawrence M. Krauss's theory that the universe emerged out of sheer "nothingness," countering the arguments using results from physics, cosmology, and the abstract mathematics of set theory.


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