E=mc2 (21 page)
Authors: David Bodanis
The work of Einstein's equation is done.
It wasn't actually E=mc
2
and his other work from 1905 that first made Einstein famous. If that were all he had done, his name would have become recognized within the specialized community of theoretical physicists, but probably not otherwise known to the public. In the 1930s he would have been just another distinguished refugee: living a quiet life perhaps, but in no special position to sign a letter warning of atomic dangers, which could be delivered to FDR in 1939.
It didn't turn out like that of course. Something else happened that built on E=mc
2
but went further—and ended up making him the most famous scientist in the world.
What Einstein published in 1905 only covered cases where objects are racing along smoothly, and gravity, with its accelerating pull, doesn't play much of a role. E=mc
2
is "true" in those cases, but will it hold true even if you get rid of those restrictions? That limitation and others had always troubled Einstein, and in 1907 he got the first hint of a wider solution: "I was sitting on a chair in my patent office in Bern when all of a sudden a thought occurred to me . . . . I was startled."
He later called this "the happiest thought of my life," for a few years later, in 1910, it led to his reflecting on the very fabric of space, and how it was affected by the mass or energy of objects at any one location in it. The work took several years, partly because although Einstein was in a league of his own in physics, he was only fair in mathematics. It wasn't quite as bad as he once described to a junior high school student in America, when he wrote her, "Do not worry about your difficulties in mathematics. I can assure you that mine are still greater." But it was enough to justify Hermann Minkowski's lament, when he saw the early drafts of Einstein's efforts: "Einstein's presentation of his subtle theory is mathematically cumbersome—I am allowed to say so because he learned his mathematics from me in Zurich."
To help him with the math, though, Einstein had his old friend from university days, Marcel Grossman, the one who'd loaned him crib sheets when they were undergraduates. (Grossman was also the friend whose father had written the letter getting Einstein the patent office job.) Grossman sat with Einstein for long hours, to explain what tools from recent mathematics he might use.
What Einstein's "happiest thought" of 1907 led him to was the idea that the more mass or energy there was at any one spot, the more that space and time would be curved tight around it. It was a far more powerful theory than what he'd come up with before, for it encompasses so much more. The 1905 work had been labeled "special" relativity. This now was general relativity.
A small, rocky object, such as our planet, has only a little bit of mass and energy, and so only curves the fabric of space and time around it a bit. The more powerful sun would tug the underlying fabric around it far more taut.
Examples of warped space-time.
MODIFIED FROM A DIAGRAM IN
THE SCIENCES
BY JAMES TREFIL AND ROBERT M. HAZEN
(NEW YORK: JOHN WILEY & SONS, 1998)
The equation that summarizes this has a great simplicity, curiously reminiscent of the simplicity of E=mc
2
. In E=mc
2
, there's an energy realm on one side, a mass realm on the other, and the bridge of the "=" sign linking them. E=mc
2
is, at heart, the assertion that Energy = mass. In Einstein's new, wider theory, the points that are covered deal with the way that all of "energy-mass" in an area is associated with all of "space-time" nearby, or, symbolically, the way that Energy-mass = space-time. The "E" and the "m" of E=mc
2
are now just items to go on one side of this deeper equation.
The entire mass-loaded Earth rolls forward, automatically following the shortest path amidst the space-time "curves" that spread rippling around us. Gravity is no longer something that happens stretching across an inert space: rather, gravity
is
simply what we notice when we happen to be traveling within a particular configuration of space and time.
The problem, though, is that it seems preposterous! How can seemingly empty space and time be warped? Clearly that would have to occur, if this extended theory, which now embedded E=mc
2
in its wider context, were to be true. Einstein
realized
that there could be something of a test—some demonstration that would be so clear, so powerful, that no one could doubt that this wild result he'd come up with was right.
But what could that be? The proving test came from the heart of the theory, that diagram of a warp in the very fabric around us. If empty space really could be tugged and curved, then we'd be able to see distant starlight "mysteriously" swiveled around our sun. It would be like watching a bank shot in billiards suddenly take place, where a ball spins around a pocket and comes out with a changed direction. Only now it would occur in the sky overhead, where nobody had ever suspected a curved corner pocket to reside.
Normally we couldn't notice this light being bent by the sun, because it would apply only to starlight that skimmed very close to the outer edge of our sun. Under ordinary circumstances the sun's glare would block out those adjacent daytime stars.
But during an eclipse?
Every hero needs an assistant. Moses had Aaron. Jesus had his disciples.
Einstein, alas, got Freundlich.
Erwin Freundlich was a junior assistant at the Royal Prussian Observatory in Berlin. I wouldn't say he had the worst luck of any individual I've read about. Possibly there was someone who survived the
Titanic,
and then decided to try a ride on the
Hindenburg.
But it's probably pretty close. Freundlich was going to make his career, he decided, by shepherding the great general relativity equations forward, and performing the observations that would prove Professor Einstein's predictions were right. He was very generous about this—in the way that Lavoisier had been generous in letting his wife help him watch metal heat and rust. As a special honeymoon treat, Freundlich brought his new bride to Zurich in 1913 just so she could be there as he discussed stellar observations with the renowned professor.
An eclipse was predicted for the very next year, in the Crimea, and Freundlich prepared everything in detail. He even carefully arrived in the Crimea two months early, in July 1914. It was probably the worst possible place for a German national to be. War was declared one month later. Freundlich was arrested, put in prison in Odessa, and had all his equipment taken away. He finally got out in a prisoner exchange for a group of Russian officers who'd been arrested in Germany, but by then the eclipse had come and gone.
He didn't give up. In 1915, back in Berlin, Freundlich decided he could help Professor Einstein by measuring the way light got bent near distant binary stars. In February he had results that backed up the new theory, and Einstein began to spread the good news in letters to his friends. Four months later, though, Freundlich's colleagues at the observatory found he'd estimated the mass of the stars all wrong, and Einstein had to take it all back. For most people (as Freundlich's young wife perhaps tried to explain) that would have been enough, but Freundlich resolved to try yet again. Why didn't they try measuring how much distant starlight got deflected near the massive planet Jupiter; the one that the great Roemer himself had so persuasively used to resolve a scientific problem in an earlier era? Freundlich proposed it to Einstein. Einstein liked his earnest young helper, and in December he wrote to Freundlich's director at the Prussian Observatory, suggesting that he be allowed to try this.
It would have been less painful just to have sent him back to the Crimean prison. Freundlich's superior was furious that anyone would dare to interfere. He threatened to fire Freundlich, insulted him in front of his colleagues, and made sure that he never, ever was allowed to get his hands on the equipment that could be used to test the prediction near the orbit of Jupiter.
But that didn't matter. Freundlich was hopeful again. A great new eclipse expedition was being planned, for 1919. If conditions allowed international travel, he'd finally be able to prove what he could do.
In November 1918 World War I ended. There were no obstacles to a German national traveling now! It's not recorded what Freundlich felt as the great expedition set out, but we know exactly where he was when the results came through. He read it in the newspaper, back in Berlin.
He hadn't been invited along.
In fact, it was a cool Englishman we've already met who led the team. Arthur Eddington wore small metal-rimmed glasses, was medium height and barely medium weight, and spoke in sentences that tapered off whenever he had to pause for thought, which was fairly often. This of course meant in the good English manner that under his meek exterior there beat a soul of wild determination. By the time Chandra encountered him in the 1930s his personality had hardened, but at this time, in the period of World War I, he had the energy of a young man.
On May 29 of each year the sun is positioned in front of an exceptionally dense group of bright stars—the Hyades cluster. That wouldn't usually help anyone, for without a solar eclipse occurring on that particular date, there would be no chance to see how that rich field of stars gets their light bent around the sun. The glare from the daytime sun would overwhelm that small effect. But in 1919 there was going to be an eclipse, precisely on May 29. As Eddington innocently noted: "Attention was called to this remarkable opportunity by the Astronomer Royal [Frank Dyson] in March 1917; and preparations were begun. . . ."
What Eddington neglected to mention was that he would have been thrown into prison if he didn't go. For as a Quaker, Eddington was a pacifist, and as a pacifist, in the middle of World War I England, one of the rough prison camps in the Midlands was in store. The soldiers guarding the pacifist camps were often recently back from the front—or embarrassed that they themselves hadn't seen service there, which could be worse. Conditions were rough. There was steady abuse and beatings; a number of deaths.
Eddington's colleagues at Cambridge didn't want him to go through this, and tried to arrange for the War Department to defer him, as being important for the nation's scientific future. A letter confirming this was sent to him, from the Home Office, which he only had to sign and send back.
Eddington knew what was in store in the prison camps, but being a pacifist isn't the same as being a coward, as the actions of many Quakers years later in the American civil rights movement showed. Eddington signed the letter, since that was only fair to his friends, but then he also added a postscript, explaining to the Home Office that if he wasn't deferred on grounds of scientific usefulness, he'd still ask to be deferred as a conscientious objector. The Home Office was not impressed, and began proceedings to send him to one of the prisons.
Arthur Eddington
AIP EMILIO SEGRE VISUAL ARCHIVES
This is the point at which the Astronomer Royal, Frank Dyson, called attention to the remarkable eclipse opportunity. If Dyson could get Eddington to arrange the expedition, could Eddington still be deferred, despite that postscript? Dyson's work was relevant to navigation, and so he was close to the admiralty. The admiralty had a word with the Home Office. Eddington was free . . . so long as he led that expedition. They had two years to prepare.
It rained during the expedition, of course, but this is only what you'd expect on an island off the African coast, just north of the Congo, where Eddington ended up. But remember, Freundlich wasn't with Eddington. The rain cleared, and Eddington got two good plates. Most of the developing would have to be done in Britain, however, and no one would know the result for several months.
Afterward, Einstein tried to pretend that he hadn't been bothered by the delay. But by mid-September, still having no word, he wrote to his friend Ehrenfest, asking, with overelaborate casualness, if perhaps
he'd
heard anything about the expedition? Ehrenfest had good connections with the British. But no, he knew nothing. He wasn't even sure if Eddington had made it back.
