So what if the universe wasn’t really divided into two distinct parts after all? What if—to use the image provided earlier—the two domed cities weren’t sitting in utter isolation on separate parts of a vast continent, but actually had a secret tunnel between them through which whatever was in one could hurtle along and take up shape in the other? What if everything in the city of E, of energy, could shoot through the tunnel and turn into mass, or M—and everything in the domed city of M, of mass, could shoot back through the tunnel and turn into energy, or E?
Imagining a tunnel between these domed cities is a bit like imagining that the energetic fire that flickered over a burning log wasn’t different in nature from the material wood of that log, but rather, in some way, the wood could explode apart into flame, or—in the other direction—the fire could be squeezed back into the wood. In shorthand, that would be like saying that energy could become mass, and mass could become energy. Or, even more briefly, that E could become M, and M could become E.
THE POSSIBILITY THAT energy and mass were one and the same wasn’t yet clear to Einstein. Yet as he was wrapping up his other work, in the summer of 1905, he realized that he could go further.
The vision of energy and mass as interlinked—of a tunnel connecting the city of M with the city of E—was at the heart of the final paper in Einstein’s 1905 series. The question that he had to answer before he could publish this radical theory was how the tunnel between M and E operates in our real world. Does it transfer items back and forth directly, or does it somehow enlarge them when they travel in one direction and shrink them when they travel in the other? In the first case, it would be as if the world had only two cities—say, Munich and Edinburgh—and an invisible tunnel whooshed people back and forth between them without changing their size: just letting them arrive with a curious ability to speak the local language. In the second case, it would be as if each city’s residents changed size when they arrived in the other city, a bit like Alice. But which city’s citizens would shrink as they traveled, and which would grow?
Einstein worked this out in the late summer of 1905. He showed that the universe was arranged so that it was the objects in the “mass” city that would automatically seem to expand as they transformed into energy. In our example of Munich and Edinburgh, the pudgy mass burghers of Munich would enter the transformation tunnel as commuters of ordinary height, but then, when they’d finished their remarkable journey into Edinburgh, they would emerge from the tunnel as totteringly huge energy beings, hundreds of feet tall, able to bestride the city like enormous walking skyscrapers. In the other direction, when Edinburghians hurtled down the tunnel to Munich, they would shrink, and diminish, so much so that when the bewildered wee things emerged in Munich, they would be smaller than the tiniest fragments of mass-dense bratwurst that they saw street-corner vendors sold.
How much did each side change as it transformed? In solving this problem, Einstein brought in an entirely new approach that had come to him in that wondrous year—an idea that was as unexpected as a brilliant move in chess. We’re used to thinking that if we’re in a parked car and turn the headlights on, the light rays that shoot forward will be traveling at a certain speed, and then if we start driving and reach 60 mph, the light rays will now be traveling 60 mph faster as well. From deep principles, however, Einstein had concluded that this wasn’t the case, and with further ingenious twists, he now managed to show that energy and mass transform into each other: that they’re just different labels for what’s actually one thing.
By this period, scientists had long known that the speed of light was very great. It’s just a bit over 670,000,000 mph: enough for a signal flashed from earth to reach the moon in under two seconds or to cross the entire solar system in just hours. This speed—approximately 670,000,000 mph—was symbolized by the letter c, from the Latin celeritas, as in the English word “celerity,” meaning “speed.”
If mass were simply magnified by the factor of the speed of light as it traveled down the transformation tunnel, it would produce a tremendous amount of energy. But Einstein’s calculations showed even that wasn’t as far as matters went. Multiply c by itself, and one creates the even larger number c2: approximately 450,000,000,000,000,000 mph2. That’s how much any bit of mass will be magnified when it’s transformed into energy. Mass can become energy, in incredibly vast amounts. The large number c2 says exactly what the change is. In shorthand, E=mc2.
Most of the time, the energy inherent in mass stays hidden, since almost all substances on earth are very stable. Einstein often described the energy inside ordinary rocks or metals as like a huge pile of coins kept by a vastly wealthy miser: able to create great effects if they were let out, but invariably kept guarded within, and thus invisible to the outside world. But even in 1905, some experts were finding ways to let little bits out.
In Paris, Marie and Pierre Curie had become famous for experiments in which they’d found that radiant heat—a form of energy—would spray out of mere specks of radium ore: hour after hour, day after day, year after year. Today we realize that all that glowing energy was coming from a very few atoms transforming, multiplying by that factor of 450,000,000,000,000,000 as it sped outward and produced heat. Einstein knew of the Curies’ work, and at the end of his final 1905 paper—still modest enough to know that any great idea requires some proof—he suggested, “Perhaps it will prove possible to test this theory using bodies whose energy content is variable to a high degree, e.g., salts of radium.”
As summer turned to fall and Einstein put the finishing touches on his fifth and final paper and sent it off to the German journal Annalen der Physik (Annals of Physics), he had no idea what lay ahead. Just forty years later, a great nation would configure purified uranium in such a way that entire ounces of that metal could be made to transform in accord with his equation—each fraction of mass becoming enhanced by the huge multiplier c2 as it “disappeared” from material existence and instantly revealed itself as pure energy instead. The result, over Hiroshima, was a rush of energy exploding outward that destroyed an entire city: creating fires, hurricane-force winds, and a light flash so staggeringly intense that it hit the moon before reflecting back to earth. When Einstein, in exile in America, heard the news over the radio in 1945, he turned to his longtime secretary and said, distraught, that if he had known what was going to happen, he wouldn’t have lifted a finger to help.
All that was far in the future. For now, the young physicist was satisfied with his work. His penultimate paper to the Annalen der Physik had been the one showing the central role that the speed of light played in a vast range of concepts. The work in that paper, published in September 1905, is what became known as special relativity. The day after it was published, the Annalen received his final paper, showing one particular consequence of that: the fact that mass and energy can be transformed into each other. This spin-off from special relativity was published on November 21, 1905, and completed his annus mirabilis—a most extraordinary year both for Einstein and for the world.
In just several months, the unknown Einstein had published several of the most significant papers in the history of science. He had seen how clearly the universe’s inner operations were arranged, as with that hitherto unimagined tunnel between mass and energy that E=mc2 so accurately described. These and the other concepts in his 1905 series would gradually revamp our understanding of everything from the operations of light to the nature of space and time. As physicists came to understand his work, they would also give its author a taste of the respect from his colleagues he so wished. Yet as the last of his papers was published in the fall of 1905, Einstein could only have guessed what lay ahead—and how much further he had yet to go.
Einstein was growing in confidence, but was still far from smug. When he first came up with the idea for his final paper, linking E and M, he had written a friend, “The idea is amusing and enticing, but whether the good Lord is laughing at me and leading me up the garden path—that I cannot
know.”
He was also exhausted from the months of intense labor. He had accomplished all this while still working six days a week, eight hours a day, at the Patent Office. When he was finally done, he and Mileva went out drinking, which was rare for them: Einstein rarely venturing beyond the occasional beer, and both of them generally had just tea or coffee at the table. Their lack of experience shows, for a postcard survives from the next day, signed by them both: “Both of us, alas, dead drunk under the table.”
FOUR
Only the Beginning
IN THE SUMMER OF 1907, Max von Laue, a personal assistant of the great Berlin physicist Max Planck, was sent to Bern on a mission to meet the man who had published those extraordinary papers in the respected Annalen der Physik back in 1905.
When von Laue arrived and made his inquiries, he found that the man who he presumed would be a Herr Doktor Professor Einstein was not at the University of Bern, but seemed to be in residence in the post office building, which housed the Patent Office. Von Laue walked there and asked for the Professor to be called. Several minutes later, a polite young man walked through the waiting room. Von Laue ignored him, waiting for the Professor. The young man seemed confused—why had he been called if there was no one to greet him?—before returning to his desk up on the third floor.
Another request was put in: surely the Professor was not taking this long to come down? After von Laue waited a while longer, Einstein entered for the second time. Only then did Planck’s assistant realize that this must be the great thinker: not a professor—not even a Doktor—but somehow a mere minor functionary in the post office building.
Maja remembered that Einstein thought his publication in the Annalen would be immediately noticed and was disappointed when it seemed to be wholly ignored. Partly this was because he hadn’t bothered to write up his results in the usual scientific form, with a multitude of footnotes referring to previous work by famous professors. There were few footnotes in his main paper, yet in the final paragraph he warmly thanked his friend Michele Besso, who had helped him through thoughtful back-and-forth discussions about physics as they’d taken long walks outside Bern. But partly it was because Einstein’s achievement was hard to grasp.
Einstein had arrived at his theories using very general principles. This technique had served him well at the Patent Office, where he had learned how to use such higher-level principles to judge whether an invention was going to work or not. If an inventor said that a device sent in for assessment used perpetual motion, for example, Einstein knew he could reject the application right away. Perpetual motion isn’t possible, not in our earthly world of friction and entropy. When applied to more ambitious projects, however, Einstein’s simple, abstract approach often made his theories difficult for his scientific peers to wrap their heads around, let alone engage with.
In his 1905 works, Einstein had used a range of such higher-order principles to come up with ideas of shocking strangeness. There was E=mc2 from his November paper, which insisted—quite accurately—that energy was just a very diffuse form of mass, and mass was simply exceptionally dense energy. For anyone schooled in mainline Victorian science, that contention was shocking enough. But that equation was just one consequence of the broader special relativity theory from his earlier, September paper—a theory that fundamentally reworked what it means to observe events in space and time.
Special relativity had other, equally bizarre implications besides those that Einstein would tease out in E=mc2. If we watched a train traveling sufficiently fast, Einstein showed in that September paper, we would see it get shorter in the direction in which it was moving. Moving fast enough, the very largest locomotive would end up no thicker than a postage stamp. Time wasn’t what we thought it was either. We’re used to thinking that time always “flows” at the same rate for everyone. But someone accelerating at high speed away from the earth would see our entire species whirring through centuries in what seemed bare minutes, while we on earth, if we could watch the traveler on the spaceship through sufficiently powerful telescopes, would see his life slooooow almost to a stop. Both an observer on earth and the traveler would feel it was his own life that was normal and the other that had changed.
Could something this odd really take place? Many physicists—at least those who bothered to study Einstein’s theory at all—objected to the notion at first. Theoretical physics was still a very small academic field, and one of its few professors, the distinguished Arnold Sommerfeld in Munich, wrote confidentially to a friend, “This unconstruable and unvisualizable dogmatism [of Einstein’s] seems to me to contain something almost unhealthy. An Englishman would scarcely have produced this theory; perhaps it reflects . . . the abstract-conceptual character of the Semite.”
Yet even Sommerfeld, when he worked through Einstein’s reasoning, saw that it was irrefutable. We don’t notice these strange consequences because they tend only to be visible at extremely high velocities, or in the rare cases when atoms are so fragilely constructed that they can fly apart, as with the radium samples that so perplexed Marie Curie. But if we ever entered into those realms, we would see that all the strange activities Einstein described were true.
Physicists may have been slowly coming around to Einstein’s thinking by mid-1907, roughly a year and a half after the last of his annus mirabilis papers was published, but von Laue was the first major scientist to visit Bern. Einstein seized the opportunity not just to rub shoulders with the scientific elite, but also to see whether, in doing so, he might find a way to get himself out of the Patent Office and into one of the academic positions that had eluded him for so long.
Einstein received dispensation to take a break from work, and he and von Laue walked through the streets of Bern, going over the latest findings from Berlin, Heidelberg, and other important scientific centers. Einstein, as always, was puffing on a cheap cigar and was generous enough to offer one to von Laue. (Von Laue, used to better-quality tobacco, deftly managed to “lose” it over the side of a bridge.) But despite Einstein’s overtures, and despite his polite follow-up letters, there still was no offer of a job after their meeting.
Einstein remained at the Patent Office, where, at an ordinary upright desk, he continued to labor for Superintendent Haller, as he had now for half a decade. In frustration he begged an old friend from his earlier days in Bern to move back and join him in the office. “Perhaps it would be possible to smuggle you in among the patent slaves,” Einstein wrote enthusiastically. “. . . Keep in mind that besides the eight hours of work, each day also has eight hours for fooling around . . . I would love to have you here.” His friend didn’t take up the offer.
With his 1905 accomplishments receding and the Patent Office remaining a six-day-a-week job—and the only scientific library in Bern still closed on Sunday—Einstein could once again feel himself slipping away from the academic world. It wasn’t that he hadn’t tried to find another post. He knew that teaching in a high school would give him better hours, and in his agony at the Patent Office, Einstein peppered his friend Marcel Grossmann with questions about how to get a permanent job in a Swiss school. Would it matter that he spoke standard German rather than the Swiss dialect? Should he mention his scientific papers? Was he to call on the administrators in person, or would the fact that he looked Jewish get in the way? Whatever advice Grossmann gave him didn’t help much. When Einstein did apply to a high school in nearby Zurich, his was one of twenty-one applications. Three applicants were selected for follow-up interviews. Patent clerk Einstein was not one of them.
Einstein also tried to teach at the University of Bern. On his first attempt, in June 1907, he was told that he needed to have finished a dissertation first. Since he didn’t have a dissertation, he sent copies of his 1905 papers instead, at least three of which were worthy of the Nobel Prize. There was the September one laying out special relativity, as well as the November one showing how E=mc2 was a consequence of it. But there was also a paper in which he produced a
great understanding of photons. Possibly a fourth paper that year—building on simple microscopic observations to prove the existence of atoms—also deserved a Nobel Prize. But the university administrators wrote back explaining very clearly that perhaps Herr Einstein had not understood. This was Switzerland. There were bureaucratic requirements. He was obliged to send a dissertation, not some motley collection of papers. His application was rejected.
STUCK AT THE Patent Office, with only occasional visits from the likes of von Laue, Einstein didn’t give up. He knew he was drawn to problems at the very limits of scientific understanding and that even the greatest minds made errors. He also knew that in 1905, he had already solved one of the great problems of science: why the universe was divided into so many separate “parts.” His remarkable answer had been that it wasn’t: that mass and energy are so deeply connected that each could be seen as a different aspect of the other. He had even revealed exactly how the universe arranged that interrelated mass and energy to shift back and forth. It was all there in E=mc2.
By finding that such apparently unrelated items were interlinked, Einstein was primed for an encore that would take him to even greater heights. If all the mass and energy in the universe were interconnected—what we can informally think of as all “things” being interconnected—why did there still remain a seemingly separate domain of empty space? To have that second domain sitting there alongside those things of mass and energy—alongside all the universe’s locomotives and planets and fire and stars—didn’t seem very unified. Why should science screech to a halt without bringing all of space and all the “things” within it together as well, under the rubric of a single, grand theory?
Einstein's Greatest Mistake Page 4