The Perfect Theory (4 page)

Here is where Einstein's insight about the nature of gravity comes into play. Sitting in an accelerating spaceship should feel no different from sitting in a spaceship at rest, feeling the pull of gravity. As Einstein had realized, at its simplest level, acceleration is indistinguishable from gravity. Someone sitting in the spaceship as it rested on the surface of a planet would see exactly the same thing as the passenger in the accelerating craft: a light ray being bent due to gravity. In other words, Einstein realized that gravity deflects light like a lens.

The gravitational pull would have to be quite strong to actually detect any such deflection—a planet might not be enough. Einstein proposed a simple observational test using a much more massive object: to measure the deflection of distant starlight as it grazed past the edges of the sun. The angular positions of distant stars would change by a tiny amount when the sun passed in front of them, about one four-thousandth of a degree, an almost imperceptible amount that was already possible to measure with telescopes at the time. Such an experiment would have to be done during a total eclipse of the sun so that the intense brightness of its rays wouldn't overwhelm any attempts at picking out the stars from the sky.

Although Einstein had found a way to actually test the validity of his new ideas, he still couldn't make any headway in actually completing his new theory. He was still winging it on that insight he had at the patent office, the freely falling man. And although he had no teaching responsibilities and all the time in the world to conjure up his thought experiments and think more deeply about his new theory, he wasn't happy. His family had grown, with another son, Eduard, born just before he arrived in Prague, but his wife was miserable and lonely, far from the world she had grown used to in Bern and then Zurich. So Einstein jumped at the opportunity, in 1912, to move back to Zurich as a full professor at the ETH.

 

During his sojourn in Prague, Einstein had begun to realize that he needed a different type of language for exploring his ideas. While he was reluctant to resort to abstruse mathematics that might obscure the beautiful physical ideas he was trying to piece together, a few weeks after arriving in Zurich, he approached one of his oldest friends, the mathematician Marcel Grossmann, and pleaded,
“You've got to help me or I'll go crazy.” Grossmann was skeptical about the slapdash way physicists went about solving problems, but he endeavored to help his friend.

Einstein was looking at how things moved if they were accelerating or being pulled by gravity. Their paths were curves in space, not the simple, straight geometric lines that one found if one looked at inertial frames. The shape and nature of this motion were more complicated and would require Einstein to go beyond simple geometry. Grossmann gave Einstein a textbook on non-Euclidean, or Riemannian, geometry.

Almost a hundred years before Einstein started grappling with his principle of relativity, in the 1820s, the German mathematician Carl Friedrich Gauss had taken the daring step of breaking free from the geometry of Euclid. Euclid had laid down the rules for lines and shapes on flat space. Euclidean geometry is what we are still taught at school today; it is what tells us that parallel lines never intersect, and that if two straight lines intersect they do so only once. We learn that the sum of the angles in a triangle is 180 degrees, and that squares are built up of four right angles. There is a whole host of rules that we learn and apply. We draw them on flat sheets of paper and chalkboards, and they serve us well.

But what if we were asked to work on curved sheets of paper? What if we tried to draw our geometrical objects on the surface of a smooth basketball? Then our simple rules break down. For example, if we draw two lines that start off by intersecting the equator at right angles, they should be parallel. And indeed they are, but if we follow them, they end up intersecting each other at one of the poles. Hence on a sphere, parallel lines do intersect. We can go further and let these parallel lines start sufficiently far apart at the equator that they intersect at a right angle at the pole. In doing so we have constructed a triangle in which the angles add up to 270 degrees instead of 180 degrees. Again, our usual rules about triangles don't apply.

In fact, every uniquely contoured surface—a sphere, a doughnut, a crumpled piece of paper—has its own geometry with its own rules. Gauss tackled the rules for the geometry of
any
general surface you might come up with. His was a democratic view: all surfaces should be considered equal, and there should be a general set of rules for how to deal with them. Gauss's geometry was powerful and hard. It was further developed in the 1850s by another German mathematician, Bernhard Riemann, into a sophisticated and difficult branch of mathematics, so difficult that even Grossmann, who had shepherded Einstein in that direction, felt that Riemann might have gone too far for his work to be of any use to a physicist. Riemann's geometry was a mess, with many functions flying around, wrapped up in hideously nonlinear construction, but it was powerful. If Einstein could come to grips with it, he might conquer his theory.

The new geometry was fiendishly difficult, but, facing an impasse in generalizing his theory of relativity, Einstein set to work trying to master it. It was a monumental challenge, like learning Sanskrit from scratch and then writing a novel in it.

By early 1913, Einstein had embraced the new geometry and collaborated with Grossmann on two articles describing his sketch, or
Entwurf
in German, of a theory. He told one colleague,
“The gravitation affair has been clarified to my full satisfaction.” Couched in the new mathematics, with Grossmann writing a section explaining the new geometry to the potentially uncomprehending community of physicists, the theory incorporated the predictions that Einstein had proposed in his first forays. Einstein had succeeded in making all the laws of physics look the same in any reference frame, not just an inertial one that wasn't accelerating. He could write electromagnetism and Newton's laws of motion just as he had done in his first, more restricted theory of relativity. In fact, he had succeeded in doing so for almost all of the laws of physics
except
for gravity. The new law of gravity that Einstein and Grossmann proposed was
still
the odd one out, refusing now to yield to a general principle of relativity. Even with the new mathematics brought in to bolster his physical intuition, gravity didn't fit. All the same, Einstein was convinced he had made a major step in the right direction and just needed to tie up some loose ends before his theory would be complete. He was wrong. Einstein's final journey to his theory of spacetime would be less of a dash and more of a stumble.

 

In 1914 Einstein finally settled down. He was invited to Berlin to head the newly created Kaiser Wilhelm Institute of Physics, where he was to be handsomely paid and made a fellow of the august Prussian Academy of Sciences. It was the pinnacle of European academia, where he would be surrounded by brilliant colleagues such as Max Planck and Walther Nernst, and required no teaching. It was the perfect job, but it came with a personal blow. Einstein's family had had enough of all his wandering throughout Europe, and this time they didn't follow him to his new post. His wife, Mileva, remained behind in Zurich with his sons. They would remain apart for five years and divorce in 1919, and Einstein would start a new life and relationship with his younger cousin Elsa Lowenthal, whom he would marry in 1919 and with whom he would remain until her death in 1936.

Einstein arrived in Berlin at the beginning of the Great War and found himself caught up
“in the madhouse,” as he put it, of German nationalism. It affected almost everyone. All around him, colleagues were going to the front or developing new weapons for the battlefield such as the dreaded mustard gas. In September 1914 a nationalist manifesto, “An Appeal to the Cultured World,” came out, supporting the German government. Signed by ninety-three German scientists, authors, artists, and men of culture, it set out to counterattack the misinformation propagated about Germany throughout the world. Or so they thought. The manifesto claimed that Germans were not responsible for the war that had just broken out. It conveniently glossed over the fact that Germany had just invaded Belgium and devastated the city of Louvain, simply stating that “the life or property of [not] even a single Belgian citizen was touched by our soldiers.” It was defiant and divisive, and much of it wasn't true.

Einstein was shocked by what was going on around him. As a pacifist and internationalist, he entered the fray with a countermanifesto, “An Appeal to Europeans.” In it, Einstein and a handful of colleagues distanced themselves from the “Manifesto of the Ninety-three,” firmly chastising their colleagues and entreating the
“educated men of all states” to fight against the destructive war around them. The “Appeal to Europeans” was, on the whole, ignored. To the outside world Einstein was just another of the German scientists who supported the document of the ninety-three, and hence he was the enemy. At least that was the view from England.

 

The Englishman Arthur Eddington was known for cycling long distances. He had devised a number, E, that encapsulated his cycling stamina. E was, put simply, the largest number of days in his life that he had cycled more than E miles. I doubt I have an E number greater than 5 or 6. I haven't biked six miles in a day more than six times in my life—a pathetic number, I know. When Eddington died, he had an E number of 87, which means he had taken eighty-seven individual bike rides that were longer than eighty-seven miles. His unique stamina and perseverance served him well and would push him to achieve quite spectacular results in all walks of life.

Whereas Einstein had struggled to begin his scientific career, Eddington had been fast-tracked into the heart of English academia. Eddington could be arrogant, dismissive, and disconcertingly stubborn when promoting his own ideas, but he was also a tenacious scientist who was rarely put off by fiendishly difficult astronomical observations or new esoteric mathematics. He had been brought up in a devout Quaker family and from early on had excelled at school. At sixteen he went to Manchester to study mathematics and physics and ended up in Cambridge, where he was the top-scoring student of his year, known as the “Senior Wrangler.” On finishing his MA, he was almost immediately made an assistant to the Astronomer Royal and fellow of Trinity College, Cambridge.

Cambridge was high octane, and Eddington was surrounded by brilliant scholars. There was J. J. Thomson, who had discovered the electron, and A. N. Whitehead and Bertrand Russell, who together had written the
Principia Mathematica,
a true bible for logicians. Over time he would be joined by Ernest Rutherford, Ralph Fowler, Paul Dirac, and a veritable who's who of twentieth-century physics. Eddington fit right in. After spending a few years at the Greenwich Observatory in London, he returned to Cambridge. At only thirty-one years of age, he was appointed to the prestigious position of Plumian Professor of Astronomy and Experimental Philosophy at the University of Cambridge. He was also appointed director of the Cambridge Observatory on the outskirts of town, and he settled there with his sister and his mother to become the leader of British astronomy. Eddington would remain there for the rest of his life, taking part in college life with its formal dinners and staid debates, regularly visiting the Royal Astronomical Society to present his results, and every now and then traveling to some far corner of the world to make measurements and observe the skies.

It was on one such trip that Eddington first came across Einstein's new ideas on gravity. Einstein's proposed bending of light had caught the fancy of a few astronomers who had taken it upon themselves to try to measure it. They would set off across the globe, to America, Russia, and Brazil, trying to capture an eclipse at just the right moment and with the sun in the right position so that they could measure the slight deflections of distant stars. While observing an eclipse in Brazil, Eddington met one such astronomer, the American Charles Perrine, and was intrigued by what he was doing. So when he returned to Cambridge, Eddington decided to look into Einstein's new ideas.

When the Great War broke out, Eddington was one of the lone voices opposing the wave of rabid nationalism that was subsuming not only his country but his colleagues. It drove him to despair. In a series of angry pieces in
The Observatory,
the mouthpiece of British astronomers, the case against working with German scientists was made forcefully by a slew of senior astronomers. The Savilian Professor of Astronomy at Oxford, Herbert Turner, put it succinctly:
“We can readmit Germany to international society and lower our standards of international law to her level or we can exclude her and raise it. There is no third way.” Such was the animosity against anything German that the president of the Royal Astronomical Society, who had a German background, was asked to resign. British scientists' relations with their German colleagues were frozen for the duration of the war.

Eddington thought and behaved differently. As a Quaker he was passionately opposed to war. During the mounting anger against the German intelligentsia, he found himself speaking out in dissent.
“Think, not of a symbolic German, but of your former friend Prof. X, for instance,” he appealed to his colleagues. “Call him Hun, pirate, baby-killer, and try to work up a little fury. The attempt breaks down ludicrously.” Eddington not only spoke out for the Germans; he refused to be sent into battle and to fight. As he witnessed some of his friends and colleagues being shipped off to the front to be killed in action, Eddington campaigned against the war. Given an exemption out of “national importance”—he was more important to the nation as an astronomer than as a foot soldier—he made few friends.

 

Alone in Berlin, surrounded by the mayhem of war, Einstein worked on perfecting his final theory. It looked correct, but he needed more math to make it right. So he set off to the University of Göttingen, then the mecca of modern mathematics, to visit the mathematician David Hilbert. Hilbert was a colossus and ruled the world of mathematicians. He had transformed the field, attempting to lay down an unshakable formal foundation from which all of mathematics could be constructed. There would be no more looseness in mathematics. Everything would have to be deduced from a basic set of principles using well-established formal rules. Mathematical truths were
really
truths only if proved according to these rules. This had become known as the “Hilbert Program.”