# A century ago, Alexander Friedmann envisioned the universe’s expansion

## He saw that Einstein’s equations predicted multiple cosmic scenarios, including a Big Bang

Contributing Correspondent

For millennia, the universe did a pretty good job of keeping its secrets from science.

Ancient Greeks thought the universe was a sphere of fixed stars surrounding smaller spheres carrying planets around the central Earth. Even Copernicus, who in the 16th century correctly replaced the Earth with the sun, viewed the universe as a single solar system encased by the star-studded outer sphere.

But in the centuries that followed, the universe revealed some of its vastness. It contained countless stars agglomerated in huge clusters, now called galaxies.

Then, at the end of the 1920s, the cosmos disclosed its most closely held secret of all: It was getting bigger. Rather than static and stable, an everlasting and ever-the-same entity encompassing all of reality, the universe continually expanded. Observations of distant galaxies showed them flying apart from each other, suggesting the current cosmos to be just the adult phase of a universe born long ago in the burst of a tiny blotch of energy.

It was a surprise that shook science at its foundations, undercutting philosophical preconceptions about existence and launching a new era in cosmology, the study of the universe. But even more surprising, in retrospect, is that such a deep secret had already been suspected by a mathematician whose specialty was predicting the weather.

A century ago this month (May 1922), Russian mathematician-meteorologist Alexander Friedmann composed a paper, based on Einstein’s general theory of relativity, that outlined multiple possible histories of the universe. One such possibility described cosmic expansion, starting from a singular point. In essence, even without considering any astronomical evidence, Friedmann had anticipated the modern Big Bang theory of the birth and evolution of the universe.

“The new vision of the universe opened by Friedmann,” writes Russian physicist Vladimir Soloviev in a recent paper, “has become a foundation of modern cosmology.”

Friedmann was not well known at the time. He had graduated in 1910 from St. Petersburg University in Russia, having studied math along with some physics. In graduate school he investigated the use of math in meteorology and atmospheric dynamics. He applied that expertise in aiding the Russian air force during World War I, using math to predict the optimum release point for dropping bombs on enemy targets.

After the war, Friedmann learned of Einstein’s general theory of relativity, which describes gravity as a manifestation of the geometry of space (or more accurately, spacetime). In Einstein’s theory, mass distorts spacetime, producing spacetime “curvature,” which makes masses appear to attract each other.

Friedmann was especially intrigued by Einstein’s 1917 paper (and a similar paper by Willem de Sitter) applying general relativity to the universe as a whole. Einstein found that his original equations allowed the universe to grow or shrink. But he considered that unthinkable, so he added a term representing a repulsive force that (he thought) would keep the size of the cosmos constant. Einstein concluded that space had a positive spatial curvature (like the surface of a ball), implying a “closed,” or finite universe.

Friedmann accepted the new term, called the cosmological constant, but pointed out that for various values of that constant, along with other assumptions, the universe might exhibit very different behaviors. Einstein’s static universe was a special case; the universe might also expand forever, or expand for a while, then contract to a point and then begin expanding again.

Friedmann’s paper describing dynamic universes, titled “On the Curvature of Space,” was accepted for publication in the prestigious *Zeitschrift für Physik* on June 29, 1922.

Einstein objected. He wrote a note to the journal contending that Friedmann had committed a mathematical error. But the error was Einstein’s. He later acknowledged that Friedmann’s math was correct, while still denying that it had any physical validity.

Friedmann insisted otherwise.

He was not just a pure mathematician, oblivious to the physical meanings of his symbols on paper. His in-depth appreciation of the relationship between equations and the atmosphere persuaded him that the math meant something physical. He even wrote a book (*The World as Space and Time*) delving deeply into the connection between the math of spatial geometry and the motion of physical bodies. Physical bodies “interpret” the “geometrical world,” he declared, enabling scientists to test which of the various possible geometrical worlds humans actually inhabit. Because of the physics-math connection, he averred, “it becomes possible to determine the geometry of the geometrical world through experimental studies of the physical world.”

So when Friedmann derived solutions to Einstein’s equations, he translated them into the possible physical meanings for the universe. Depending on various factors, the universe could be expanding from a point, or from a finite but smaller initial state, for instance. In one case he envisioned, the universe began to expand at a decelerating rate, but then reached an inflection point, whereupon it began expanding at a faster and faster rate. At the end of the 20th century, astronomers measuring the brightness of distant supernovas concluded that the universe had taken just such a course, a shock almost as surprising as the expansion of the universe itself. But Friedmann’s math had already forecast such a possibility.

No doubt Friedmann’s deep appreciation for the synergy of abstract math and concrete physics prepared his mind to consider the notion that the universe could be expanding. But maybe he had some additional help. Although he was the first scientist to seriously propose an expanding universe, he wasn’t the first person. Almost 75 years before Friedmann’s paper, the poet Edgar Allan Poe had published an essay (or “prose poem”) called *Eureka*. In that essay Poe described the history of the universe as expanding from the explosion of a “primordial particle.” Poe even described the universe as growing and then contracting back to a point again, just as envisioned in one of Friedmann’s scenarios.

Although Poe had studied math during his brief time as a student at West Point, he had used no equations in *Eureka*, and his essay was not recognized as a contribution to science. At least not directly. It turns out, though, that Friedmann was an avid reader, and among his favorite authors were Dostoevsky and Poe. So perhaps that’s why Friedmann was more receptive to an expanding universe than other scientists of his day.

Today Friedmann’s math remains at the core of modern cosmological theory. “The fundamental equations he derived still provide the basis for the current cosmological theories of the Big Bang and the accelerating universe,” Israeli mathematician and historian Ari Belenkiy noted in a 2013 paper. “He introduced the fundamental idea of modern cosmology — that the universe is dynamic and may evolve in different manners.”

Friedmann emphasized that astronomical knowledge in his day was insufficient to reveal which of the possible mathematical histories the universe has chosen. Now scientists have much more data, and have narrowed the possibilities in a way that confirms the prescience of Friedmann’s math.

Friedmann did not live to see the triumphs of his insights, though, or even the early evidence that the universe really does expand. He died in 1925 from typhoid fever, at the age of 37. But he died knowing that he had deciphered a secret about the universe deeper than any suspected by any scientist before him. As his wife remembered, he liked to quote a passage from Dante: “The waters I am entering, no one yet has crossed.”