E=mc2 (7 page)

The reader might wonder when we'll get to the theory of relativity. The answer is that we've already been using it! All these points about a speeding shuttle and its expanding mass are central to what Einstein published in 1905.

Einstein's work changed the two separate visions scientists had taken from the nineteenth-century work on conservation laws. Energy isn't conserved, and mass isn't conserved—but that doesn't mean there is chaos. Instead, there's actually a deeper unity, for there's a link between what happens in the energy domain and what happens in the seemingly distinct mass domain. The amount of mass that's gained is always going to be balanced by an equivalent amount of energy that's lost.

Lavoisier and Faraday had seen only part of the truth. Energy does not stand alone, and neither does mass. But the sum of mass plus energy will always remain constant.

This, finally, is the ultimate extension of the separate conservation laws the eighteenth- and nineteenth-century scientists had once thought complete. The reason this effect had remained hidden, unsuspected, all the time before Einstein, is that the speed of light is so much higher than the ordinary motions we're used to. The effect is weak at walking speed, or even at the speed of locomotives or jets, but it's still there. And as we'll see, the linkage is omnipresent in our ordinary world: all the energy is held quiveringly ready inside even the most ordinary substances.

Linking energy and mass via the speed of light was a tremendous insight, but there's still one more detail to get clear. A famous cartoon shows Einstein at a board, trying out one possibility after another: E=mc
¹
, E=mc
²
, E=mc
³
,. . . But he didn't really do it that way, arriving at the squaring of "c" by mere chance.

So why did the conversion factor turn out to be c
²
?

²
6

Enlarging a number by "squaring" it is an ancient procedure. A garden that has four paving slabs on one edge, and four on the other, doesn't have eight stones in it. It has 16.

The convenient shorthand that summarizes this action of building up a "square"—of multiplying a number by itself—went through almost the same range of permutations as did the Western typography for the equals sign. But why should it appear in physics equations? The story of how an equation with a "squared" in it came to be plucked from all other possibilities for representing the energy of a moving object takes us back to France once more—to the early 1700s—and the generation halfway between Roemer and Lavoisier.

He went out and probably had a moment to recognize the carriage of the Chevalier de Rohan, an unpleasant, yet staggeringly rich man whom he'd mocked in public when they'd recently attended a play at the Comedie Francaise. Then de Rohan's bodyguards got to work, beating Arouet while de Rohan watched, delighted, from inside his carriage, "supervising the workers," as he later described it. Somehow, Arouet managed to get back inside the gates, and into de Sully's home. But instead of sympathy or even outrage, Arouet encountered only laughter. De Sully and his friends were amused: a preposterous wordsmith had been put in his place by someone who really mattered. Arouet vowed to avenge himself; he would challenge de Rohan to a duel, and kill him.

That was getting too serious. De Rohan's family had a word with the authorities; there was a police hunt; Arouet was arrested, then put in the Bastille.

When he finally got out he crossed the Channel, falling in love with England, and especially—estate agents take note—with the bucolic wonderland of Wandsworth, far from the grime of the busy city. He was exhilarated to find that there was a new concept in the air, the works of Newton, which represented what could be the opposite of the ancient, locked-in aristocratic system he'd known in France.

Newton had created a system of laws that seemed to detail, with superb accuracy, how every part of our universe moved about. The planets swung through space at a rate and in directions that Newton's laws described; a cannonball fired in the air would land exactly where Newton's calculations of its trajectory showed that it would land.

It really was as if we were living inside a vast windup clock, and all the laws Newton had seen were simply the gears and cogs that made it work. But if we could demand a rational explanation of the grand universe beyond our planet, Arouet wondered, shouldn't we be able to demand the same down here on earth? France had a king who demanded obedience, on the grounds that he was God's regent on earth. Aristocrats got authority from the king, and it was impious to question this. But what if the same analysis used in science by Newton could be used to reveal the role of money or vanity or other hidden forces in the political world as well?

By the time Arouet went back to Paris, three years later, he had begun pushing his new ideas, in private letters and printed essays. In a world of clear, levelheaded analysis of true forces, his humiliation outside the gates of de Sully would never have been allowed. Arouet would support Newton's new vision accordingly his whole life long. He was a good supporter to have, for Arouet was only the name he'd been born with. He'd already largely put it to the side for the pen name by which he was better known: Voltaire.

But even a skilled writer, however eager to push a particular thinker, can't shift a nation on his own. Voltaire needed
to he
able to place his talents within a switching center that could multiply them. The king's Academy of Sciences was too backward-looking; too locked into the old guard's way of thinking. The salons of Paris wouldn't do either. The usual hostesses were rich enough to keep a tame poet or two ("If you neglect to enroll yourself among the courtesans," Voltaire observed, "you are . . . crushed"), but there was no space for a real thinker. He needed help. And he found it.

. . .

He'd actually met her without realizing it, fifteen years before, visiting her father when she was just a girl. Emilie de Breteuil's family lived overlooking the Tuileries gardens in Paris, in an apartment with thirty rooms and seventeen servants. But although her brothers and sisters turned out as expected, Emilie was different, as her father wrote: "My youngest flaunts her mind, and frightens away the suitors. . . . We don't know what to do with her."

When she was sixteen they brought her to Versailles, but still she stood out. Imagine the actress Geena Davis, Mensa member and onetime action-film star, trapped in the early eighteenth century. Emilie had long black hair and a look of perpetual startled innocence, and although most other debutante types wanted nothing more than to use their looks to get a husband, Emilie was reading Descartes's analytic geometry, and wanted potential suitors to keep their distance.

She'd been a tomboy as a child, loving to climb trees, and she was also taller than average, and—best of all -since her parents had been worried she'd end up clumsy, they'd paid for fencing lessons for years. She challenged Jacques de Brun, whose position was roughly equivalent to head of the king's bodyguard detail, to a demonstration duel, in public, on the fine wood floor of the great Hall of Arms. She was fast enough, and strong enough, with the thrusts and parries, to remind any overeager suitors that they would be wise to leave her alone.

Her intellect left her isolated at Versailles, for there was no one with whom she could share her excitement about the wondrous insights she was discovering through the work of Descartes and other researchers. (At least there were certain advantages in being immersed in equations—she found it easy to memorize cards at the blackjack table.)

When Emilie was nineteen, she chose one of the least objectionable courtiers as a husband. He was a wealthy soldier named du Châtelet, who would conveniently be on distant campaigns much of the time. It was a pro forma arrangement, and in the habit of the time, her husband accepted her having affairs while he was away. There were a number of lovers, one of the closest being a onetime guards officer, Pierre-Louis Maupertuis, who had resigned his post, and was in the process of becoming a top physicist. Their courtship had begun in studying calculus and more advanced work together, but he was leaving on a polar expedition, and in 1730s France, no twenty-something young woman—however bright, however athletic—would be allowed
to go
along.

Now Emilie was at loose ends. Where could she turn for warmth? She had a few desultory affairs while Maupertuis was ordering his final supplies, but who, in France, could fill Maupertuis's place? Enter Voltaire.

"I was tired of the lazy, quarrelsome life led at Paris," Voltaire recounted later, " . . . of the privilege of the king, of the parties and cabals among the learned. . . . In the year 1733 I met a young lady who happened to think nearly as I did. . . ."

She met Voltaire at the opera, and although there was some overlap with Maupertuis, that was no problem. Voltaire composed a stirring poem for Maupertuis, complimenting him as a modern-day argonaut, for his boldness in venturing to the far north for science; he then wrote a romantic poem to du Châtelet, comparing her to a star, and noting that he, at least, was not so faithless as to exchange her for some expedition to the Arctic pole. It wasn't entirely fair to Maupertuis, but du Châtelet didn't mind. Anyway, what could Voltaire do? He was in love.

Emilie du Châtelet

PAINTING BY MAURICE QUENTIN DE LA TOUR. LAUROS-GIRAUDON

. . . is changing staircases into chimneys and chimneys into staircases. Where I ordered the workmen to construct a library, she tells them to place a salon. . . . She's planting lime trees where I'd planned to place elms, and where I only planted herbs and vegetables . . . only a flowerbed will make her happy.

Within two years it was complete. There was a library comparable to that of the Academy of Sciences in Paris, the latest laboratory equipment from London, and there were guest wings, and the equivalent of seminar areas, and soon there were visits from the top researchers in Europe. Du Châtelet had her own professional lab, but the wall decorations in her reading areas were original paintings by Watteau; there was a private wing for Voltaire, yet also a discreet passageway conveniently connecting his bedroom with hers. (Arriving one time when she didn't expect him, he discovered her with another lover, and she tried putting him at ease by explaining that she'd only done this because she knew he hadn't been feeling well and she hadn't wanted to trouble him while he needed his rest.)

The occasional visitors from Versailles who came to scoff saw a beautiful woman willingly staying inside, working at her desk well into the evening, twenty candles around her stacks of calculations and translations; advanced scientific equipment stacked in the great hall. Voltaire would come in, not merely wanting to gossip about the court—though, being Voltaire, he was unable to resist this entirely—but also to compare Newton's Latin texts with some of the latest Dutch commentaries.

At several times she came close to jump-starting future discoveries. She performed a version of Lavoisier's rust experiment, and if the scales she'd been able to get machined had been only a bit more accurate, she might have been the one to come up with the law of the conservation of mass, even before Lavoisier was born.

The Cirey team kept up a supporting correspondence with other new-style researchers; supplying them with whatever evidence, diagrams, calculations might be needed. The scientific visitors such as Koenig and Bernoulli sometimes stayed for weeks or months at a time. Voltaire was pleased that crisp, Newtonian science was gaining ground through their efforts. But when he and du Châtelet engaged in their teasing, their mock battling, it wasn't the case of a worldly, widely read man deciding when to let his young lover win. Du Châtelet was the real investigator of the physical world, and the one who decided that there was one key question that had to be turned to now: What is energy?

But du Châtelet knew that there had once been a famous competing view to Newton's, due to Gottfried Leibniz, the great German diplomat and natural philosopher. For Leibniz, the important factor to focus on was mv
²
. If a 5-pound ball is going at 10 mph, it has 5 times 102, or 500 units of energy.

Which view was true? It might seem a mere quarreling over definitions, but there was something deeper going on behind it. We're used to science being separated from religion, but in the seventeenth and eighteenth centuries it wasn't.

Newton felt that highlighting where mv
¹
occurs would prove that God had to exist. If two identical beer wagons crash head-on, there's an almighty bang, and possibly some grinding as their bumpers crumple into each other, but then there's stillness. Right before they hit there was a lot of mv
¹
in the universe: the two speeding carts were each loaded with the stuff. One cart had been going full speed due east, for example; the other had been going full speed due west. After they hit, though, and had become stationary chunks of wood and metal, the two separate parts of the v
¹
were gone. The "going due east" had exactly canceled out the "going due west."

In Newton's view, this meant that all the energy the carts had once possessed had now vanished. A hole had been created, leading out from our visible universe. Since collisions like this happen all the time, if we live within a great, coglike clockwork, that clock would always need winding. But look around you. We don't find that as the years pass, fewer and fewer objects are able to move. That's the proof. The fact that the universe continues operating was, in Newton's view, a sign that God's reassuring hand was reaching in, to nurture us and to support us; to supply all the motive forces we otherwise lost.