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gravitational ideas could be used to determine the universe's behavior. Einstein had always been attracted to that age-old question: Is the universe infinite or finite in extension? “I compare space to a cloth…one can observe a certain portion,” he mused. “… We speculate how to extrapolate the cloth, what holds its tangential tension in equilibrium…whether it is infinitely extended, or finite and closed.” Einstein decided that the universe was closed, what is also referred to as a spherical universe, the four-dimensional equivalent of a spherical Earth. Though this shape has neither a beginning nor an end, its volume is finite. Travel forward through it long enough and you return right back to your starting point, just as you would circumnavigating our globe. In this scheme matter is so plentiful that space-time bends profoundly, so much that it literally wraps itself up into a hyperdimensional ball. Recognizing how frightfully odd this sounded, Einstein told a friend, “It exposes me to the danger of being confined to a madhouse.” But he stuck with this strange notion, as it helped him get around other problems in applying general relativity to the cosmos. Einstein also preferred this model because, given his astronomical knowledge at the time, he assumed the universe was filled with matter and stable. In 1917 it certainly appeared to him to be steady and enduring. Truth be told, he liked the idea of an immutable cosmos, a large collection of stars fixed forever in the void.

From a theorist's perspective, this choice was mathematically beautiful, but it also presented a problem. Even Newton knew that matter distributed throughout a finite space would eventually coalesce into larger and larger lumps. Stellar objects would be gravitationally drawn to one another, closer and closer over time. Ultimately, the universe would collapse under the inescapable pull of gravity. So, to avoid this cosmic calamity and match his theory with then-accepted astronomical observations, Einstein altered his famous equation, adding the term λ (the Greek letter lambda), a fudge factor that came to be called the “cosmological constant.” This new ingredient was an added energy that permeated empty space and exerted an outward “pressure” on it. This repulsive field—a kind of antigravity, actually—exactly balanced the inward gravitational attraction of all the matter in his closed universe, keeping it from moving. As a result, the universe remained immobile, “as required by the fact of the small velocities of the stars,” wrote Einstein in his classic 1917 paper.

Willem de Sitter

(Courtesy of the Archives, California

Institute of Technology)

Others soon followed up on Einstein's cosmological endeavor, most important Willem de Sitter. The esteemed Dutch astronomer, a tall and slender man with a neatly trimmed Vandyke beard, started keeping track of general relativity's development as early as 1911 and was one of the first to recognize its deep significance to astronomy. After meeting with Einstein in Leiden on several occasions in 1916, discussions in fact that inspired Einstein to conceive his spherical universe, de Sitter soon corresponded with Eddington on the subject. Intrigued by de Sitter's insights, Eddington asked him to write up his impressions of general relativity for the Monthly Notices of the Royal Astronomical Society, which resulted in three long papers on the topic, the first articles to make Einstein's accomplishment widely known to scientists outside Germany. De Sitter was obviously stimulated by the assignment, for in his third paper he offered up his own cosmological solution to the equations of general relativity, one that was very different from Einstein's.

When scientists originate an equation to describe some phenomenon, their job is far from done. They must still solve the equation—in the case of general relativity, figure out what values for those Rs and Ts make the equation come out right. This is a tall order. So, to progress, a researcher will often introduce a simplifying assumption about the equation that makes