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.
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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.”
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