E=mc2
Page 3
When Einstein did finally make it into the Federal Institute of Technology—after his first delicious romance, with the eighteen-year-old daughter of his Aarau host—the physics lecturers there were still teaching the Victorian gospel, of a great overarching energy force. But Einstein felt his teachers had missed the point. They were not treating it as a live topic, honestly hunting for what it might mean, trying to feel for those background religious intimations that had driven Faraday and others forward. Instead, energy and its conservation was just a formalism to most of them, a set of rules. There was a great complacency throughout much of Western Europe at the time. European armies were the most powerful in the world; European ideas were "clearly" superior to those of all other civilizations. If Europe's top thinkers had concluded that energy conservation was true, then there was no reason to question them.
Einstein was easygoing about most things, but he couldn't bear complacency. He cut many of his college classes—teachers with that attitude weren't going to teach him anything. He was looking for something deeper, something broader. Faraday and the other Victorians had managed to widen the concept of energy until they felt it had encompassed every possible force.
But they were wrong.
Einstein didn't see it yet, but he was already on the path. Zurich had a lot of coffeehouses, and he spent afternoons in them, sipping the iced coffees, reading the newspapers, killing time with his friends. In quiet moments afterward, though, Einstein thought about physics and energy and other topics, and began getting hints of what might be wrong with the views he was being taught. All the types of energy that the Victorians had seen and shown to be interlinked—the chemicals and fires and electric sparks and blasting sticks—were just a tiny part of what might be. The energy domain was perceived as very large in the nineteenth century, but in only a few years Einstein would locate a source of energy that would dwarf what even the best, the most widely hunting of those Victorian scientists had found.
He would find a hiding place for further vast energy, where no one had thought to look. The old equations would no longer have to balance. The amount of energy God had set for our universe would no longer remain fixed. There could be more.
= 3
Most of the main typographical symbols we use were in place by the end of the Middle Ages. Bibles of the fourteenth century often had text that looked much like telegrams:
IN THE BEGINNING GOD CREATED THE HEAVEN
AND THE EARTH AND THE EARTH WAS WITHOUT
FORM AND VOID AND DARKNESS WAS UPON THE
FACE OF THE DEEP
One change that took place at various times was to drop most of the letters to lowercase:
In the beginning God created the heaven and the earth and the earth was without form and void and darkness was upon the face of the deep
Another shift was to insert tiny round circles to mark the major breathing pauses:
In the beginning God created the heaven and the earth. And the earth was without form and void and darkness was upon the face of the deep.
Smaller curves were used as well, for the minor breathing pauses:
In the beginning, God created the heaven and the earth
Major symbols were locked in rather quickly once printing began at the end of the 1400s. Texts began to be filled in with the old ? symbols and the newer ! marks. It was a bit like the Windows standard in personal computers driving out other operating systems.
Minor symbols took longer. By now we take them so much for granted that, for example, we almost always blink when we see the period at the end of a sentence. (Watch someone when they're reading and you'll see it.) Yet this is an entirely learned response.
For more than a thousand years, one of the world's major population centers used this symbol for addition, since it showed someone walking toward you (and so was to be "added" to you), and for subtraction. These Egyptian symbols could easily have spread to become universally accepted, just as other Middle Eastern symbols had done. Phoenician symbols, for example, were the source of the Hebrew —aleph and beth— and also the Greek α and β—alpha and beta—as in our word alphabet.
Through the mid-1500s there was still space for entrepreneurs to set their own mark by establishing the remaining minor symbols. In 1543, Robert Recorde, an eager textbook writer in England, tried to promote the new-style "+" sign, which had achieved some popularity on the Continent. The book he wrote didn't make his fortune, so in the next decade he tried again, this time with a symbol, which probably had roots in old logic texts, that he was sure would take off. In the best style of advertising hype everywhere, he even tried to give it a unique selling point: ". . . And to avoide the tediouse repetition of these woordes: is equalle to: I will sette . . . a pair of parallels, or . . . lines of one lengthe, thus: bicause noe .2. thynges, can be moare equalle. . . ."
It doesn't seem that Recorde gained from his innovation, for it remained in bitter competition with the equally plausible / / and even with the bizarre [; symbol, which the powerful German printing houses were trying to promote. The full range of possibilities proffered at one place or another include, if we imagine them put in the equation:
Not until Shakespeare's time, a generation later, was Recorde's victory finally certain. Pedants and schoolmasters since then have often used the equals sign just to summarize what's already known, but a few thinkers had a better idea. If I say that 15+20=35, this is not very interesting. But imagine if I say:
(go 15 degrees west)
+
(then go 20 degrees south)
=
(you'll find trade winds that can fling you across
the Atlantic to a new continent in 35 days).
Then I am telling you something new. A good equation is not simply a formula for computation. Nor is it a balance scale confirming that two items you suspected were nearly equal really are the same. Instead, scientists started using the = symbol as something of a telescope for new ideas—a device for directing attention to fresh, unsuspected realms. Equations simply happen to be written in symbols instead of words.
This is how Einstein used the " = " in his 1905 equation as well. The Victorians had thought they'd found all possible sources of energy there were: chemical energy, heat energy, magnetic energy, and the rest. But by 1905 Einstein could say, No, there is another place you can look where you'll find more. His equation was like a telescope to lead there, but the hiding place wasn't far away in outer space. It was down here—it had been right in front of his professors all along.
He found this vast energy source in the one place where no one had thought of looking. It was hidden away in solid matter itself.
m Is for mass 4
For a long time the concept of "mass" had been like the concept of energy before Faraday and the other nineteenth-century scientists did their work. There were a lot of different material substances around—ice and rock and rusted metal—but it was not clear how they related to each other, if they did at all.
What helped researchers believe that there had to be some grand links was that in the 1600s, Isaac Newton had shown that all the planets and moons and comets we see could be described as being cranked along inside an immense, God-created machine. The only problem was that this majestic vision seemed far away from the nitty-gritty of dusty, solid substances down here on earth.
To find out if Newton's vision really did apply on Earth—to find out, that is, if the separate types of substance around us really were interconnected in detail—it would take a person with a great sense of finicky precision; someone willing to spend time measuring even tiny shifts in weight or size. This person would also have to be romantic enough to be motivated by Newton's grand vision—for otherwise, why bother to hunt for these dimly suspected links between all matter?
This odd mix—an accountant with a soul that could soar—might have been a character portrait of Antoine-Laurent Lavoisier. He, as much as anyone else, was the man who first showed that all the seemingly diverse bits of tree a
nd rock and iron on earth—all the "mass" there is—really were parts of a single connected whole.
Lavoisier had demonstrated his romanticism in 1771 by rescuing the innocent thirteen-year-old daughter of his friend Jacques Paulze from a forced marriage to an uncouth, gloomy—yet immensely rich—ogre of a man. The reason he knew Paulze well enough to do the good deed for the daughter, Marie Anne, was that Paulze was his boss. The way he rescued Marie Anne was to marry her himself.
It turned out to be a good marriage, despite the difference in age, and despite the fact that soon after the handsome twenty-eight-year-old Lavoisier rescued Marie Anne, he shifted back to being immersed in the stupendously boring accountancy work he did for Paulze, within the organization called the "General Farm."
This was not a real farm, but rather an organization with a near monopoly on collecting taxes for Louis XVI's government. Anything extra, the Farm's owners could keep for themselves. It was exceptionally lucrative, but also exceptionally corrupt, and for years had attracted old men wealthy enough to buy their way in, but unable to do any detailed accounting or administration. It was Lavoisier's job to keep this vast tax-churning device in operation.
He did that, head down, working long hours, six days a week on average for the next twenty years. Only in his spare time—an hour or two in the morning, and then one full day each week—did he focus on his science. But he called that single day his "jour de bonheur"—his "day of happiness."
Perhaps not everyone would comprehend why this was such a "bonheur." The experiments often resembled Lavoisier's ordinary accounting, only dragged out even longer. Yet the moment came when Antoine, in that irrational exuberance young lovers are known for, said his bride could now help him with a truly major experiment. He was going to watch a piece of metal slowly burn, or maybe just rust. He wanted to find out whether it would weigh more or less than it did before.
(Before going on, the reader might wish to actually guess: Let a piece of metal rust—think of an old fender or underbody panel on your car—and it ends up weighing
a)less
b) the same
c) more
than it did before. Remember your answer.)
Most people, even today, probably would say it would weigh less. But Lavoisier, ever the cool accountant, took nothing on trust. He built an entirely closed apparatus, and he set it up in a special drawing room of his house. His young wife helped him: she was better at mechanical drawing than he was, and a lot better at English. (This would later be useful in keeping up with what the competition across the Channel was doing.)
They put various substances in their drawing room apparatus, sealed it tight, and applied heat or started an actual burn to speed up the rusting. Once everything had cooled down, they took out the mangled or rusty or otherwise burned-up metal and weighed it, and also carefully measured how much air may have been lost.
Each time they got the same result. What they found, in modern terms, was that a rusted sample does not weigh less. It doesn't even weigh the same. It weighs more.
This was unexpected. The additional weight was not from dust or metal shards left around in the weighing apparatus—he and his wife had been very careful. Rather, air has parts: there are different gases within the vapor we breathe. Some of the gases must have flown down and stuck to the metal. That was the extra weight he had found.
What was really happening? There was the same amount of stuff overall, yet now the oxygen that had been in the gases floating above was no longer in the air. But it had not disappeared. It had simply stuck on to the metal. Measure the air, and you would see it had lost some weight. Measure the chunk of metal, and you would see it had been enhanced—by exactly that same amount of weight the air had lost.
With his fussily meticulous weighing machine, Lavoisier had shown that matter can move around from one form to another, yet it will not burst in and out of existence. This was one of the prime discoveries of the 1700s—on a level with Faraday's realizations about energy in the basement of the Royal Institution a half century later. Here too, it was as if God had created a universe, and then said, I am going to put a fixed amount of mass in my domain, I will let stars grow and explode, I will let mountains form and collide and be weathered away by wind and ice; I will let metals rust and crumble. Yet throughout this the total amount of mass in my universe will never alter; not even to the millionth of an ounce; not even if you wait for all eternity. If a city were to be weighed, and then broken by siege, and its buildings burned by fire—if all the smoke and ash and broken ramparts and bricks were collected and weighed, there would be no change in the original weight. Nothing would have truly vanished, not even the weight of the smallest speck of dust.
To say that all physical objects have a property called their "mass," which affects how they move, is impressive, yet Newton had done it in the late 1600s. But to get enough detail to show exactly how their parts can combine or separate? That is the further step Lavoisier had now achieved.
Whenever France's scientists make discoveries at this level, they're brought close to the government. It happened with Lavoisier. Could this oxygen he'd helped clarify be used to produce a better blast furnace? Lavoisier had been a member of the Academy of Sciences and now was given funds to help find out. Could the hydrogen he was teasing out from the air with his careful measurements be useful in supplying a flotilla of balloons, capable of competing with Britain for supremacy in the air? He got grants and contracts for that as well.
In any other period this would have guaranteed the Lavoisiers an easy life. But all these grants and honors and awards were coming from the king, Louis XVI, and in a few years Louis would be murdered, along with his wife and many of his ministers and wealthy supporters.
Lavoisier might have avoided being caught up with the other victims. The Revolution was only at its most lethal phases for a few months, and many of Louis' closest supporters simply lived out those periods in quiet. But Lavoisier could never drop the attitude of careful measuring. It was part of his personality as an accountant; it was the essence of his discoveries in science.
Now it would kill him.
The first mistake seemed innocuous enough. Outsiders constantly bothered members of the Academy of Sciences, and long before the Revolution, one of them, a Swiss-born doctor, had insisted that only the renowned Lavoisier would be wise enough, and understanding enough, to judge his new invention. The device was something of an early infrared scope, allowing the doctor to detect the shimmering heat waves rising from the top of a candle, or of a cannonball, or even—on one proud occasion, when he'd lured the American representative to his chambers—from the top of Benjamin Franklin's bald head. But Lavoisier and the Academy turned him down. From what Lavoisier had heard, the heat patterns that the doctor was searching for couldn't be measured with precision, and to Lavoisier that was anathema. But the Swiss-born hopeful—Dr. Jean-Paul Marat—never forgot.
The next mistake was even more closely linked to Lavoisier's obsession with measurement. Louis XVI was helping America fund its revolutionary war against the British, an alliance that Benjamin Franklin had been central in sustaining. There were no bond markets, so to get the money Louis had to turn to the General Farm. But taxes already were high. Where could they go to get more?
In every period of incompetent administration France has suffered—and Louis's successors in the 1930s would have given him a good run—there almost always has been a small group of technocrats who've decided that since no one who was officially in power was going to take charge, then they would have to do it themselves. Lavoisier had an idea. Think of the measuring apparatus in his drawing room, the one where he and Marie Anne had been able to keep exact track of everything going in and out. Why not enlarge it, wider and wider, so that it encompassed all of Paris? If you could track the city's incomings and outgoings, he realized, you could tax them.
There once had been a physical wall around Paris, but it dated from medieval times, and had long since become
nearly useless for taxation. Tollgates were crumbling, and many areas were so broken that smugglers could just walk in.
Lavoisier decided to build another wall, a massive one, where everyone could be stopped, searched, and forced to pay tax. It cost the equivalent, in today's currency, of several hundred million dollars; it was the Berlin Wall of its time. It was six feet high, of heavy masonry, with dozens of solid tollgates and patrol roads for armed guards.
Parisians hated it, and when the Revolution began, it was the first large structure they attacked, two days before the storming of the Bastille: they tore at it with firebrands and axes and bare hands till it was almost entirely gone. The culprit was known, as an antiroyalist broadsheet declared: "Everybody confirms that M. Lavoisier, of the Academy of Sciences, is the 'beneficent patriot' to whom we owe the . . . invention of imprisoning the French capital. . . ."
Even this he might have survived. A mob's passions are brief, and Lavoisier hurriedly tried to show he was on their side. He personally directed the gunpowder mills that supplied the Revolutionary Armies; he tried to have the Academy of Sciences show new, reformist credentials by getting rid of the grand tapestries in its Louvre offices. He even seemed to be succeeding—until one never-forgiving figure from his past emerged.