The Perfect Theory (7 page)

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. Eddington 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 redshift effect, in which distant galaxies seemed to be more redshifted than closer ones, hinted that there was something not completely understood about de Sitter's model. With Hermann Weyl, one of David Hilbert's disciples from Göttingen, Eddington examined de Sitter's solution more closely and found that if one sprinkled stars or galaxies all over spacetime, a very tight, linear relationship between the redshifts and distances of each star or galaxy emerged. An object that was twice as far from Earth as another would have a redshift that was correspondingly twice as large. This pattern of redshifting became known as the de Sitter effect.

When, in 1924, Lemaître took a closer look at de Sitter's universe and
Eddington and Weyl's findings, he realized the equations in de Sitter's paper were written in an odd way. De Sitter had formulated his theory using a static universe with a strange property: his universe had a center, and for an observer positioned at its center, there was a horizon beyond which nothing could be seen. This was at odds with one of Einstein's basic assumptions about the universe, that all places were equal. When Lemaître reformulated de Sitter's universe so that the horizon went away and all points in space were considered equal, he found that the de Sitter universe behaved in a completely different way. Now, in Lemaître's simpler way of looking at the universe, the curvature of space evolved with time and the geometry evolved as if points in space were hurtling away from each other. It was this evolution that could explain the de Sitter effect. Just like Friedmann a couple of years before, Lemaître had stumbled upon the evolving universe. Lemaître's discovery that redshift was associated with an expanding universe had something that Friedmann's earlier discovery did not: it could be tested with real-world observations.

Lemaître took his analysis a step further and looked for more solutions. To his surprise, he found that the static models that Einstein and de Sitter had been promoting were very special cases, almost aberrations of Einstein's theory of spacetime. While de Sitter's model could be recast as an evolving universe, Einstein's model suffered from an instability that could rapidly kick it off-kilter. If, in Einstein's universe, there was even the smallest degree of imbalance between matter and the cosmological constant, the universe would rapidly start to expand or contract, rolling away from the placid state that Einstein so desired. In fact, as Lemaître found, Einstein's and de Sitter's models were but two in a vast family of models, all of which expanded with time.

 

The de Sitter effect had not gone unnoticed among astronomers. In fact, in 1915, even before de Sitter first proposed his model and its hallmark signature, an American astronomer,
Vesto Slipher, had measured the redshifts of smudges of light, known as nebulae, scattered throughout the sky. He achieved this by measuring the spectra of these nebulae. The individual elements that make up a light-emitting object, be it a light bulb, a hot piece of coal, a star, or a nebula, emit a unique pattern of wavelengths of light. When measured with a spectrometer, these wavelengths appear as a series of lines like a bar code. This bar code is known as an object's spectrum.

Slipher used his equipment at the Lowell Observatory in Flagstaff, Arizona, to measure the spectra of nebulae scattered all over the sky. He then compared his measured spectra with what he would have obtained if he had measured an object made of the same elements sitting on his desk in his office. (The spectra for the elements making up the nebulae were perfectly well known so he didn't actually need to repeat the experiment in his office.) He found that his measurements of the nebulae's spectra were all displaced relative to what he expected. The bar codes were shifted either to the left or to the right.

The shift in the spectra implied that the measured objects were in motion. When a source of light is moving away from an observer, the wavelengths in its spectrum appear to stretch. The net effect is that light will look redder. Conversely, if a source of light is moving toward the observer, its spectrum is shifted to shorter wavelengths and will look bluer. This effect, known as the Doppler effect, is something you have probably experienced in the context of sound. Imagine a speeding ambulance coming down the street toward you—the pitch of its siren changes as it passes by, shifting to a lower pitch as it moves away. This same effect in light enabled Slipher to figure out how things were moving in the universe.

Slipher's results weren't altogether surprising. He expected things to move around, buffeted by the gravitational pull of nearby objects. In fact, one of his first measurements seemed to indicate that one of the brighter nebulae, Andromeda, was moving closer to us: its light was blueshifted. But Slipher was systematic and recorded spectra of a few more nebulae. What he found was puzzling—almost all the nebulae seemed to be drifting away from us. There was a trend.

In 1924, a young Swedish astronomer named Knut Lundmark
took Slipher's data and made a rough guess of how far away from us the different nebulae were. Lundmark still couldn't tell exactly how far away each nebula was and wasn't entirely sure about his results. But lying there in front of him was the telltale trend—the farther away the nebulae were, the quicker they seemed to move.

Now, in 1927, the Abbé Lemaître had rederived the trend that appeared in de Sitter's model and that Slipher seemed to see in the data. Indeed, his calculations predicted that measuring the redshifts
and
distances of faraway galaxies should reveal a linear relation between the two. Plotted on a graph, with distance on the horizontal axis and redshift on the vertical axis, the galaxies should all fall approximately on a straight line. Unaware of Friedmann's work, Lemaître wrote up his results for his doctorate and published them in an obscure Belgian journal. He included his calculations and a short section discussing the observational evidence, working out the slope of the linear relation that Eddington, Weyl, and he himself had found. The observational evidence for expansion was tentative and contained large errors, but it was tantalizing how everything seemed to fit together.