The Perfect Theory (6 page)

The day after the Burlington House meeting, Thomson's words appeared in the London
Times.
Next to a clutch of headlines celebrating the anniversary of the armistice and praising the “Glorious Dead” was an article with the headline
“Revolution in Science. New Theory of the Universe. Newton's Ideas Overthrown,” describing the results from the eclipse expeditions. News and opinions about Einstein's new theory and Eddington's expedition spread like wildfire through the English-speaking world. By the tenth of November news had reached America, where the
New York Times
published its own eye-catching headlines: “All Lights Askew in the Heavens,” “Einstein's Theory Triumphs,” and the more convoluted “Stars Not Where They Seemed or Were Calculated to Be but Nobody Need Worry.”

Eddington's gamble had paid off. By testing and actually understanding Einstein's new general theory of relativity, he had established himself as the prophet of the new physics. From then on, Eddington would be one of the few pundits to whom everyone would defer when discussing the new relativity, and his opinions would be sought, above anyone else's, as a guide to how Einstein's theory should be interpreted or developed.

And, of course, Eddington's spectacular mission had made Einstein a superstar. His findings would transform Einstein's life and propel his general theory of relativity, at least for a while, to a level of popularity and fame rarely experienced by a scientist. He had dethroned Newton, who had reigned supreme for hundreds of years. Even though his theory was opaque and couched in a mathematical language that very few people understood, it had passed Eddington's test with flying colors. Furthermore, Einstein had stopped being the enemy. The war was over, and while a lingering animosity against the German scientists remained, Einstein was excused. It was now publicly known that he hadn't signed the Manifesto of the Ninety-three, and in fact he wasn't even a German, but a Swiss Jew. As Einstein wrote in an article in the
Times
shortly after Eddington's historic announcement at the RAS,
“In Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be represented as a bête noire, the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English.”

From being an unknown patent clerk, with a tendency toward insolence, admired by a few specialists in his field, Einstein had become a cultural icon, invited to give lectures in America, Japan, and throughout Europe. And his general theory of relativity, which had first seen the light of day in a simple thought experiment in his office in Bern, was now fully formed as a new, completely different way of doing physics. Mathematics had taken a firm foothold in the physics of relativity, resulting in a set of intricate and beautiful equations that were ready to be let loose on the world. It was time for others to start figuring out what they meant.

Chapter 3

E
INSTEIN'S FIELD EQUATIONS
were complicated, a tangle of many unknown functions, yet they could in principle be solved by anyone with the right ability and determination. In the decades that followed Einstein's discovery, an eclectic Soviet mathematician and meteorologist named Alexander Friedmann and Abbé Georges Lemaître, a brilliant, determined Belgian priest, took the equations of general relativity and constructed a radical new view of the universe, a view that Einstein himself refused to accept for a very long time. Through their work, the theory gained a life of its own, beyond Einstein's control.

When Einstein first formulated his field equations in 1915, he had wanted to solve them himself. Finding a solution to his equations that could accurately model the whole universe seemed a good place to start. In 1917 he set about doing so, making some simple assumptions. In Einstein's theory, the distribution of matter and energy told spacetime what to do. To model the universe as a whole, he needed to consider
all
the matter and energy in the universe. The simplest and most logical assumption, and the one Einstein adopted in his first attempt, was that matter and energy are spread evenly throughout the whole of space. In doing so, Einstein was just continuing a line of reasoning that had transformed astronomy in the sixteenth century. Then, Nicolaus Copernicus had made the brave proposal that the Earth wasn't the center of the cosmos and that, in fact, it orbited around the sun. This “Copernican” revolution had succeeded throughout the centuries in making our place in the cosmos ever more insignificant. By the mid-nineteenth century, it became clear that not even the sun was of great import and lay somewhere nondescript in one of the spiral arms of the Milky Way, our galaxy. When Einstein tackled his equations, he was merely extending the idea that anywhere in the universe should look more or less the same to its logical consequences: there should be no preferred place or center that stands out.

The assumption that the universe was full of stuff, evenly spread out, made the field equations much simpler, but it also led to a very strange result: Einstein's equations predicted that such a universe would start to evolve. At some point, all the evenly distributed bits of energy and matter would start moving relative to each other in an organized manner. On the largest scales, nothing would stay still. Eventually everything could even fall in on itself, pulling spacetime along with it and causing the entire universe to collapse out of existence.

In 1916, astronomers' general view of the cosmos was parochial at best. While they had a pretty good map of the Milky Way, there was little, if any, sense of what lay beyond it. No one had a clear indication of what the universe was doing as a whole. All observations seemed to show that stars were moving about a little bit, but not dramatically and definitely not in a concerted, organized manner on a large scale. To Einstein, as to most people, the sky seemed static, and there was no evidence that the universe was collapsing or expanding. Letting his physical intuition and prejudice get the better of him, Einstein proposed a fix to eradicate the evolving universe from his theory. He attached a new constant term to his field equations. This cosmological constant would stabilize the universe by exactly compensating for all the stuff in it. All the ordinary stuff, the energy and matter that Einstein had spread out evenly in the universe, tried to pull spacetime in on itself, and the cosmological constant pushed back, preventing the universe from collapsing. This push and pull kept the universe in a delicate, balanced state: fixed and static, exactly as Einstein believed it should be.

Shying away from the conclusion that the universe was evolving immensely complicated Einstein's own theory. As he himself would later admit,
“The introduction of such a constant implies a considerable renunciation of the logical simplicity of the theory.” By adding the constant, he told a friend he had “committed something in the theory of gravitation that threatens to get me interned in a lunatic asylum.” But it did the job.

In the crescendo that led up to the discovery of relativity, Einstein would often write and discuss his work with Willem de Sitter, a Dutch astronomer at Leiden University, in Holland. Living in a neutral country during the First World War, de Sitter had been instrumental in relaying information about Einstein's theory to England, where Eddington had studied his work in detail; de Sitter was the quiet man who had played a pivotal role in the lead-up to the 1919 eclipse expedition.

A mathematician by training, de Sitter was well equipped to tackle the Einstein field equations. The moment he received a draft of Einstein's paper describing a static universe born out of the field equations mangled with the cosmological constant, de Sitter realized that Einstein's solution was not the only possibility. In fact, he pointed out, it was possible to construct a universe containing nothing but the cosmological constant. He proposed a realistic model of a universe that could contain stars, galaxies, and other matter, but in such small quantities that they would have no effect on spacetime and would be unable to balance out the cosmological constant. As a result, the geometry of de Sitter's universe would be completely determined by Einstein's fix, the cosmological constant.

Both Einstein's and de Sitter's universes were static and unevolving, exactly as Einstein's prejudices had led him to believe. Yet de Sitter's universe had a strange property that de Sitter himself noted in his papers. De Sitter had built his universe so that spacetime was static, just as Einstein had before him. The universe's geometry, such as how curved space was at each point, would remain unchanged over time. But if you now scattered a few stars and galaxies in de Sitter's universe—a reasonable thought exercise given that our own universe seems to be full of such things—they would all start to move in a concerted manner, drifting away from the universe's center. Even though the
geometry
in de Sitter's universe was completely static and stayed the same for all time, objects within his universe wouldn't stay still.

A few weeks after receiving Einstein's paper describing his static universe, de Sitter had already written up his own solution and sent it back to Einstein. While Einstein recognized that de Sitter's model was mathematically valid, he was not impressed and he hated the idea of a universe completely empty of the planets and stars that we can see in the night sky. For Einstein, all that stuff was essential and was what made us have a sense that we were moving or turning. Only relative to the firmament of stars could we say if we were accelerating, slowing down, or spinning. They gave us a reference for applying all the laws of physics. Without all that stuff, Einstein's intuition failed him. He wrote back to Paul Ehrenfest expressing his irritation at this world devoid of matter.
“To admit such possibilities,” he wrote, “seems senseless.” Despite Einstein's grumbling, within just a few years of its creation, general relativity had spawned two static models of the universe that were very different at their core.

 

While Einstein was working on his general theory of relativity, Alexander Friedmann was bombing Austria. As a pilot for the Russian army, Friedmann had volunteered in 1914, serving first in an air reconnaissance unit on the northern front and later on in Lvov. For a short while, it almost seemed that the Russians would prevail against the enemy. On regular night flights over southern Austria, he would join his colleagues in bringing towns that were blockaded by the Russian army into submission. Town by town, the occupying Russians were taking control.

Friedmann was different from the other pilots. While his colleagues dropped their bombs by eye, making rough guesses of where they would land, Friedmann was more careful. He had come up with a formula that would take into account his speed, the bomb's velocity, and its weight and would predict where he had to drop it to hit the desired target. As a result, Friedmann's bombs always hit their marks. He was awarded the Cross of St. George for his bravery in combat.

Having specialized in pure and applied mathematics before 1914, Friedmann had a great talent for calculation. He often threw himself into problems that were too difficult to solve exactly in the era before computers. Friedmann was fearless and would strip his equations down to their bare essentials, simplifying the messiness wherever he could and getting rid of any extra baggage. If he still couldn't solve them, he would draw graphs and pictures that would gently approximate the right results, giving him the answers he wanted. With a voracious appetite for solving problems, Friedmann tackled everything, from weather forecasting to the behavior of cyclones and the flow of fluids to the trajectories of his bombs. He was undaunted by difficulty.

At the beginning of the twentieth century, Russia was changing. The Tsarist regime lurched from crisis to crisis, ill equipped to deal with the growing discontent among a hugely impoverished population and facing the increasing turmoil in an ever more unstable Europe. Friedmann was enthusiastic about playing a part in the social changes around him. As a high school student, he fought alongside his fellow students during the first Russian Revolution of 1905, leading some of the school protests that shook the country. As an undergraduate at Saint Petersburg University he stood out for his brilliance, and during the war he led from the front, flying, bombing, teaching aeronautics, and running an industrial plant for producing navigational instruments.

After the war, Alexander Friedmann settled as a professor in Petrograd (later to become known as Leningrad). The “relativity circus,” as Einstein called it, had arrived in Russia. Intrigued by the weird and wonderful mathematics, Friedmann decided to deploy his formidable mathematical skills in attempting to solve Einstein's equations. Just as Einstein had done before him, Friedmann untangled the complicated knot of equations by assuming that the universe was simple on the largest scales, that matter was distributed evenly, and that the geometry of space could be described solely in terms of one number, its overall curvature. Einstein had argued that this number was fixed once and for all as a result of the delicate balance between his cosmic term, the cosmological constant, and the density of matter, in the form of stars and planets sprinkled through space.

Friedmann ignored Einstein's results and started from scratch. By studying how matter and the cosmological constant affected the geometry of the universe, he came up with a startling fact: that one number, the overall curvature of space, evolved with time. The ordinary stuff in the universe, the stars and galaxies sprinkled all over the place, would cause space to contract and fall in on itself. If the cosmological constant was a positive number, it would push space apart, making it expand. Einstein had balanced these two effects against each other, the pulling and the pushing, so that space stayed still. But Friedmann found that this static solution was only a particular special case. The general solution was that the universe
had to
evolve, contracting or expanding depending on whether matter or the cosmological constant played the dominant role.