E=mc2 (5 page)

By the mid-1800s, scientists accepted the vision of energy and mass as being like two separate domed cities. One was composed of fire and crackling battery wires and flashes of light—this was the realm of energy. The other was composed of trees and rocks and people and planets—the realm of mass.

Each one was a wondrous, magically balanced world; each was guaranteed in some unfathomable way to keep its total quantity unchanged, even though the forms in which it appeared could vary tremendously. If you tried to get rid of something within one of the realms, then something else within that same realm would always pop up to take its place.

Everyone thought that nothing connected the two realms, however. There were no tunnels or gaps to get between the blocking domes. This is what Einstein was taught in the 1890s: that energy and mass were different topics; that they had nothing to do with each other.

Einstein later proved his teachers wrong, but not in the way one might expect. It is common to think of science as building up gradually from what came before. The telegraph is tinkered with and turns into the telephone; a propeller airplane is developed, and studied, and then improved planes are built. But this incremental approach does not work with deep problems. Einstein did find that there was a link between the two domains, but he didn't do it by looking at experiments with weighing mass and seeing if somehow a little bit was not accounted for, and might have slipped over to become energy. Instead he took what seems to be an immensely roundabout path. He seemed to abandon mass and energy entirely, and began to focus on what appeared to be an unrelated topic.

He began to look at the speed of light.

c Is for celeritas
5

"c" is different from what we've looked at so far. "E" is the vast domain of energies, and "m" is the material stuff of the universe. But "c" is simply the speed of light.

It has this unsuspected letter for its name probably out of homage for the period before the mid 1600s when science was centered in Italy, and Latin was the language of choice.
Celeritas
is the Latin word meaning "swiftness" (and the root of our word
celerity).

What this chapter looks at is how "c" came to play such an important role in E=mc
²
: how this particular speed—what might seem an arbitrary number—can actually control the link between all the mass and all the energy in the universe.

For a long time even measuring the speed of light was considered impossible. Almost everyone was convinced that light traveled infinitely fast. But if that were so, it could never have been used in a practical equation. Before anything more could be done—before Einstein could have possibly thought of using "c"—someone had to confirm that light travels at a finite speed, but that wouldn't be easy.

. . .

Galileo was the first person to clearly
conceive of
measuring the speed of light, well before he was undergoing house arrest in his old age, nearly blind. By the time he published, though, he was too old to carry out the experiment himself, and the Inquisition had given strict orders controlling where he went. That was little more than a challenge to him and his friends. A few years after his death, when members of an academy for experimental studies in Florence came to hear of his work, they let it be known that they would do the observations he had proposed.

The idea was as simple as all Galileo's work had been. Two volunteers were to stand holding lanterns on hillsides a mile apart one summer evening. They would open their lantern shutters one after the other, and then time how much of a delay there was for the light to cross the valley.

The experiment was a good idea, but the technology of the time was too poor to get any clear result. Galileo had been aware of the need in other experiments to breathe regularly, so as not to speed his heartbeat when an experiment was under way, for he used his pulse to measure short intervals of time. But that evening, probably in the hills outside of Florence, the volunteers found the light was too quick. All they noticed was a quick blur, a movement that seemed instantaneous. This could have been seen as a failure, and for most people it was just another proof that light traveled at infinite speed. But the Florentines didn't accept that it meant Galileo's speculations were wrong. Rather, the Academy concluded, it would just have to be left to someone from a future generation to find a way to time this impossibly fast burst.

In 1670, several decades after Galileo's death in 1642, Jean-Dominique Cassini arrived in Paris to take up his position as head of the newly established Paris Observatory. There was a lot of new construction to supervise, and he could sometimes be seen in the street doing that—not far from the shadows of the Port Libre prison, where Lavoisier in the next century would await his death—but his most important task was to shake some life into French science. He also had a personal incentive to make the new institution succeed, for his name wasn't actually Jean-Dominique but Giovanni Domenico. And he wasn't French, but newly arrived from Italy, and although the king was on his side, and the funding was said to be guaranteed, who knew how long that really would last?

Cassini sent emissaries to the fabled observatory of Uraniborg, on an island in the Danish straits not far from Elsinor Castle. Their goal was to fix the coordinates of Uraniborg, which would help in measuring distances for navigation; they might also find skilled researchers to recruit from other observatories. The founder of the Uraniborg observatory, Tycho Brahe, had made the observations on which Kepler and even Newton based their work. Brahe had created unimagined luxuries: there were exotic species of trees, gardens with artificial canals and fish ponds around the central castle, an impressive intercomlike communication system, and rotating automata that terrified local peasants; there were even rumors of an automatic flush toilet.

Cassini's right-hand man, Jean Picard, reached Uraniborg in 1671, sailing the misty waters from Copenhagen. He was excited about finally getting to see the fabled stronghold—then dismayed at finding it was a complete wreck.

Those sophisticated findings that had impressed Kepler dated from almost a century before. The observatory's founder had been a powerful personality, but when he had died, no one really took over. Everything was decayed or broken when Picard arrived: the fish ponds filled in, the quadrants and celestial globe long gone; only a few of the foundation stones of the main house were still recognizable.

Picard did get his readings, however, and also managed to bring back to Paris a bright twenty-one-year-old Dane named Ole Roemer. Others might be humbled to meet the great Cassini when they arrived back, for Cassini was a world authority on the planet Jupiter, and especially on the orbits of its satellites as they rotated around the planet. But although today we think of Denmark as a small nation, at that time it ran an empire that encompassed a good stretch of northern Europe. Roemer was cockily proud, enough to try making his own name.

It's doubtful whether Cassini was especially pleased with the upstart. It had taken a long time for him to make the switch from Giovanni Domenico to Jean-Dominique. He had accumulated numerous detailed observations of Jupiter's satellites, and he was certainly going to use them to maintain his worldwide reputation. But what if Roemer plundered his findings to prove that the conclusions Cassini was drawing from them were all wrong?

The reason this was possible was that there was a problem with the innermost moon of Jupiter, the one called Io. It was supposed to travel around its planet every 42½ hours. But it never stuck honestly to schedule. Sometimes it was a little quicker, sometimes a little slower. There was no discernible pattern anyone could tell.

But why? To solve the problem, Cassini insisted on more measurements and calculations. The effort might
he
exhausting for the observatory's director, and of course it might entail more staff and more equipment and more funds and more patronage, and all that embarrassing public exposure, but if that was necessary, it could be done. To Roemer, however, what was needed was not the sort of complex measurements only middle-aged administrators could manage. What was needed was the brilliance, the inspiration, that a young outsider applying his mind could provide.

And this is what Roemer did. Everyone—even Cassini—assumed that the problem was in how Io traveled. Possibly it was ungainly and wobbled during its orbit; or possibly there were clouds or other disturbances around Jupiter that obscured Io unevenly. Roemer reversed the problem. Cassini had made observations of Io, and the observations showed that something about its orbit was not smooth. But why should the flaw be assumed to rest far away near Jupiter? The question wasn't how Io was traveling, thought Roemer.

It was how Earth was traveling.

To Cassini, this couldn't possibly matter. Although he may once have considered a different possibility, like almost everyone else, he was convinced that light traveled as an instantaneous flash. Any fool could see that. Hadn't Galileo's own experiment shown that there was no evidence to the contrary?

Roemer ignored all that. Suppose—just suppose-that light did take some time to travel the great distance from Jupiter. What would that mean? Roemer imagined he was straddling the solar system, watching the first flicker of Io's light burst out from behind the planet Jupiter, and rush all the way to Earth. In the summer, for example, if Earth was closer to Jupiter, the light's journey would be shorter, and Io's image would arrive sooner. In the winter of the same year, though, Earth could have swung around to the other side of the solar system. It would take a lot longer for Io's signal to reach us.

Roemer went through Cassini's stacked years of observations, and by the late summer of 1676 he had his solution: not just a hunch, but an exact figure for how many extra minutes light took to fly that extra distance when Earth was far from Jupiter.

What should he do with such a finding? By protocol, Roemer should have let Cassini present it as his own work, and simply nod modestly, perhaps, when the observatory chief paused to remark that he couldn't have done it without the help of this young man whose future career was worth watching.

Roemer didn't go along with that. In August, at the esteemed public forum of a journal all serious astronomers read, he proclaimed a challenge. Astronomy is an exact science, and even seventeenth-century tools were good enough to determine that the satellite Io was scheduled to appear from behind Jupiter on the coming November 9, sometime in the late afternoon. By Cassini's reasoning, it would be detected at 5:27 P.M. on that day. That was what he extrapolated from when it had last been clearly sighted, in August.

Roemer declared that Cassini was going to be wrong. In August, he explained, the earth had been close to Jupiter. In November it would be farther away. There would be nothing visible at 5:27—the light, though fast, would still be on its way, since it had to travel that extra distance. Even at 5:30 or 5:35 it wouldn't have made it across the solar system. Only at 5:37 precisely would anyone be able to get their first sighting on November 9.

There are many ways to make astronomers happy. A new supernova
is
good; a renewed grant from the government is good; tenure is extremely good. But an out-and-out battle between two of your distinguished colleagues? It was heaven. Roemer had thrown down his challenge partly out of pride, but also because he knew that Cassini was a much better political operator than he was. Roemer would only be able to claim credit if his prediction was
so clear
that Cassini and his minions couldn't wangle out of it if they were wrong.

The prediction was announced in August. On November 9, observatories in France and across Europe had their telescopes ready. 5:27 P.M. arrived. No 10.

5:30 arrived. Still no 10.

5:35 P.M.

And then it appeared, at 5:37 and 49 seconds exactly.

And Cassini declared he had not been proven wrong! (Spin-doctoring was not invented in the era
of
television.) Cassini had lots of supporters, and support him they did. Who'd ever said Io was expected at 5:25? That had only been Roemer, they now declared. Besides, everyone realized 10's arrival time was never certain. It was so far away, so hard to see exactly, that perhaps those clouds from Jupiter's upper atmosphere were producing a distorting haze; or maybe the high angle of its orbit was what made definite observations so difficult. Who knew?

In the usual history of science accounts, it's not supposed to happen this way. Roemer had performed an impeccable experiment, with a clear prediction, yet Europe's astronomers still did not accept that light traveled at a finite speed. Cassini's supporters had won: the official line remained that the speed of light was just a mystical, unmeasurable figure; that it should have no impact on astronomical measurements.

Roemer gave up, and went back to Denmark, spending many years as the director of the port of Copenhagen. Only fifty years later—after a further generation had passed, and Jean-Dominique Cassini was gone—did further experiments convince astronomers that Roemer had been right. The value he had estimated for light's speed was close to the best current estimate, which is about 670,000,000 mph. (In fact the exact speed is a fraction higher, but for convenience we'll round it off to 670 million for the rest of this book.)

To emphasize how big a number this is, at 670,000,000 mph, you could get from London to Los Angeles in under 1/20th of a second. That explains why Galileo's experiment could not detect the time it took light to cross a valley outside Florence; the distance was much too small.

There's another comparison: Mach 1
is
the speed of sound, about 700 mph. A 747 jet travels at a little under Mach 1. The space shuttle, after full thrust, can surpass Mach 20. The asteroid or comet that splashed a hole in the ocean floor and destroyed the dinosaurs impacted at about Mach 70.

The number for "c" is Mach 900,000.

This vast speed leads to many curious effects. Let someone irritatingly speak into a cell phone just a few tables away from you in a restaurant, and it seems as if you're hearing his voice almost as soon as the words leave his mouth. But air only can carry a sound wave at the lowly speed of Mach 1, whereas radio signals shooting upward from the cell phone travel as fast as light. The person on the receiving end of the phone—even if she's hundreds of miles away—will hear the words
before
they've trundled the few yards through the air in the restaurant to reach you.

It was a difficult time for Faraday. His memory was failing and he could often barely get through a morning without extensive notes to remind him of what he was supposed to do. Even worse, Faraday also knew that the world's great physicists, almost all of whom had gone to elite universities, still patronized him. They accepted his practical lab findings, but nothing else. To standard physicists, when electricity flowed through a wire it was basically like water flowing through a pipe: once the underlying mathematics was finally worked out, they believed, it would not be too different from what Newton and his numerous mathematically astute successors could describe.

Faraday, however, still went on about those strange circles and other wending lines from his religious upbringing. The area around an electromagnetic event, Faraday held, was filled with a mysterious "field," and stresses within that field produced what were interpreted as electric currents and the like. He insisted that sometimes you could almost see their essence, as in the curving patterns that iron filings take when they are sprinkled around a magnet. Yet almost no one believed him—except, now, for this young Scot named Maxwell.