E=mc2 (3 page)
Authors: David Bodanis
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.
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.
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), andfor
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.