The Day We Found the Universe (24 page)

Soon Einstein was not satisfied with that adjustment alone. Special relativity was just that—special. It could only explain the properties of objects moving at an unvarying velocity. But that restricted its use to a great extent. Most events in nature don't behave so methodically. What if something were speeding up, slowing down, or changing direction? What if an object were accelerating under the force of gravity? Einstein knew that he had to develop a more
general
theory to deal with these situations, and he struggled with the problem for nearly a decade. It was a formidable job, as he had to do nothing less than recast Newton's venerable laws of gravity in the light of relativity.

For years success eluded him as he struggled to figure out how to make his equations truly universal and still reproduce Newton's law of gravity for the simplest cases, when gravity was weak and velocities were low. After all, Einstein couldn't just throw out a law that had been time-tested for more than two centuries. His new theory had to agree very closely with Newton's in the everyday realm where physicists had long been conducting experiments, a place where spacetime distortions were too small to be overt. But then the theory would have to merge smoothly into either the intense gravity or high-velocity regimes in which the strange effects of relativity at last become obvious. “In all my life I have labored not nearly as hard,” he wrote a colleague in the midst of his deliberations. “… Compared with this problem, the original relativity is child's play.”

The breakthrough for the thirty-six-year-old physicist finally came in November 1915. Over that month Einstein reported weekly to the Prussian Academy of Sciences on his final progress toward a new theory of gravitation. A key moment arrived in mid month, when he was able to successfully explain a small displacement in the orbit of Mercury, a nagging mystery to astronomers for decades. Einstein later remarked that he had palpitations of the heart upon seeing this result: “I was beside myself with ecstasy for days.”

Complete success arrived on November 25, the day he presented his concluding paper. In this culminating talk, Einstein presented the decisive modifications that allowed him to secure a comprehensive theory. Written in the terse notation of tensor calculus—shorthand for a larger set of more complex functions—the general theory of relativity looks deceptively like a simple algebraic equation. It fits on one line and is the embodiment of mathematical elegance:

R
_uv
− ½
g
_uv
R = −kT
_uv

On the left side are quantities that describe the gravitational field as the geometry of spacetime. In fact, the Rs denote how much spacetime is curved. On the right side is a representation of mass-energy and how it is distributed. The equal sign sets up an intimate relationship between these two entities. As Princeton physicist John Archibald Wheeler liked to put it, “Spacetime tells mass how to move and mass tells spacetime how to curve.”

Einstein showed that the three dimensions of space and the additional dimension of time join up to form a real, palpable object. While it's impossible for us to visualize these four dimensions, it can be pictured in three. Think of spacetime as a boundless rubber sheet. Masses, such as a star or planet, then indent this flexible mat, curving spacetime. The more massive the object, the deeper the depression. Planets thus circle the Sun not because they are held by invisible tendrils of force, as Newton had us think, but because they are caught in the natural hollow formed by the Sun in four-dimensional spacetime, much as a rolling marble would circle around a bowling ball sitting in a trampoline. With this image in mind, the pull of gravity could now be easily explained; it's merely matter sliding like a downhill skier along the undulations of spacetime. When Einstein's younger son, Eduard, later asked his father why he was so famous, Einstein singled out this elegant and lucid illustration of gravity as curving spacetime. “When a blind beetle crawls over the surface of a curved branch, it doesn't notice that the track it has covered is indeed curved,” he explained. “I was lucky enough to notice what the beetle didn't notice.”

This realization was why Einstein was so excited by his successful result regarding the planet Mercury. It was clear evidence of this fantastic new image of gravity, its geometric representation. His insight centered on the fact that planets do not orbit the Sun in perfect circles but rather in ellipses, one end being slightly closer to the Sun than the other. And it was long known that the point of Mercury's orbit that is closest to the Sun—its perihelion—shifts around over time due to the combined gravitational tugs of the other planets. But there is an added shift—an extra 43 seconds of arc (or arcseconds) per century—that could never be adequately explained. Astronomers had even postulated an undiscovered planet called Vulcan—even closer to the Sun than Mercury—to explain the anomaly.

Here's where the relativistic geometry makes a difference: Because Mercury is situated so close to the Sun, whose mass has created a sizable spacetime crater, it has more of a “dip” to contend with, more so than the other planets. Einstein declared that the added shift in Mercury's orbit was caused solely by Mercury's proximity to the Sun, not by some yet-to-be-observed inner planet. This wasn't just a vague prediction; the equations of general relativity accounted for Mercury's extra 43 arcseconds of shift per century with utmost precision.

Arthur Eddington, for one, was immediately smitten by Einstein's groundbreaking opus. “Whether the theory ultimately proves to be correct or not, it claims attention as being one of the most beautiful examples of the power of general mathematical reasoning,” he wrote in his account of general relativity, the first book on the subject to appear in English. With Eddington acting as Einstein's translator and champion, the two were often linked in people's minds. An accomplished popularizer of science, Eddington said that Einstein had taken “Newton's plant, which had outgrown its pot, and transplanted it to a more open field.” Eddington was becoming so proficient at explaining relativity that “people seem to forget that I am an astronomer and that relativity is only a side issue,” he lamented after one wearying interview with reporters.

Arthur Eddington (
AIP Emilio Segrè Visual Archives)

For Eddington to serve as a spokesman for a radical new theory was somewhat out of character for him. He was usually reserved to the point of shyness, so shy, said physicist Hermann Bondi, that “he couldn't talk at all… When anybody was with him … he played with his pipe, and emptied it and re-stuffed it, and occasionally said a word about the weather.” A thin man of average height but with penetrating eyes, he lived with his sister, who served as homemaker and hostess at their Cambridge Observatory residence. A devout Quaker and pacifist, Eddington remained at Cambridge University in Great Britain during World War I, having been declared valuable to the “national interest” at his university post.

As both an astronomer and a theorist, Eddington divined early on the revolutionary significance of Einstein's ideas: that the general theory of relativity was offering a means to comprehend the workings of the cosmos within a rational and mathematical framework. While Newton's laws were fine for predicting the behavior of comets, planets, and stars, only general relativity could deal with the immensity of spacetime as a whole. And at the moment Eddington was beginning to work on a translation of general relativity for his colleagues, Einstein was already at work applying his revolutionary new theory to the universe at large.

For Newton, space was eternally at rest, merely an inert and empty container, a three-dimensional stage through which objects moved about. But general relativity changed all that. Now the stage itself became an active player, since the matter within the cosmos sculpts its overall curvature. With this new insight into gravity, physicists could at last make predictions about the universe's behavior, an innovation that moved cosmology out of the realm of philosophy, its long-standing home, and transformed it into a working science.

Einstein was the first to do this. In 1917, just as Shapley in California was revamping the Milky Way, he published a paper in Germany titled “Cosmological Considerations Arising from the General Theory of Relativity.” In it he explored how his new 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 spacetime 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 the problem easier. If a solution is found in this way—and there is no guarantee—the scientist trusts it will shed some light on the overall problem, leading them to a more complete understanding.