Einstein's Greatest Mistake

by David Bodanis

  In the world before Einstein, everyone believed that of course two events that one person finds simultaneous have to be just as simultaneous for everyone else. But Einstein’s work revealed that this is not so. Even several years after World War I ended by our reckoning of time, there were locations beyond our galaxy from which the vast numbers of deaths in the trenches and on other battlefields had not yet occurred.

  This was not just an artifact of measurement or a fantasy of the mystics, as with William Blake’s “I see the Past, Present, and Future, existing all at once/Before me.” If we could be in one of those far-off locations right now, we, too, would be living at a time when a friend or husband who had been shot was still alive. The catch, however, was that those perspectives involved such tremendous speeds and relative accelerations that, Einstein’s equations showed, we would never be able to access them, since we could never travel fast enough to get there: present-day technologies could bring us nowhere near the required speeds.

  Still, the knowledge that such realities were possible, even if only on a theoretical level, gave comfort to many—including Einstein himself. Many years later, when his friend Michele Besso died and he himself was seventy-six—with heart and other health problems, and knowing his own end was near—he wrote to Besso’s family of the deep understanding he drew from this view: “Now he has preceded me briefly in his departure from this strange world. This means nothing. For those of us who believe in physics, the distinction between past, present, and future is only an illusion, however tenacious this illusion may be.”

  Despite—or more likely because of—its ballooning popular appeal, much of Einstein’s theoretical work became distorted in popular understanding. Almost immediately after Eddington’s results were publicized, books, lectures, and radio broadcasts went out about the great man’s work, many of which got his theories wrong. But enough of what Einstein had achieved made its way through.

  No other scientist had ever been so acclaimed, even if no one—​not Rutherford, not Einstein himself—could be sure why that was the case. Yet whatever the reasons, practically overnight, multitudes of people came to think of Einstein as someone who had seen what mankind had never imagined—who had reached into the heavens and brought down, if not salvation, at least a glimpse of what deeper reality there might be.

  ELEVEN

  Cracks in the Foundation

  EINSTEIN SHOULD HAVE been happy. Revered worldwide since Eddington’s confirmation of his theory in 1919, he was awarded the Nobel Prize of 1921 for his work in theoretical physics. Movie stars and royalty wanted to be near him; the mobbed appearances continued. But amidst that acclaim, amidst that fame, Einstein began to worry about one consequence of his celebrated theory—and his professional angst was also compounded by growing stress in his personal life.

  His divorce from Mileva Marić (which had finally come through in 1919) had given him freedom, but it had distanced him from his two beloved sons. He tried writing them long chatty letters, but they were in no mood to accept their father’s overtures. When he got them to visit him in Berlin, he purchased a telescope and put it on his balcony for them to use, but this didn’t help either. When Einstein did travel to Switzerland to take them on the sort of walking holidays they had liked before, everything was mannered, stilted. Once, in exasperation, he wrote to the elder boy, Hans Albert, from Berlin, taking him to task for being so cold. But Hans Albert was just as angry: his father was abandoning them, so how could he expect any kindness in return? Hans Albert later remembered that he felt as if a “gloomy veil” had come over what was left of their family life.

  Einstein raged at Marić for poisoning his children’s minds against him, but he must have known that he was partly responsible—and for what? Life with Elsa Lowenthal hadn’t worked out as he had hoped. He had intended to keep the liaison strictly on his terms, having written to Besso in 1915 that it was “[an] excellent and truly enjoyable relationship . . . ; its stability will be guaranteed by the avoidance of marriage.” Lowenthal, however, had a different view, and in June 1919—while Eddington was still on the tropical island of Principe—they had married. Almost immediately after the wedding, something changed. Marić may have been resentful of the way she was left out of his scientific discussions, but at least she had understood the main lines of his work. Yet although Lowenthal’s lack of scientific education had been fine when Einstein was on the rebound, now he was discovering that behind her natural ebullience lay an intellect that left much to be desired. “She is no mental brainstorm,” he later remarked.

  During their courtship, Lowenthal had agreed with Einstein about the pleasures of an informal life and had enjoyed his mocking of wealthy, established Berliners. But once they moved into her seven-room apartment in a building with a grand lobby and a uniformed doorman, he felt trapped among her Persian carpets, heavy furniture, and display cabinets filled with fine porcelain. Some of her friends were thoughtful, but the majority, he was coming to see, were just chattering socialites. Worst of all, she began babying him. “I recall,” her daughter wrote, “that my mother often said during lunch, ‘Albert, eat: don’t dream!’” It was all very far from romantic.

  Soon Einstein began to have affairs. His mere presence, an architect who knew him well remembered, “acted upon women as a magnet acts on iron filings.” Some of these women were younger than Elsa, some richer, and some both. What they saw was one of the most famous men on the planet, yet one who was unlike the stereotype of the desiccated intellectual. He was still fit and broad-shouldered (as friends who saw him take off his shirt noted); he loved telling wry Jewish jokes, and he had a direct, Swabian use of language. Actresses such as the renowned Luise Rainer soon wished to be seen with him. He spent evenings with a wealthy widow at her villa in Berlin and accompanied another woman, a fashionable entrepreneur, to concerts or the theater, riding with her in her chauffeured limousine.

  Einstein with the German actress Luise Rainer, mid-1930s. Her husband was jealous of her flirting with the great scientist, although the peak of his philandering had actually occurred a decade earlier.

  The contrast between these other women and Elsa, with her chatter and her increasingly baffled disappointment, was painful for everyone. Einstein liked to go sailing, and when he did manage to find free time would head to their country house near a lake not far from Berlin, where he kept his sailboat Tümmler (German for “porpoise”). He would go out alone in the boat for hours, dreamingly adjusting the tiller as the winds skidded him here and there. His housekeeper described one regular visitor to the summer house when Elsa was away. “The Austrian woman was younger than Frau Professor,” the maid recalled, “and was very attractive, lively, and liked to laugh a lot, just like the Professor.” On one memorable occasion, Elsa found another woman’s “article of clothing” still on the boat, and they had an argument that, in its cold fury, continued for weeks. Men and women were not designed to be monogamous, he insisted. Elsa confided to a few close friends that living with a genius was not easy—not easy at all.

  This was not the marriage either of them had wished for. In the letter Einstein wrote to Besso’s adult children, consoling them after their father’s death, he concluded: “What I admired most in him as a person was the fact that he managed for many years to live with his wife not only in peace but in continuing harmony—something in which I have rather shamefully failed twice.”

  If this were Einstein’s only failure, it might have been bearable. But he was confronting an even worse problem. Even as early as 1917, at what should have been the peak of his accomplishment, Einstein had discovered what seemed to be a catastrophic flaw in his great G=T equation, and it had been preying on him ever more as the 1920s went on.

  IMMEDIATELY AFTER coming up with the equation that explained gravitation in December 1915, Einstein had been jubilant but exhausted. Only as 1916 went on did he begin any other work, and only by the end of 1916 did he have the energy to return to G=T.

  Everything h
e’d done so far with that equation had focused on how it applied to particular objects, such as the orbit of Mercury in our solar system, or the path of light from particular distant stars as it traveled near our sun. Now, he decided, “[I] wish to take larger portions of the physical universe into consideration.” The idea was to explore how G=T might apply to the mass of the entire universe.

  This is when Einstein found what seemed to be a catastrophic flaw. The scientists of his era believed that the universe was static, fixed, unchanging: filled with a collection of stars, stretching away to a very great distance, some of which might slightly move from place to place but which, overall, never changed at all. Yet G=T predicted something quite different. If the “things” floating in space were already separated enough from one another, his equation allowed their random motion to start sending them even farther away from one another. But worse, his equation also appeared to allow another possible scenario. If a certain number of the “things” floating around in space were close enough so that they did start clustering together, the curvature in space that created might make even more objects start sliding toward them, thereby producing a runaway collapse.

  The effect would be as if an enormous object landed in the Pacific Ocean and generated such a great whirlpool that everything on the planet—water, then islands, and soon entire continents—started being sucked toward it. The equivalent on the scale of our universe would be a sky-spanning “valley” taking shape in space, making everything tumble into it. Even more, the valley would start folding in on itself as the density of all the things accumulating in it—all the mass and energy that fell in—made the geometrical curve ever greater, as space itself began to collapse.

  Einstein wasn’t an astronomer, but he did know the basics—enough to believe that the scenario his theory was generating seemed impossible. Our solar system has planets that spin around a single, central sun. Our Milky Way galaxy is full of similar stars: some bigger, some smaller, but all, it was believed, hovering in fairly fixed positions. That’s all there was. It was what the philosopher Immanuel Kant had described as an “island universe”: fixed, stable, unchanging for all time. That’s why the constellations the ancients had spoken of—Virgo, Sagittarius, and the like—were still roughly in the same positions in the night sky. But Einstein now saw that if his simple G=T equation of 1915 was true, that couldn’t be the case, and everything would constantly move.

  Thus his dilemma. He loved his equation’s simplicity and clarity. It was wonderful to think the universe was arranged to follow such a simple, beautiful law. It made exciting, crisp predictions about what was happening within our solar system, as with starlight veering off course near the sun. Yet his equation also seemed to predict that on a far larger scale, the universe as a whole was changing—that all the stars in the heavens would one day either fly away forever or start falling together in a giant collapse. Every respected astronomer, however, was insistent that was false, for all their observations seemed to show that the universe was fixed, stable, forever unchanging in size. How could the consensus of all the world’s top astronomers be wrong?

  Something had to give, Einstein decided, and if the observable facts about the universe wouldn’t change, he’d have to. Since his 1915 equation predicted that the universe was changing, he had to fix the equation so that it wouldn’t make that prediction. What it said about small-scale effects, such as our sun making space sag enough to deflect starlight passing nearby, would still be allowed to hold. But what it said about larger-scale effects—those shaping the universe as a whole ​—would have to be corrected. In February 1917, accordingly, addressing the Prussian Academy in Berlin, Einstein declared, “The fact is, I have come to the conclusion that the equations of gravitation hitherto presented by me need to be modified, in order to avoid these fundamental difficulties.”

  He’d need to change his beautiful G=T equation, but how?

  Einstein had mulled over the problem at length, and in his 1917 address he presented the only possible patch he could think of. He would have to insert an extra term in his original equation. This new term would take away some of the power on the left-hand side of the equation—the one concerned with the geometry of space. It would come to be known as the cosmological constant, because it was a fixed, or constant, number that operated on the level of the cosmos. Einstein simply represented the new factor by the Greek letter lambda (Λ). Instead of G=T—so beautiful an equation, so symmetrical—he would now have the hobbled G-Λ=T.

  The details of how Einstein came up with the cosmological constant are subtle, but one can think of it like this: G represents the geometry of our universe, and it’s so tightly curved that it has a high value, enough to make the stars come crashing down, like boulders falling into a vast pit. Take away a certain amount from that pull, and the stars won’t crash, but will instead remain floating, fairly still, as almost all astronomers of the time believed was the case. It would be as if Einstein redrew the depth of that pit so it wasn’t so deep, and the boulders no longer started tumbling headlong into it. That’s what inserting the lambda did.

  He was uncomfortable with the change from the very beginning. “That term,” Einstein declared about the lambda from the podium in Berlin, “is necessary only for the purpose of making possible a near-static distribution of matter, as required by the fact of the small velocities of the stars.” Astronomers had assured him that all the stars we saw only moved fairly slowly or randomly among one another, and this “near-static distribution of matter” would not result from his original equation. Only with the change he now unhappily put in could he stay true to what observational evidence seemed to show.

  The lambda may have been necessary to bring Einstein’s equation into line with the latest astronomical findings, but he felt the addition was “gravely detrimental to the formal beauty of the theory.” To Einstein, simplicity and beauty were our best signs of an underlying truth. He didn’t believe that any deity or force of nature would have started creating a universe in accord with ultrasimple principles, then awkwardly thrown in such a correction. The original G=T from 1915 could have been a vision of God’s hand, revealing a creation that delighted in simplicity. Its two symbols arose from the nature of the universe: the G from the essence of how space curved, and the T from the sheer existence of things in space. The new, ungainly Λ, however, was just an arbitrary component, added to the left-hand side to make the pull of gravity weaker—in our image above, to make the “pit” of our universe less steep, so that the stars (the “boulders” in the image) would not tumble down into it.

  In the string quartets that Einstein loved playing, every note had its place, every instrument its role. No one would suddenly drag a large tuba into the room and randomly blast out noise to halt the score’s natural direction. That’s what changing the direct G=T to the ungainly G-Λ=T was like.

  But the word of the world’s astronomers was unequivocal. Our sun exists in an island of stars called the Milky Way. They insisted it was not expanding, that there was just infinite blackness beyond. If Einstein hadn’t so deeply believed in the need to respond to experimental evidence, he might not have put in this correction. But at that stage in his life, facts were absolutely as important to him as the sheer play of intuition. Since his 1915 equation predicted the opposite of what the facts seemed to show, then that equation had to be wrong.

  This was his first great mistake.

  The full effect of his error would not become clear until years later, but in the meantime Einstein tried to convince himself that his original theory wasn’t a total failure. The effect that he needed the lambda to counterbalance only became noticeable over immensely large distances. Its value could be set so small that on the scale of our solar system, calculations would still be accurate, as if the original, simple equation G=T was all that applied. That’s why the predictions Eddington was working with remained valid.

  While he could take comfort in Eddington’s findings, Einstein could not
make peace with the fact that his beautiful, original theory appeared to have been fundamentally incorrect. What especially tormented him was the question of why the universe had been built to have that extra term in there at all.

  Despite these inner doubts, he started to defend the ungainly G-Λ=T, accepting that the vision he had briefly glimpsed of the perfect, ultrasimple G=T was somehow not how the universe worked. He didn’t love the change but became used to it.

  Although Eddington’s 1919 results had brought Einstein great fame and made him seem an image of perfection, the reality of his life was different. The world thought Einstein was a kindhearted, humble man at ease with how his life had worked out. Yet his second marriage was far from what he’d hoped for, and the sons he loved were slipping away.

  The world also thought he had created equations of remarkable insight, approaching the wisdom of God himself. Yet Einstein, with his insertion of the lambda, knew that was a lie: either he hadn’t yet reached the deepest level of truth, or the universe lacked the simplicity he so wanted to believe was there.

  Part IV

  RECKONING

  Einstein on his favorite sailboat in Germany, 1920s

  TWELVE

  Rising Tensions

  EINSTEIN WAS NOT alone in doubting the need for the lambda in his gravitational equation. So, too, did a Russian mathematician named Alexander Friedmann.