E=mc2

by David Bodanis

  The passengers in the car will agree. Their CD player is fine, they'll say, and the young Michael Jackson is warbling along as quickly as ever. It's the people outside the car who seem slow, with hotel doormen seeming to lift their arms in laborious heaviness, then puffing out their cheeks like stately deep-sea fish whenever they blow a whistle to hail a taxi.

  These effects are summarized in relativity by saying that when someone watches an object recede away from them, that object will be seen to undergo mass dilation, length changes, and time dilation. The bystanders will see it in the car; the driver of the car, looking back, will see it in the bystanders.

  The first time one reads of this, it seems like nonsense. Even Einstein found it hard to accept—as with the inexplicable tension he felt in his long talk with Michele Besso, on the summer day when he was still trying to work out these relations. But it's only hard to accept because we never actually interact with each other at speeds close to the 670 million mph of light (and the effects are too slight to notice at our ordinary speeds). Think, for example, of a portable music player at a picnic. To someone standing next to it, it's loud. To someone who walks a few hundred yards away, the music is soft. We accept that there's no answer about how loud it "really" is. But that's simply because we're capable of walking quickly enough to cover that few hundred yards in a brief time. To an ant or some smaller creature, one that took many generations to migrate far enough from the music player to detect any change in its volume, our view—that music can appear to be at different volumes to different observers-would seem crazy.

  The Web site gives the details of how physicists show that all this must follow from such simple observations as light's constancy. But there are a number of ordinary objects around us, which always do work at the high speeds where these effects become apparent. The electrons that shoot from the back of traditional TV sets to the screen at the front, for example, travel so fast that they really will respond to us as if they've grown in mass as they travel. Engineers have to take that into account when they design the magnets that focus the screen's image. If they didn't we would see a blur.

  The Global Positioning System (GPS) of navigational satellites, which fly overhead and beam down location signals for cars and jets and hikers, are also traveling so fast that from our perspective, time on board them seems to be slow. The circuits in the handheld GPS location devices we use to locate our positions, or in the larger GPS devices that banks use to synchronize payments, are programmed to correct for this—in exact accord with the equations Einstein worked out in 1905.

  Einstein never especially liked the label relativity for what he'd created. He thought it gave the wrong impression, suggesting that anything goes: that no exact results any longer occur. That's not so. The predictions are precise.

  The label is also misleading because all Einstein's equations are cohesive, and exactly linked up. Although each of us might view things in the universe differently, there will be enough synchronization where these different views join to ensure that it all fits. The old notions that mass never changes and that time flows at the same rate for everyone made sense when people only noticed the ordinary, slow-moving objects around them. In the true wider universe, however, they're not correct-but there are exact laws to explain how they change.

  This is an achievement that has occurred very few times in history. Imagine being able to make a shimmering crystalline model, small enough to hold in your closed fist. Now open your hand—and see the entire universe soar out; glowing into full existence. Newton was the first person to have done that, back in the 1600s: conceiving a complete system of the world, that could be described in but a handful of equations, yet also contained the rules for how to move out from the summary and go on to creating the full world.

  Einstein was the next.

  Just to make the bond more impressive, both Einstein and Newton achieved much of their work in impossibly brief periods in their mid-twenties. For Newton, back at his mother's Lincolnshire farm after his university had been closed because of the Plague, there were about eighteen months in which he did fundamental work on developing calculus, conceiving the law of universal gravitation, as well as working on key concepts for a mechanics that would apply throughout the universe. For Einstein, in a period of under eight months in 1905—and while still putting in full days at the patent office, Monday through Saturday—there was his first theory of relativity, and E=mc2, as well as his work that helped lay the path for lasers, computer chips, key aspects of the modern pharmaceutical and bioengineering industry, and all Internet switching devices. He really was, as Newton described himself when similarly in his mid-twenties, "in the prime of my age for invention." In each area, Einstein pushed beyond what was known; he unified fields that had remained separate, questioning assumptions that everyone until then had simply accepted.

  The few researchers around 1905 who had uncovered a small part of what he later deduced had no chance of matching him. Poincare got closer than almost anyone else, but when it came to breaking our usual assumptions about time's flow or the nature of simultaneity, he backed off, unable to consider the consequences of such a new view.

  Why was Einstein so much more successful? It's tempting to say it was just a matter of being brighter than everyone else. But several of Einstein's Bern friends were highly intelligent, while someone like Poincare would have been off the scale on any IQ test. Thorstein Veblen once wrote a curious little essay that I think gets at a deeper reason. Suppose, Veblen began, a young boy learns that everything in the Bible is true. He then goes to a secular high school, or university, and is told that's wrong. "What you learned at your mother's knee is entirely false. What we teach you here, however, will be entirely true." Some students would say, Oh, fine, I'll accept that. But others will be more suspicious. They'd been fooled once before, taking on faith an entire traditional world. They're not going to be fooled again. They would learn what was on offer, but always hold it critically, as just one possibility among others. Einstein was Jewish, and even though his immediate family wasn't observant, this meant he was immersed in a culture with different views about personal responsibility, justice, and belief in authority than the standard German and Swiss consensus.

  There's more, though. When Einstein was a little boy, he was fascinated with how magnets worked. But instead of being teased about it by his parents, they accepted his interest. How did magnets work? There had to be a reason, and that reason had to be based on another reason, and maybe if you traced it all the way, you'd reach . . . what would you reach?

  At one time, in the Einstein household, there had been a very clear answer to what would ultimately be reached. When his grandparents had been growing up, most Jews in Germany were still close to traditional Orthodoxy. It was a world suffused by the Bible, as well as by the crisply rational accumulated analysis of the Talmud. What counted was to push through to the very edge of what was knowable, and comprehend the deepest patterns God had decreed for our world. Einstein had gone through an intense religious period when he was approaching his teens, though by the time he was at the Aarau high school that literal belief was gone. Yet the desire to see the deepest underpinnings was still there, as was the trust that you would find something magnificent waiting if you made it that far. There was a waiting "slot": things could be clarified, and in a comprehensible, rational way. At one time the slot had been filled in by religion. It could easily enough be extended now to science. Einstein had great confidence that the answers were waiting to be found.

  It also helped that Einstein had the space to explore his ideas. The patent job meant that he didn't have to churn out academic papers ("a temptation to superficiality," Einstein wrote, "which only strong characters can resist"), but rather he could work on his ideas for as long as it took. Most of all, his family trusted him, which is a great boost to confidence, and they also encouraged a playful, distancing tone. It's just what's needed for "stepping back" from ordinary assumptions, and imagining such od
dities as a space shuttle pushed up against a barrier at the speed of light, or someone chasing toward a skedaddling beam of light.

  His sister, Maja, later gave a hint of this gently self-teasing tone. When Einstein got in a temper as a little child, she recounted, he sometimes threw things at her. Once it was a large bowling ball; another time he used a child's hoe "to try to knock a hole" in her head. "This should suffice," she commented, "to show that it takes a sound skull to be the sister of an intellectual." When she described the high school Greek teacher who complained that nothing would ever become of her brother, she added: "And in fact Albert Einstein never did attain a professorship of Greek grammar."

  To crank it all forward, there need to be driving tensions, and these Einstein had aplenty. There was the failure of being in his mid-twenties, isolated from other serious scientists, when university friends were already making careers for themselves. There was also thunderous guilt from seeing the difficulties his father was having in his own business career. Einstein had grown up with his father fairly prosperous in the electrical contracting business in Munich, but when Einstein was a teenager, possibly because key contracts stopped being given to Jewish firms, his father had moved the family to Italy to set up again. In the move, and in a series of near-successes that never quite made it, his father was exhausted in paying back loans to a brother-in-law, the constantly nagging Uncle Rudolf "The Rich" (as Einstein mockingly called him). It wrecked his father's health; yet through it all the family had insisted on finding the money to pay for Einstein to study. ("He is oppressed by the thought that he is a burden on us, people of modest means," as his father had remarked in the 1901 letter.) There was a huge obligation for Einstein to show he had been worth it after that.

  Eventually a few other physicists did begin to pay attention to Einstein, sometimes visiting Bern to talk over the equation and other results. It was just what Einstein and Besso had hoped for, but it also meant that they started being pulled apart. For Einstein was gradually going beyond the ideas his best friend could follow. Although Besso was bright, he'd chosen a life in industry. ("I prodded him very much to become a [university teacher], but I doubt . . . he'll do it. He simply doesn't want to.") Besso couldn't follow the next level.

  Besso adored his younger friend, and had gone out of his way to help him back when Einstein was still a student. He even tried, hard, in their evenings sharing Gruyere and sausages and tea, to keep up with the further ideas Einstein was seeing now. Einstein himself was kind about the growing distance from his friends. He never declared to Besso that he was no longer interested in him. They continued country walks, stops for a drink, musical evenings, and practical jokes with the others. But it's a bit like two old school friends breaking off once both have started moving separate ways at university, or in their first jobs afterward. Each one would really like things not to be like that, but everything they care about now is pulling them apart. They can talk about the old days when they're together, but the enthusiasm is forced, even though neither of them wants to admit it.

  A similar distancing happened with Einstein's wife, Mileva. She'd been a physics student with him, and very bright. Men in the sciences rarely marry fellow specialists— how many are there?—and Einstein was almost smug to his college friends about how lucky he'd been. His first letters to her had started neutrally:

  Zurich, Wednesday [16 February 1898]

  I have to tell you what material we covered. . . .

  Hurwitz lectured on differential equations (exclusive of partial ones), also on Fourier series. . . .

  But the relationship developed, as extracts from a series of letters written in August and September 1900 show:

  Once again a few lazy and dull days flitted past my sleepy eyes, you know, such days on which one gets up late because one cannot think of anything proper to do, then goes out until the room has been made up. . . . Then one hangs around and looks halfheartedly forward to the meal. . . .

  However things turn out, we are getting the most delightful life in the world. Beautiful work, and together. . . .

  Be cheerful, dear sweetheart. Kissing you tenderly, your

  Albert

  The life they shared started out happily. His wife wasn't going to be at his level, but she really was a good student—on the university final exams where he scored 4.96, she came close, with a 4.0, and she certainly could have followed his work. (The myth that she had been responsible for his key work stems from nationalist Serb propaganda in the 1960s, as her family had originally been from near Belgrade.) But once their children came, and with their income so low that they only had part-time help, all the traditional sexism took over. When educated friends came to visit, his wife would try to join in, but this is never easy with an attention-frantic three-year-old son on your lap. You want to stay a part of the conversation, but after too many interruptions for getting toys and drawing pictures and picking up spilled food, the guests no longer stop their talk to recap things and bring you in. You're left out.

  Einstein finally left the patent office—though even when he did, in 1909, his chief was mystified as to why this young man was willing to turn his back on such a good career. He was finally offered a position in the Swiss university system, and then after a stint in Prague—where he played music and engaged in discussions at a salon that occasionally included a shy young man named Franz Kafka—Einstein ended up as a professor in Berlin. His success had now isolated him almost completely from his Bern friends. He was legally separated from his wife, and only occasionally got to see his adored two children.

  By that time, Einstein was taking his personal work in a different direction. The equation E=mc2 was just a small part of the entire special theory of relativity. By 1915, he'd perfected an even grander theory, so powerful that the entire special theory was just one small part of that. (The Epilogue gives some highlights of that 1915 work—"Compared with this problem, the original theory of relativity is child's play.") He would be involved with the equation only once more, briefly, when he was a much older man.

  Mileva and Albert Einstein

  MAX FLUCKIGER, EINSTEIN IN BERN. COPYRIGHT BY PAUL HAUPT, BERN. AIP EMILIO SEGRE VISUAL ARCHIVES

  At this point there's a major shift in our story. The equation's first theoretical development was over; Einstein's personal contribution fades away. Europe's physicists accepted that E=mc2 was true: that, in principle, matter could be transformed so that the frozen energy it was composed of could be let out. But no one knew how actually to get that to happen.

  There was one hint. It came in the strange objects that Marie Curie and others were investigating: the dense metals of radium, and uranium, and other substances, which were somehow able to pour out energy week after week, month after month; never using up whatever "hidden" source of supply they contained inside.

  A number of laboratories began to study how that might be happening. But to see what mechanisms were creating these great outwellings of energy, it wouldn't be enough to continue looking at the surface of things, simply measuring the weight or color or surface chemical properties of the mysteriously warm radium or uranium.

  Instead, the researchers would have to go within, deep into the very heart of these substances. That, ultimately, would show how the energy that E=mc2 promised could be accessed. But what would they find, as they tried to peer into the smallest, inner structures within ordinary matter?

  Into the Atom 8

  University students in 1900 were taught that ordinary matter—bricks and steel and uranium and everything else—was made of smaller particles, called atoms. But what atoms were made of no one knew. One common view was that they were something like tough and shiny ball bearings: mighty glowing entities that no one could see inside. It was only with the research of Ernest Rutherford, a great, booming bear of a man working at England's Manchester University, in the period around 1910, that anyone got a clearer view.

  Rutherford was at Manchester, rather than at Oxford or Cambridge, not jus
t because he was from rural New Zealand, and spoke with a common man's accent. If a research assistant was self-effacing enough, that could be overlooked. The problem rather was that when Rutherford had been a student at Cambridge he had refused to show proper deference to his superiors. He'd even suggested creating a joint-venture business to earn money from one of his inventions—and that was a mortal sin. Yet the reason he became the scientist who got the first clear glimpse of the inside of atoms was, to a large extent, because his heightened awareness of discrimination made him the kindest leader of men. The bluff booming exterior was just window dressing. He was good in nurturing skilled assistants, and his key experiment was monitored by a young man who would end up perfecting a most useful mobile radiation detection unit, of Rutherford's suggested design: the audibly clicking counter was to be Hans Geiger's claim to fame.

  Ernest Rutherford

  PHOTOGRAPH BY C. E. WYNN-WILLIAMS. AIP EMILIO SEGRE VISUAL ARCHIVES

  Their finding is so widely taught in schools today that it's hard to get back to the time when it was still surprising. What Rutherford realized was that these solid, impregnable atoms were almost entirely empty. Imagine that a meteor plummets into the Atlantic Ocean, but instead of staying down there, ultimately plonking against the seabed, we hear a great roaring, and see it come hurtling back out. Think how hard it would be to break through our preconceptions, and realize that the only way to explain it was that under the surface of the Atlantic there really wasn't smooth water all the way down. Rather, the analogy with what Rutherford had to deduce would be that the Atlantic's surface was just a thin liquid-rubbery film, and underneath it, where we had always thought there were deep waves and currents and tons of water, there was . . . Nothing.