E=mc2

by David Bodanis

  Albert Einstein at his high school graduation inAarau, Switzerland

  ETH, ZURICH

  He managed to get a few physics articles published, but they weren't especially impressive. He was always aiming for grand linkages—his very first paper, published back in 1901, had tried to show that the forces controlling the way liquid rises up in a drinking straw were similar, fundamentally, to Newton's laws of gravitation. But he could not quite manage to get these great linkages to work, and he got almost no response from other physicists. He wrote to his sister, wondering if he'd ever make it.

  Even the hours he had to keep at the patent office worked against him. By the time he got off for the day, the one science library in Bern was usually closed. How would he have a chance if he couldn't even stay up to date with the latest findings? When he did have a few free moments during the day, he would scribble on sheets he kept in one drawer of his desk—which he jokingly called his department of theoretical physics. But Haller kept a strict eye on him, and the drawer stayed closed most of the time. Einstein was slipping behind, measurably, compared to the friends he'd made at the university. He talked with his wife about quitting Bern and trying to find a job teaching high school. But even that wasn't any guarantee: he had tried it before, only four years earlier, but never managed to get a permanent post.

  And then, on what Einstein later remembered as a beautiful day in the spring of 1905, he met his best friend, Michele Besso ("I like him a great deal," Einstein wrote, "because of his sharp mind and his simplicity"), for one of their long strolls on the outskirts of the city. Often they just gossiped about life at the patent office, and music, but today Einstein was uneasy. In the past few months a great deal of what he'd been thinking about had started coming together, but there was still something Einstein felt he was very near to understanding but couldn't quite see. That night Einstein still couldn't quite grasp it, but the next day he suddenly woke up, feeling "the greatest excitement."

  It took just five or six weeks to write up a first draft of the article, filling thirty-some pages. It was the start of his theory of relativity. He sent the article to Annalen der Physik to be published, but a few weeks later, he realized that he had left something out. A three-page supplement was soon delivered to the same physics journal. He admitted to another friend that he was a little unsure how accurate the supplement was: "The idea is amusing and enticing, but whether the Lord is laughing at it and has played a trick on me—that I cannot know." But in the text itself he began, confidently: "The results of an electrodynamic investigation recently published by me in this journal lead to a very interesting conclusion, which will be derived here." And then, four paragraphs from the end of this supplement, he wrote it out.

  E=mc2 had arrived in the world.

  PART 2

  Ancestors of

  E=mc2

  E Is for Energy 2

  The word energy is surprisingly new, and can only be traced in its modern sense to the mid 1800s. It wasn't that people before then had not recognized that there were different powers around—the crackling of static electricity, or the billowing gust of a wind that snaps out a sail. It's just that they were thought of as unrelated things. There was no overarching notion of "Energy" within which all these diverse events could fit.

  One of the men who took a central role in changing this was Michael Faraday, a very good apprentice bookbinder who had no interest, however, in spending his life binding books. As an escape hatch from poverty in the London of the 1810s, though, it was a job that had one singular advantage: "There were plenty of books there," he mused years later to a friend, "and I read them." But it was fragmentary reading, and Faraday recognized that, just snatching glimpses of pages as they came in to be bound. Occasionally he had evenings alone, next to the candles or lamps, reading longer sixteen-or thirty-two-page bound sheaves.

  He might have stayed a bookbinder, but although social mobility in Georgian London was very low, it wasn't quite zero. When Faraday was twenty, a shop visitor offered him tickets to a series of lectures at the Royal Institution. Sir Humphry Davy was speaking on electricity, and on the hidden powers that must exist behind the surface of our visible universe. Faraday went, and realized he had been granted a lucky glimpse of a better life than he had working at the shop. But how could he enter it? He had not been to Oxford, or to Cambridge or, indeed, even attended much of what we call secondary school; he had as much money as his blacksmith father could give him—none—and his friends were just as poor.

  Michael Faraday

  ENGRAVING BYJ. COCHRAN OF PAINTING BY H. W. PICKERGILL, ESQ., R.A. AIP EMILIO SEGRE VISUAL ARCHIVES

  But he could bind an impressive-looking book. Faraday had always been in the habit of taking notes when he could, and he'd brought back to the shop notes he'd taken at Davy's lectures. He wrote them out, and inserted a few drawings of Davy's demonstration apparatus. Then he rewrote the manuscript—all his drafts are kept today with the attention due a sacred relic, in the basement Archive Room of London's Royal Institution— took up his leather, awls, and engraving tools, and bound together a terrific book, which he sent to Sir Humphry Davy.

  Davy replied that he wanted to meet Faraday. He liked him, and despite a disconcerting series of starts and stops, finally hired him away from the binder as a lab assistant.

  Faraday's old shopmates might have been impressed, but his new position was not as ideal as he'd hoped. Sometimes Davy behaved as a warm mentor, but at other times, as Faraday wrote to his friends, Davy would seem angry, and push Faraday away. It was especially frustrating to Faraday, for he'd been drawn to science in large part by Davy's kind words; his hints that if one only had the skill and could see what had hitherto been hidden, everything we experience could actually be linked.

  It took several years for Davy finally to ease up, and when he did it appeared to coincide with Faraday being asked to understand an extraordinary finding out of Denmark. Until then, everyone knew that electricity and magnetism were as unrelated as any two forces could be. Electricity was the crackling and hissing stuff that came from batteries. Magnetism was different, an invisible force that made navigators' needles tug forward, or pulled pieces of iron to a lodestone. Magnetism was not anything you thought of as part of batteries and circuits. Yet a lecturer in Copenhagen had now found that if you switched on the current in an electric wire, any compass needle put on top of the wire would turn slightly to the side.

  No one could explain this. How could the power of electricity in a metal wire possibly leap out and make a magnetic compass needle turn? When Faraday, now in his late twenties, was asked to work on how this link might occur his letters immediately became more cheerful.

  Sir Humphry Davy

  PHOTO RESEARCHERS, INC.

  He started courting a girl ("You know me as well or better than I do myself," he wrote. "You know my former prejudices, and my present thoughts—you know my weaknesses, my vanity, my whole mind") and the girl liked being courted: in mid-1821, when Faraday was twenty-nine, they got married. He became an official member of the church which his family had been a part of for many years. This was a gentle, literalist group called the Sandemanians, after Robert Sandeman, who'd brought the sect to England. Most of all, Faraday now had a chance to impress Sir Humphry: to pay him back for his initial faith in hiring a relatively uneducated young binder, and to cross, finally, the inexplicable barriers Davy had raised between them.

  Faraday's limited formal education, curiously enough, turned out to be a great advantage. This doesn't happen often, because when a scientific subject reaches an advanced level, a lack of education usually makes it impossible for outsiders to get started. The doors are closed, the papers unreadable. But in these early days of understanding energy it was a different story. Most science students had been trained to show that any complicated motion could be broken down into a mix of pushes and pulls that worked in straight lines. It was natural for them, accordingly, to try to see if there were any straight-line p
ulls between magnets and electricity. But this approach didn't show how the power of electricity might tunnel through space to affect magnetism.

  Because Faraday did not have that bias of thinking in straight lines, he could turn to the Bible for inspiration. The Sandemanian religious group he belonged to believed in a different geometric pattern: the circle. Humans are holy, they said, and we all owe an obligation to one another based on our holy nature. I will help you, and you will help the next person, and that person will help another, and so on until the circle is complete. This circle wasn't merely an abstract concept. Faraday had spent much of his free time for years either at the church talking about this circular relation, or engaged in charity and mutual helping to carry it out.

  He got to work studying the relationship between electricity and magnetism in the late summer of 1821. It was twenty years before Alexander Graham Bell, the inventor of the telephone, would be born; more than fifty years before Einstein. Faraday propped up a magnet. From his religious background, he imagined a whirling tornado of invisible circular lines swirling around it. If he were right, then a loosely dangling wire could be tugged along, caught in those mystical circles like a small boat getting caught up in a whirlpool. He connected the battery.

  And immediately he had the discovery of the century.

  Later, the apocryphal story goes—after all the announcements, after Faraday was made a Fellow of the Royal Society—the prime minister of the day asked what good this invention could be, and Faraday answered: "Why, Prime Minister, someday you can tax it."

  What Faraday had invented, in his basement laboratory, was the basis of the electric engine. A single dangled wire, whirling around and around, doesn't seem like much. But Faraday had only a small magnet, and was feeding in very little power. Rev it up, and that whirling wire will still doggedly follow the circular patterns he had mapped out in seemingly empty air. Ultimately one could attach heavy objects to a similar wire, and they would be tugged along as well—that's how an electric engine works. It doesn't matter whether it is the featherweight spinning plate of a computer drive that's being dragged along, or the pumps that pour tons of fuel into a jet engine.

  Faraday's brother-in-law, George Barnard, remembered Faraday at the moment of discovery: "All at once he exclaimed, 'Do you see, do you see, do you see, George?' as the wire began to revolve. . . . I shall never forget the enthusiasm expressed in his face and the sparkling in his eyes!"

  Faraday was sparkling because he was twenty-nine years old and had made a great discovery, and it really did seem to suggest that the deepest ideas of his religion were true. The crackling of electricity, and the silent force fields of a magnet—and now even the speeding motion of a fast twirling copper wire—were seen as linked. As the amount of electricity went up, the available magnetism would go down. Faraday's invisible whirling lines were the tunnel—the conduit-through which magnetism could pour into electricity, and vice versa. The full concept of "Energy" had still not been formed, but Faraday's discovery that these different kinds of energy were linked was bringing it closer.

  It was the high point of Faraday's life—and then Sir Humphry Davy accused him of stealing the whole idea.

  Davy began to let it be known that he had personally discussed the topic with a different researcher who had been investigating it—a properly educated researcher— and Faraday must have just overheard them.

  The story was false, of course, and Faraday tried to protest, begging on the basis of their past friendship to let him explain, but Davy would have none of it. There were further crude hints, from others, if not from Davy himself: What else could you expect from a lower-class boy, from someone so junior, who was trying to wangle his way up as an apprentice; who knew nothing of what a more in-depth education could teach? After a few months Davy backed off, but he never apologized, and left the charges to dangle.

  In notes and private journal entries Davy often wrote how important it was to encourage young men. The problem was that he just couldn't bring himself to do it. The issue was nothing as simple as youth versus old age. Davy was little more than a decade older than Faraday. But Davy loved being lionized as the leader of British science, and all the time he spent away from the lab, soaking up praise in London high society with his status-keen wife, meant that the praise was increasingly false. He wasn't really on top of the latest research. When he corresponded with thinkers on the Continent he knew they were impressed at getting a letter from someone so prominent in the Royal Institution, but he avoided offering fresh ideas.

  Hardly anyone else recognized this, but Faraday did. He was more like Davy than anyone else. Both men had started at a level much below that of their contemporaries in London science. Faraday made no excuses for that, but Davy did everything he could to hide his past. Faraday's quiet presence was a constant reminder of what they'd both once shared.

  Faraday never spoke out against Davy. But for years after the charges of plagiarism and their repercussions, he stayed warily away from front-line research. Only when Davy died, in 1829, did he get back to work.

  Faraday lived into old age, in time becoming prominent in the Royal Institution himself. His rise was typical of the move from gentlemanly to professional science. Davy's slurs against him were long forgotten. He went on to make other discoveries; he became very famous, and was often in demand, receiving such letters as this:

  May 28 th, 1850

  Dear Sir,

  It has occurred to me that it would be extremely beneficial to a large class of the public to have some account of your late lectures on the breakfast-table. . . . I should be exceedingly glad to have . . . them published in my new enterprise. . . .

  With great respect and esteem I am Dear Sir,

  Your faithful servant,

  Charles Dickens

  By the last decade of his life, though, Faraday—like Davy—was no longer able to follow the latest results. But the energy concept had taken on a life of its own. All the world's seemingly separate forces were slowly, majestically, being linked to create this masterpiece of the Victorian Age: the huge, unifying domain of Energy. Since Faraday had shown that even electricity and magnetism were linked—two items that had once seemed totally distinct—the scientific community was more confident that every other form of energy could similarly be shown to be deeply connected. There was chemical energy in an exploding gunpowder charge, and there was frictional heat energy in the scraping of your shoe, yet they were linked too. When a gunpowder charge went off, the amount of energy it produced in air blasts and falling rocks would be exactly the same as what had been in the resting chemical charge inside.

  It's easy to miss how extraordinary a vision was the energy concept that Faraday's work helped create. It's as if when God created the universe, He had said, I'm going to put X amount of energy in this universe of mine. I will let stars grow and explode, and planets move in their orbits, and I will have people create great cities, and there will be battles that destroy those cities, and then I'll let the survivors create new civilizations. There will be fires and horses and oxen pulling carts; there will be coal and steam engines and factories and even mighty locomotives. Yet throughout the whole sequence, even though the types of energy that people see will change, even though sometimes the energy will appear as the heat of human or animal muscle, and sometimes it will appear as the gushing of waterfalls or the explosions of volcanoes: despite all those variations, the total amount of energy will remain the same. The amount I created at the beginning will not change. There will not be one millionth part less than what was there at the start.

  Expressed like this it sounds like the sheerest mumbo jumbo—Faraday's religious vision of a single universe, with just one single force spreading all throughout it. It's something like Obi-Wan Kenobi's description in Star Wars: "The Force is the energy field created by all living things; it binds the galaxy together."

  Yet it's true! When you swing closed a cupboard door, even if it's in the stillness of your home
at night, energy will appear in the gliding movement of the door, but exactly that much energy was removed from your muscles. When the cupboard door finally closes, the energy of its movement won't disappear, but will simply be relocated to the shuddering bump of the door against the cupboard, and to the heat produced by the grinding friction of the hinge. If you had to dig your feet slightly against the floor to keep from slipping when closing the door, the earth will shift in its orbit and rebound upward by exactly the amount needed to balance that.

  The balancing occurs everywhere. Measure the chemical energy in a big stack of unburned coal, then ignite it in a train's boiler and measure the energy of the roaring fire and the racing locomotive. Energy has clearly changed its forms; the systems look very different. But the total is exactly, precisely the same.

  Faraday's work was part of the most successful program for further research the nineteenth century had seen. Every quantity in these energy transformations that Faraday and others had now unveiled could be computed and measured. When that was done, the results confirmed, always, that indeed the total sum had never changed—it was "conserved." This became known as the Law of the Conservation of Energy.

  Everything was connected; everything neatly balanced. In the last decade of Faraday's life, Darwin seemed to have proven that God wasn't needed to create the living species on our planet. But Faraday's vision of an unchanging total Energy was often felt to be a satisfactory alternative: a proof that the hand of God really had touched our world, and was still active amid us.

  This concept of energy conservation is what the science teachers in Einstein's cantonal high school in Aarau, in northern Switzerland, had taught him when he arrived there for remedial work in 1895, twenty-eight years after Faraday's death. Einstein had been sent to the school not because he'd had any desire to go there—he had already dropped out of one perfectly good high school in Germany, vowing that he'd had enough—but because he had failed his entrance exams at the Federal Institute of Technology in Zurich, the only university that offered a chance of taking a high school dropout. One kindly instructor there had thought he might have some merit, so instead of turning him away entirely, the institute's director had suggested this quiet school—set up on informal, student-centered lines—in the northern valleys.