The Theory of Relativity, Then and Now

"I am exhausted. But the success is glorious.”

It was a hundred years ago this November, and Albert Einstein was enjoying a rare moment of contentment. Days earlier, on November 25, 1915, he had taken to the stage at the Prussian Academy of Sciences in Berlin and declared that he had at last completed his agonizing, decade-long expedition to a new and deeper understanding of gravity. The general theory of relativity, Einstein asserted, was now complete.

The month leading up to the historic announcement had been the most intellectually intense and anxiety-ridden span of his life. It culminated with Einstein’s radically new vision of the interplay of space, time, matter, energy and gravity, a feat widely revered as one of humankind’s greatest intellectual achievements.

At the time, general relativity’s buzz was only heard by a coterie of thinkers on the outskirts of esoteric physics. But in the century since, Einstein’s brainchild has become the nexus for a wide range of foundational issues, including the origin of the universe, the structure of black holes and the unification of nature’s forces, and the theory has also been harnessed for more applied tasks such as searching for extrasolar planets, determining the mass of distant galaxies and even guiding the trajectories of wayward car drivers and ballistic missiles. General relativity, once an exotic description of gravity, is now a powerful research tool.

The quest to grasp gravity began long before Einstein. During the plague that ravaged Europe from 1665 to 1666, Isaac Newton retreated from his post at the University of Cambridge, took up refuge at his family’s home in Lincolnshire, and in his idle hours realized that every object, whether on Earth or in the heavens, pulls on every other with a force that depends solely on how big the objects are—their mass—and how far apart they are in space—their distance. School kids the world over have learned the mathematical version of Newton’s law, which has made such spectacularly accurate predictions for the motion of everything from hurled rocks to orbiting planets that it seemed Newton had written the final word on gravity. But he hadn’t. And Einstein was the first to become certain of this.

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In 1905 Einstein discovered the special theory of relativity, establishing the famous dictum that nothing—no object or signal—can travel faster than the speed of light. And therein lies the rub. According to Newton’s law, if you shake the Sun like a cosmic maraca, gravity will cause the Earth to immediately shake too. That is, Newton’s formula implies that gravity exerts its influence from one location to another instantaneously. That’s not only faster than light, it’s infinite.

Einstein would have none of it. A more refined description of gravity must surely exist, one in which gravitational influences do not outrun light. Einstein dedicated himself to finding it. And to do so, he realized, he would need to answer a seemingly basic question: How does gravity work? How does the Sun reach out across 93 million miles and exert a gravitational pull on the Earth? For the more familiar pulls of everyday experience—opening a door, uncorking a wine bottle—the mechanism is manifest: There is direct contact between your hand and the object experiencing the pull. But when the Sun pulls on the Earth, that pull is exerted across space—empty space. There is no direct contact. So what invisible hand is at work executing gravity’s bidding?

Newton himself found this question deeply puzzling, and volunteered that his own failure to identify how gravity exerts its influence meant that his theory, however successful its predictions, was surely incomplete. Yet for over 200 years, Newton’s admission was nothing more than an overlooked footnote to a theory that otherwise agreed spot on with observations.

In 1907 Einstein began to work in earnest on answering this question; by 1912, it had become his full-time obsession. And within that handful of years, Einstein hit upon a key conceptual breakthrough, as simple to state as it is challenging to grasp: If there is nothing but empty space between the Sun and the Earth, then their mutual gravitational pull must be exerted by space itself. But how?

Einstein’s answer, at once beautiful and mysterious, is that matter, such as the Sun and the Earth, causes space around it to curve, and the resulting warped shape of space influences the motion of other bodies that pass by.

Here’s a way to think about it. Picture the straight trajectory followed by a marble you’ve rolled on a flat wooden floor. Now imagine rolling the marble on a wooden floor that has been warped and twisted by a flood. The marble won’t follow the same straight trajectory because it will be nudged this way and that by the floor’s curved contours. Much as with the floor, so with space. Einstein envisioned that the curved contours of space would nudge a batted baseball to follow its familiar parabolic path and coax the Earth to adhere to its usual elliptical orbit.

It was a breathtaking leap. Until then, space was an abstract concept, a kind of cosmic container, not a tangible entity that could effect change. In fact, the leap was greater still. Einstein realized that time could warp, too. Intuitively, we all envision that clocks, regardless of where they’re located, tick at the same rate. But Einstein proposed that the nearer clocks are to a massive body, like the Earth, the slower they will tick, reflecting a startling influence of gravity on the very passage of time. And much as a spatial warp can nudge an object’s trajectory, so too for a temporal one: Einstein’s math suggested that objects are drawn toward locations where time elapses more slowly.

Still, Einstein’s radical recasting of gravity in terms of the shape of space and time was not enough for him to claim victory. He needed to develop the ideas into a predictive mathematical framework that would precisely describe the choreography danced by space, time and matter. Even for Albert Einstein, that proved to be a monumental challenge. In 1912, struggling to fashion the equations, he wrote to a colleague that “Never before in my life have I tormented myself anything like this.” Yet, just a year later, while working in Zurich with his more mathematically attuned colleague Marcel Grossmann, Einstein came tantalizingly close to the answer. Leveraging results from the mid-1800s that provided the geometrical language for describing curved shapes, Einstein created a wholly novel yet fully rigorous reformulation of gravity in terms of the geometry of space and time.

But then it all seemed to collapse. While investigating his new equations Einstein committed a fateful technical error, leading him to think that his proposal failed to correctly describe all sorts of commonplace motion. For two long, frustrating years Einstein desperately tried to patch the problem, but nothing worked.

Einstein, tenacious as they come, remained undeterred, and in the fall of 1915 he finally saw the way forward. By then he was a professor in Berlin and had been inducted into the Prussian Academy of Sciences. Even so, he had time on his hands. His estranged wife, Mileva Maric, finally accepted that her life with Einstein was over, and had moved back to Zurich with their two sons. Though the increasingly strained family relations weighed heavily on Einstein, the arrangement also allowed him to freely follow his mathematical hunches, undisturbed day and night, in the quiet solitude of his barren Berlin apartment.

By November, this freedom bore fruit. Einstein corrected his earlier error and set out on the final climb toward the general theory of relativity. But as he worked intensely on the fine mathematical details, conditions turned unexpectedly treacherous. A few months earlier, Einstein had met with the renowned German mathematician David Hilbert, and had shared all his thinking about his new gravitational theory. Apparently, Einstein learned to his dismay, the meeting had so stoked Hilbert’s interest that he was now racing Einstein to the finish line.

A series of postcards and letters the two exchanged throughout November 1915 documents a cordial but intense rivalry as each closed in on general relativity’s equations. Hilbert considered it fair game to pursue an opening in a promising but as yet unfinished theory of gravity; Einstein considered it atrociously bad form for Hilbert to muscle in on his solo expedition so near the summit. Moreover, Einstein anxiously realized, Hilbert’s deeper mathematical reserves presented a serious threat. His years of hard work notwithstanding, Einstein might get scooped.

The worry was well-founded. On Saturday, November 13, Einstein received an invitation from Hilbert to join him in Göttingen on the following Tuesday to learn in “very complete detail” the “solution to your great problem.” Einstein demurred. “I must refrain from traveling to Göttingen for the moment and rather must wait patiently until I can study your system from the printed article; for I am tired out and plagued by stomach pains besides.”

But that Thursday, when Einstein opened his mail, he was confronted by Hilbert’s manuscript. Einstein immediately wrote back, hardly cloaking his irritation: “The system you furnish agrees—as far as I can see—exactly with what I found in the last few weeks and have presented to the Academy.” To his friend Heinrich Zangger, Einstein confided, “In my personal experience I have not learnt any better the wretchedness of the human species as on occasion of this theory....”

A week later, on November 25, lecturing to a hushed audience at the Prussian Academy, Einstein unveiled the final equations constituting the general theory of relativity.

No one knows what happened during that final week. Did Einstein come up with the final equations on his own or did Hilbert’s paper provide unbidden assistance? Did Hilbert’s draft contain the correct form of the equations, or did Hilbert subsequently insert those equations, inspired by Einstein’s work, into the version of the paper that Hilbert published months later? The intrigue only deepens when we learn that a key section of the page proofs for Hilbert’s paper, which might have settled the questions, was literally snipped away.

In the end, Hilbert did the right thing. He acknowledged that whatever his role in catalyzing the final equations might have been, the general theory of relativity should rightly be credited to Einstein. And so it has. Hilbert has gotten his due too, as a technical but particularly useful way of expressing the equations of general relativity bears the names of both men.

Of course, the credit would only be worth having if the general theory of relativity were confirmed through observations. Remarkably, Einstein could see how that might be done.

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General relativity predicted that beams of light emitted by distant stars would travel along curved trajectories as they passed through the warped region near the Sun en route to Earth. Einstein used the new equations to make this precise—he calculated the mathematical shape of these curved trajectories. But to test the prediction astronomers would need to see distant stars while the Sun is in the foreground, and that’s only possible when the Moon blocks out the Sun’s light, during a solar eclipse.

The next solar eclipse, of May 29, 1919, would thus be general relativity’s proving ground. Teams of British astronomers, led by Sir Arthur Eddington, set up shop in two locations that would experience a total eclipse of the Sun—in Sobral, Brazil, and on Príncipe, off the west coast of Africa. Battling the challenges of weather, each team took a series of photographic plates of distant stars momentarily visible as the Moon drifted across the Sun.

During the subsequent months of careful analysis of the images, Einstein waited patiently for the results. Finally, on September 22, 1919, Einstein received a telegram announcing that the eclipse observations had confirmed his prediction.

Newspapers across the globe picked up the story, with breathless headlines proclaiming Einstein’s triumph and catapulting him virtually overnight into a worldwide sensation. In the midst of all the excitement, a young student, Ilse Rosenthal-Schneider, asked Einstein what he would have thought if the observations did not agree with general relativity’s prediction. Einstein famously answered with charming bravado, “I would have been sorry for the Dear Lord because the theory is correct.”

Indeed, in the decades since the eclipse measurements, there have been a great many other observations and experiments—some ongoing—that have led to rock-solid confidence in general relativity. One of the most impressive is an observational test that spanned nearly 50 years, among NASA’s longest-running projects. General relativity claims that as a body like the Earth spins on its axis, it should drag space around in a swirl somewhat like a spinning pebble in a bucket of molasses. In the early 1960s, Stanford physicists set out a scheme to test the prediction: Launch four ultra-precise gyroscopes into near-Earth orbit and look for tiny shifts in the orientation of the gyroscopes’ axes that, according to the theory, should be caused by the swirling space.

It took a generation of scientific effort to develop the necessary gyroscopic technology and then years of data analysis to, among other things, overcome an unfortunate wobble the gyroscopes acquired in space. But in 2011, the team behind Gravity Probe B, as the project is known, announced that the half-century-long experiment had reached a successful conclusion: The gyroscopes’ axes were turning by the amount Einstein’s math predicted.

There is one remaining experiment, currently more than 20 years in the making, that many consider the final test of the general theory of relativity. According to the theory, two colliding objects, be they stars or black holes, will create waves in the fabric of space, much as two colliding boats on an otherwise calm lake will create waves of water. And as such gravitational waves ripple outward, space will expand and contract in their wake, somewhat like a ball of dough being alternately stretched and compressed.

In the early 1990s, a team led by scientists at MIT and Caltech initiated a research program to detect gravitational waves. The challenge, and it’s a big one, is that if a tumultuous astrophysical encounter occurs far away, then by the time the resulting spatial undulations wash by Earth they will have spread so widely that they will be fantastically diluted, perhaps stretching and compressing space by only a fraction of an atomic nucleus.

Nevertheless, researchers have developed a technology that just might be able to see the tiny telltale signs of a ripple in the fabric of space as it rolls by Earth. In 2001, two four-kilometer-long L-shaped devices, collectively known as LIGO (Laser Interferometer Gravitational-Wave Observatory), were deployed in Livingston, Louisiana, and Hanford, Washington. The strategy is that a passing gravitational wave would alternately stretch and compress the two arms of each L, leaving an imprint on laser light racing up and down each arm.

In 2010, LIGO was decommissioned, before any gravitational wave signatures had been detected—the apparatus almost certainly lacked the sensitivity necessary to record the tiny twitches caused by a gravitational wave reaching Earth. But now an advanced version of LIGO, an upgrade expected to be ten times as sensitive, is being implemented, and researchers anticipate that within a few years the detection of ripples in space caused by distant cosmic disturbances will be commonplace.

Success would be exciting not because anyone really doubts general relativity, but because confirmed links between the theory and observation can yield powerful new applications. The eclipse measurements of 1919, for example, which established that gravity bends light’s trajectory, have inspired a successful technique now used for finding distant planets. When such planets pass in front of their host stars, they slightly focus the star’s light causing a pattern of brightening and dimming that astronomers can detect. A similar technique has also allowed astronomers to measure the mass of particular galaxies by observing how severely they distort the trajectory of light emitted by yet more distant sources. Another, more familiar example is the global positioning system, which relies on Einstein’s discovery that gravity affects the passage of time. A GPS device determines its location by measuring the travel time of signals received from various orbiting satellites. Without taking account of gravity’s impact on how time elapses on the satellites, the GPS system would fail to correctly determine the location of an object, including your car or a guided missile.

Physicists believe that the detection of gravitational waves has the capacity to generate its own application of profound importance: a new approach to observational astronomy.

Since the time of Galileo, we have turned telescopes skyward to gather light waves emitted by distant objects. The next phase of astronomy may very well center on gathering gravitational waves produced by distant cosmic upheavals, allowing us to probe the universe in a wholly new way. This is particularly exciting because waves of light could not penetrate the plasma that filled space until a few hundred thousand years after the Big Bang—but waves of gravity could. One day we may thus use gravity, not light, as our most penetrating probe of the universe’s earliest moments.

Because waves of gravity ripple through space somewhat as waves of sound ripple through air, scientists speak of “listening” for gravitational signals. Adopting that metaphor, how wonderful to imagine that the second centennial of general relativity may be cause for physicists to celebrate having finally heard the sounds of creation.

Editors' Note, September 29, 2015: An earlier version of this article inaccurately described how GPS systems operate. The text has been changed accordingly.

Brian Greene | | READ MORE

Science columnist Brian Greene is a mathematician and physicist at Columbia University, the author of bestselling cosmology books such as The Hidden Reality, co-founder of the World Science Festival and the prime mover behind the online education resource World Science U. Photo: Lark Elliott.