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.
In 1922, Friedmann published his seminal paper, “On the Curvature of Space,” in which he showed that not only Einstein’s but also de Sitter’s universes were merely very special cases of a much wider range of possible behaviors for the universe. In fact, the most general solutions were for universes that either contracted or expanded in time. A certain class of models could even expand and grow and then contract again, leading to a never-ending succession of cycles. Friedmann’s results also released Einstein’s cosmological constant from its duty of keeping the universe static. There was nothing to pin the cosmological constant to any particular value, unlike in Einstein’s original model. In the conclusions of his paper, Friedmann wrote dismissively, “The cosmological constant . . . is undetermined . . . since it is an arbitrary constant.” By giving up Einstein’s requirement that the universe be static, Friedmann had shown that Einstein’s cosmological constant was, to all effects, irrelevant. If the universe evolved, there was no need to complicate the theory with an arbitrary fix as Einstein had done.
Here was a paper that came out of nowhere. Friedmann had not taken part in the discussions with Einstein, had not sat through the succession of lectures that Einstein had given to the Prussian Academy of Sciences. He was an outsider who had become enthused by the wave of euphoria that had followed Eddington’s eclipse expedition. A mathematical physicist first and foremost, all Friedmann had done was deploy the same skills and techniques he had used for studying bombs and the weather, and he had uncovered a result that went against Einstein’s gut feeling.
For Einstein, the possibility that the universe was evolving was absurd. When Einstein first read Friedmann’s paper, he refused to accept that his theory would serve up such a possibility. Friedmann must be wrong, and Einstein set about trying to prove it. He carefully worked through Friedmann’s paper and found what he took to be a fundamental mistake. Once that mistake was corrected, Friedmann’s calculation delivered up a static universe just as Einstein had predicted. Einstein rapidly published a note in which he asserted that “the significance” of Friedmann’s work was to prove that the universe’s behavior was constant and immutable.
Friedmann was mortified by Einstein’s note. He was sure he hadn’t made a mistake and that Einstein himself had miscalculated. Friedmann wrote a letter to Einstein showing where Einstein had gone wrong and added at the end: “If you find the calculations presented in my letter correct, please be so kind as to inform the editors of the Zeitschrift für Physik about it.” He sent off his letter to Berlin, hoping Einstein would act swiftly.
Einstein would never receive the letter. His fame had propelled him into an endless succession of seminars and conferences, forcing him to travel around the world, from Holland and Switzerland to Palestine and Japan, and keeping him away from Berlin where Friedmann’s letter sat gathering dust. It was only by chance that Einstein ran into one of Friedmann’s colleagues while passing through the Leiden Observatory and learned about Friedmann’s response. And so it was that, almost six months later, Einstein published a correction to his correction of Friedmann’s paper, rightfully acknowledging Friedmann’s main result and admitting “there are time varying solutions” to the universe. The universe could indeed evolve in his general theory of relativity. But still, all Friedmann had done was show that there were solutions to Einstein’s theory that led to an evolving universe. That was just mathematics, according to Einstein, not reality. His prejudice still led him to believe that the universe had to be static.
Friedmann gained notoriety for having corrected the great man himself. But even though he set some of his doctoral students to extend his ideas even further, and he himself continued publicizing Einstein’s work throughout what had by then become known as the Soviet Union, he returned to his work on meteorology. Friedmann died in 1925, at the age of thirty-seven, from typhoid fever caught while he was on holiday in Crimea, and his mathematical model of an evolving universe was to lie dormant for a number of years.
Georges Lemaître came to math and religion at a young age. He was good with equations, clever at coming up with clean, new solutions to the mathematical conundrums he was set in school. Having attended a Jesuit school in Brussels, Lemaître went on to study mining engineering and was still doing so when he was called up for the war in 1914. While Einstein and Eddington were campaigning for peace, Georges Lemaître was fighting in the trenches when the Germans invaded Belgium. The Germans destroyed the city of Louvain and outraged the international community, leading to the infamous manifesto of the ninety-three German scientists that so poisoned relations between English and German science. Lemaître was an exemplary soldier, becoming a gunner and rising in the ranks to become an artillery officer. Like Alexander Friedmann, he applied his knack for solving intricate problems to ballistics. When the war ended, he was cited for bravery in the Belgian army’s Orders.
Lemaître’s experience of the carnage of battle, the devastating effect of chlorine gas in the trenches, and the brutality of the front affected him profoundly. Following active duty, he not only studied physics and mathematics but also entered the Maison Saint Rombaut in 1920 and by 1923 had been ordained a Jesuit priest. For the rest of his life, Lemaître would pursue his fascination for mathematics alongside his spiritual devotion, rising through the ranks of the Catholic Church to become the president of the Pontifical Academy of Sciences. He was a scientist priest who would turn his sights to solving the equations of the universe.
While at university, Lemaître had already been enticed by Einstein’s general theory of relativity, giving seminars and writing short reviews on the topic at the University of Louvain. In 1923, he spent time in Cambridge, England, boarding at a house for Catholic clergymen and working with Eddington on relativity. Eddington pointed Lemaître to the foundations of relativity, giving him a front-row seat as the search for the true theory of the universe unfolded. E
ddington was impressed by Lemaître, finding him “a very brilliant student, wonderfully quick and clear-sighted, and of great mathematical ability.” When Lemaître moved to Cambridge, Massachusetts, in 1924, the unsolved problem of how to accurately model the universe became his main concern, one he delved into deeply as he worked on his PhD at MIT.
When Lemaître turned to cosmology in 1923, the two world models of Einstein and de Sitter were still at play. They were still the only two mathematical models to have come out of Einstein’s equations, yet they remained just that: two mathematical models without any observations privileging one above the other. Alexander Friedmann’s evolving universe had failed to make any impact, and Einstein’s prejudice against an evolving universe held enough weight to prevent anyone from pursuing it. According to the prevailing view, the universe was still very static. But Eddington had been intrigued by de Sitter’s model, in which stars and galaxies drifted away from the center of the universe. De Sitter had argued there might be a distinct observational signature of his universe. In such a universe, distant objects would look peculiar. Their light would be redshifted.
We can think of light as a collection of waves with different wavelengths corresponding to different energy states. Red light has a longer wavelength and lower energy state than blue light, at the other end of the spectrum. When we look at a star or galaxy, or any bright object, the light it emits is a mixture of these waves, some more energetic than others. What de Sitter found was that the light of any faraway object would be invariably pushed toward the red, appearing to have a longer wavelength and less energy than similar objects nearby. The farther away an object was, the redder it would be. A sure way to test de Sitter’s model would be to look for this phenomenon in the real universe.
The Perfect Theory Page 5
