Einstein's Greatest Mistake

by David Bodanis

  Both the geometry of space and the movement of objects within it, Einstein realized, are determined by distortions in space caused by the objects themselves. If space has nothing in it, there’s no distortion at all: it’s like a flat, geometrical plane. If there is a single planet on that plane, then there will be some distortion, as the planet makes the space around it sag downward. There will be even more dips and distortions if there are dozens of planets, all tugging the space around them.

  This realization fundamentally changed the way we understand the fabric of our universe. In 1816 the mathematician Gauss had written, “Perhaps in another life we will be able to obtain insight into the nature of space, which is now unattainable.” Less than a century later, Einstein had done that. The domain of Things, and the Geometry of the domain of the space surrounding it, were not separate after all. There was a deep link. Place a huge agglomeration of rock into a new spot—let the vast bulk of the earth itself take up some position in our solar system—and its tremendous mass sags space enough to press humans, and apple trees, and entire mountain chains tightly to the surface; enough to guide aircraft, and space shuttles, and even the distant moon as well. That’s how our sun leads the earth along: it’s as if the sun has opened up a furrow around it, and we whirl along within it. The reason we feel at every moment as if we’re going straight forward is that we’re unable to step way back and “see” that giant curving path that we’re gliding along. Yet, in his mind, Einstein had done just that.

  SYMBOLS ARE MORE precise than words. To say “mass and energy lead to a sagging of space” is only a very rough approximation. What Einstein wrote can, still roughly, be better expressed as saying that there are “things” at one location—what we can call T for short. And there’s a distorted geometry that those things produce near them. Let’s call that distorted geometry G for short.

  Einstein’s insight—as summarized in the trampoline drawings—is that any arrangement of things (T) produces a distinctive new geometry (G) around it. The groups of things that exist at some location—be they hands, or mountains, or exploding flares—make the geometry around them bend or shift. A change in T, in other words, leads to a change in G around it.

  The simplicity of Einstein’s realization was stunning, and it came out in an extremely “brief” equation. How to tell how things are going to move? Simply look at the distorted geometry of space around them. In successively briefer phrasing:

  The geometry of space—our sagging trampoline—guides how things move.

  Geometry guides Things.

  G guides T.

  G→T.

  G=T.

  And how to tell how space is contorted? Simply look at the things sitting in it. Again, in briefer and briefer phrasing:

  Things distort the geometry of space—of our sagging trampoline—around them.

  Things distort Geometry.

  T distorts G.

  T→G.

  T=G.

  How extraordinarily symmetrical the equation at the heart of how our universe configures itself turns out to be! Almost the whole structure and dynamics of the universe are there, in just two neatly balancing phrases. Things distort geometry. Geometry guides things. Use the equal sign as a shorthand to summarize those mutual operations, and briefest of all, combining both, one gets a single equation: G=T. Einstein’s symbols had further detailed characteristics, but although G=T is only a metaphor, it’s a quite close one, and matches the essence of what Einstein wrote.

  It was a fabulous discovery: that what seems odd and random to our senses, such as the tumbling of planets through space, actually comes from very clear, very exact laws. Best of all, human reasoning was able to uncover it.

  Einstein tried to be modest about this equation, which would become the core of his general theory of relativity. He later said, “When a man after long years of searching chances on a thought which discloses something of the beauty of this mysterious universe, he should not be personally celebrated.” But at the time, he couldn’t resist. In 1915 he wrote exuberantly, “[This] is the greatest satisfaction of my life.” And to his friend Michele Besso, he was even less guarded. “My boldest dreams have now come true,” Einstein wrote after he had cracked it in November 1915, before signing off, “regards from your content, but kaput, Albert.”

  Part III

  GLORY

  Einstein and his second wife, Elsa Lowenthal, in Berlin, early 1920s

  NINE

  True or False?

  EINSTEIN ALWAYS BELIEVED that there was an invisible framework to our universe, waiting to be found. He had always suspected, moreover, that this cosmic architecture would be very simple, and very exact, and very clear. And what could be simpler, or more exact, or clearer than an idea like G=T? It seemed impossible that his theory about space and gravitation could be false.

  In the immediate wake of his breakthrough in November 1915, Einstein showed no hint of self-doubt—yet he knew that others had doubted him before. His earliest ideas about gravity, dating back to his thoughts in the Patent Office in 1907, had had only a limited impact. Even his initial elaborations, during his Prague years, had remained largely a private matter. But as Einstein’s recognition among physicists had grown, resistance to his work in this area had grown as well. When he’d presented his extended theoretical elaborations at a conference in Vienna in 1913, seemingly the whole audience of distinguished faculty members had claimed that he must be deluded. At the time, Einstein had tried to stay calm, but later he admitted how shaken he had been. “My colleagues concerned themselves with my theory,” he remembered, “. . . only with the intention of killing it dead.” Even Max Planck, then Europe’s most respected scientist, had had doubts, writing to Einstein, “As an older friend, I must advise against [publicizing this new theory] . . . You won’t succeed, and no one will believe you.”

  Einstein knew he needed to convince his colleagues that his theory was legitimate, but perhaps most of all, he needed to reassure himself. Newton’s theory of gravitation had been the bedrock of scientific thought for centuries. There was nothing in it about warped space. To one of his closest confidants, the Dutch theoretician Hendrik Lorentz, whom Einstein revered almost as a father figure, he admitted, “My business still has so many major hitches that my confidence . . . fluctuates.”

  Einstein was still fairly young, and had only recently received professional esteem. What he was attempting with G=T was terrifyingly bold. In essence, he was telling his colleagues that, like the inhabitants of Flatland, they had been blind to the fact that they existed within a higher dimension that they could not see. Now he claimed to have discovered it. No wonder they were skeptical.

  What Einstein really needed was a test—some way of confirming the existence of this higher dimension around us. But how to pull out a test from something as seemingly abstract as the relation G=T?

  He already had one possible way of proving his theory correct. He had been able to show, on the basis of his new equation, that the planet Mercury would advance in a fashion ever so slightly different from what Newton had predicted. The problem was that this wasn’t really news; astronomers had already recognized that Mercury orbited differently than those predictions. Although no one—apart from Einstein—had been able to explain why this might be the case, cynical observers could always say that Einstein had started with those known facts about the orbit and worked backward to create a theory that would “produce” such an orbit.

  What would be far more impressive would be if he could show that his new theory predicted something that nobody had imagined could possibly occur—and then go ahead, test that prediction, and show it was true. As early as his time in Prague, in 1912, Einstein had thought about this, and now he realized there might be a way to pull it off.

  REMEMBER THE BALL bearing flicked forward on the taut trampoline. When it traveled where the trampoline was flat, it rolled forward in a quick straight line. When it got close to the sag at the center of the trampoline, where a
small rock was bending it down—a rock that represented our sun—then the ball bearing veered inward as it dipped along that sag. Our sun is so massive that it produces a huge “sag” in space around it, and this is what the earth glides along, like a ball caught in a roulette wheel, with only the earlier forward motion preventing it from rolling even farther toward the sun.

  In thinking about how to test his theory of gravitation, Einstein realized that according to his theory, it wasn’t just the planets that would be pulled along by space’s curvature in this way. Light, too, would be “bent” by gravity.

  At first glance, that seems impossible. We’re taught that if you shine a flashlight beam from one manned balloon to another, it shouldn’t matter whether the balloons are high over the empty Pacific Ocean or whether they’re floating right beside Mount Everest: the flashlight beam is going to travel in a straight line. It’s not going to be tugged sideways simply because a massive mountain is beside it.

  But the belief that light only travels in straight lines is a delusion, simply based on the fact that we live on a planet with weak gravity—or so Einstein suspected. If we could peer at realms where gravity was much stronger than it is on earth, we should, in fact, be able to detect invisible gullies opening up in space by seeing light swerve as it hurries along.

  A variation of Einstein’s simplest thought experiment shows how he arrived at this hypothesis. Instead of having a drugged explorer waking up floating freely in a closed room, imagine that you’re the victim. And this time, instead of floating weightlessly, you feel a comfortable force pulling you down to the floor. Like the explorer’s flotation, this force, too, is ambiguous. It could mean you’ve safely landed on the ground on earth, your terrifying journey is over, and when the airlock opens you’ll get to step outside to a waiting, applauding crowd. But it also could mean that you are in a room out in space: one that has been hijacked by merciless marauders, who’ve attached a hook and are now tugging you forward to their evil mother ship. If their acceleration is calibrated right, you’ll be pressed down to the floor with exactly the same intensity—no more, no less—than someone would feel in an elevator car waiting calmly for the door to open on the ground floor on earth. (This is an effect we recognize when we’re in a car that suddenly accelerates, and we get pushed back against the seat. Close your eyes, ignore the roar of the engine, and you could be on a planet whose gravitational pull is tugging you into the seat just as hard.)

  Suppose you’re in the second scenario of Einstein’s thought experiment—a hijacked, accelerating room, not a room resting on earth—and you manage to find a window, perhaps by lifting up a metal plate that had covered it. And suppose that, as you do so, the beam from a lighthouse on a convenient exuperant planet shines brightly into your window. If you weren’t moving, you’d see the light beam come into the room and hit against the far wall, exactly opposite the window where it entered. But since your kidnappers are accelerating your own vessel upward, the light will not fall in exactly the same place it would if you were motionlessly suspended in space. Rather, in the time it takes for the light beam to move across your room, your vessel will have moved up a little, so that when the beam of light hits the far wall, it won’t be exactly opposite the window where it came in, but instead will have curved to hit a little bit lower down.

  This second part of the thought experiment reflects one of Einstein’s driving views, what might be called observational democracy: the belief that just as no one automatically deserves superior rights in life, so no one observer can say that their vantage point in viewing some event is automatically superior to that of everyone else’s. In the thought experiment at hand, what this means is that no one can possibly tell if they’re being tugged in distant space, or if they’re standing still in a closed room on earth—not if the tug pulling them along is of the right intensity. What someone sees inside one of those rooms will have to be exactly what they’d see if they were in the other one.

  To see how this would hold true in the thought experiment, imagine how seeing the lighthouse from a stationary room on earth might compare to seeing the lighthouse from a hijacked room in space. In the tugged room, where you’re held down to the floor with a force of 1 g (because the evil pirates are tugging you along), light bends as it travels across the room. In the static room on earth, where you’re also held down to the floor with a force of 1 g (because the earth produces “real” gravity), light will also have to bend as it travels across the room. (Why? Because if the light bending wasn’t the same, you’d be able to tell the difference between the two places, and that’s what we’ve agreed is impossible.)

  From this simple thought experiment, Einstein deduced that light bends in a gravitational field just as it would if viewed from an accelerating position. And that was the sort of prediction he could test. The rough approach had been in his mind early in his long years of work leading up to general relativity, although the details only became properly refined as he reached the final theory in 1915.

  The real-life experiment Einstein envisioned was also simple, at least in scientific terms. He just needed to find a vastly ponderous mass, one bulky enough to create a huge sag in space near it, and then see if speeding light beams in fact veered off course as they passed close by, like a high-speed race car banking hard as it follows a curve. By observing the light beams that were visible around the periphery of such a massive object, Einstein predicted, one should be able to see what was behind it—all because the curvature of space caused by gravity would redirect the light from the hidden object to the observer’s eyes.

  In our solar system, Einstein realized, there was only one suitable candidate for such a test: the sun. It is so massive, and should bend space so significantly, that it should have a noticeable effect on the light around it. But there was one problem with this idea. Even if the sun did cause light near it to curve, Einstein knew, most of the time this would be too hard to detect. The effect would be quite small, just a fraction of a degree. During the day, when we can see the sun, its flames and explosions are so bright that they make it impossible to see the distant starlight that might be whipping close beside it.

  But during a total eclipse? Then the best of both worlds combine. The sky is dark, but the sun is right overhead. Distant starlight that arrived in line with its edge would suddenly be visible. If that light had been bending, we would be able to see it.

  Einstein had conceived of this test when he was first trying to elaborate the relationship between G and T, which he would finally pinpoint in his November 1915 breakthrough. But there was a reason he had been unable to report the results of such a test when he formally presented his theory of general relativity, with G=T at its core, to Germany’s greatest scientists late that year. Einstein had been entrusting the tests to an eager young astronomer named Erwin Freundlich, who had impressed him with his knowledge and keenness to help (and whose surname, appropriately, is German for “friendly”). But Freundlich turned out to be a man of stunning, probability-busting bad luck.

  Freundlich’s first suggestion to Einstein had been not to wait for an eclipse at all, but to go through old photographic plates stored at the Hamburg Observatory to see if those had inadvertently captured eclipses under the conditions Einstein required. Einstein wrote back with his support for the idea. Freundlich got permission from the observatory’s director, started scanning and measuring plates, and found that although there were many—very many—plates in the observatory’s archives, astronomers had repeatedly just missed recording the starlight deflections that would prove Einstein’s theory true and win Freundlich respect and fame.

  Freundlich was ever optimistic. Why not see if one could perhaps glimpse distant stars during the day and use measurements taken that way, rather than wait for an eclipse to darken the daytime sky? This was such an exciting idea that in 1913 he made a special trip to Zurich to talk it over with his new friend Einstein. Unfortunately, it was also Freundlich’s honeymoon, which meant that his new w
ife had to sit politely while her husband attended a lecture on relativity, then as they shared lunch with Einstein, and finally as they all went for a long walk after lunch. One imagines that for her it was a very long day.

  Later, in the weeks after Freundlich left, Einstein did some checking. It was obvious, he found, that the glare was just too strong and that no telescope—not even the great instruments on Mount Wilson in California, a letter from its director confirmed—would be able to carry out the procedure Freundlich had proposed.

  Freundlich’s next idea seemed better. There was a total solar eclipse coming up in August 1914, roughly a year off, and it would be visible not too far away, in the beautiful Crimea of southern Russia, near the sophisticated port city of Sebastopol. The Imperial Russian Battle Fleet had its headquarters there, which meant there would be restaurants and fine hotels nearby where he could celebrate when the imaging was done. At that time, Germany and Russia had been at peace for many years, so there was no reason to think anything could go wrong.

  Freundlich’s enthusiasm to confirm Einstein’s initial ideas grated on some of the older researchers who constituted the astronomical establishment in Germany, and the official funding bodies resisted giving as much money as would be needed. Einstein couldn’t believe how little belief they had in Freundlich. There wasn’t much time to prepare! Before 1913 was out, he wrote Freundlich, “If the Academy won’t play ball, then we’ll get that little bit [of cash] from private quarters . . . If everything fails, I’ll pay for the thing out of my own slight savings . . . [but] go ahead and order the plates . . . Don’t let time slip by because of the money question.”