The Perfect Theory

by Pedro G. Ferreira

  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.

  To Lemaître’s utter dismay, his work was completely ignored by relativity’s leading theorists, including Eddington, his former adviser. When Lemaître met Einstein at a conference later that year, Einstein was unimpressed by Lemaître’s work. Einstein graciously pointed out to Lemaître that his work merely replicated Alexander Friedmann’s findings. While Einstein had conceded that Friedmann’s calculations were correct, he clung to his belief that these strange expanding solutions were a mathematical curiosity, unrepresentative of the real universe, which he knew to be static. He concluded his appraisal of Lemaître’s work with a dismissive zinger: “Although your calculations are correct, your physics is abominable.” And with that, at least for a while, Lemaître’s universe disappeared into the wilderness.

  Edwin Hubble was much more respected for his problem-solving skills than for his charming personality. He had studied at the University of Chicago, where he had become a boxing champion, or so he claimed. Then he spent a few years as a Rhodes Scholar at the University of Oxford, picking up an infuriating faux English accent that would stick with him for the rest of his life. He complemented his pompous demeanor with a tweed suit and pipe, the embodiment of an English country squire. After Oxford, Hubble had fought in the Great War, like Friedmann and Lemaître, but had arrived just as the war ended.

  In the late 1920s, people paid attention to Hubble’s work because he had struck gold a few years before. At the beginning of the twentieth century it was well established that we live in a vast whirlpool of stars that make up our galaxy, the Milky Way. At the time, an unanswered question hung over astronomy: Was the Milky Way the only galaxy, a lonely island in the emptiness of space, or was it one of many galaxies in the cosmos? If you looked out at the night sky, among the stars and planets, there were faint, mysterious smudges of light, the same nebulae that Slipher had looked at and measured. Were these nebulae just developing stars in the Milky Way or distant other galaxies in the making? If the nebulae were indeed other galaxies, that meant that the Milky Way was only one galaxy among many.

  Hubble answered that question b
y measuring the distance of one particular nebula, Andromeda. He had realized that he could use very bright stars known as Cepheids as beacons. By measuring how much dimmer the Cepheids he could see in Andromeda were compared to ones close by, he was able to figure out Andromeda’s distance from Earth. The dimmer it looked, the farther away it had to be. The distance to Andromeda that Hubble came up with was enormous: almost a million light-years, five to ten times more than what was then the estimate of the size of the Milky Way. Andromeda couldn’t be part of the Milky Way—it was too far away. The natural explanation was that Andromeda was simply another galaxy, just like the Milky Way. And if this was true of Andromeda, why shouldn’t it be true of many other nebulae? With that one measurement, in 1925, Hubble made the universe a much bigger place.

  In 1927, Hubble attended an International Astronomical Union meeting in Holland. He heard the fuss that was being made about de Sitter, Eddington, and Weyl’s prediction for the redshift effect in the nebulae and learned how Slipher’s measurements just might be the first hint that the effect was in the data. Lundmark’s attempt to piece together a plot comparing velocities with distance showing a relation between the two had been published in 1924, just before Hubble’s measurement of the distance to Andromeda, and his results had been met with skepticism. The Abbé Lemaître had used Hubble’s distance measurements for his 1927 paper, but it had been published in an obscure Belgian journal, in French, and no one had read it. Hubble saw an opportunity to step in and detect the de Sitter effect himself, superseding all the previous attempts and positioning himself as the discoverer.

  Hubble enlisted a member of the technical staff on Mount Wilson, Milton Humason. Night after night, Hubble had Humason set up the prisms at the telescope on Mount Wilson high in the mountains above Pasadena, California, and measure spectra. It was thankless work. The dome was cold and dark, and the iron floor left Humason’s feet numb and sore. His back would ache from peering awkwardly through the eyepiece trying to find the spectral lines of his selection of nebulae. He knew that he had to do better than Slipher and look at really faint nebulae. The fainter they were, the farther away they would be. But he was battling with an instrument that wasn’t really set up to do these kinds of measurements. It would take him two or three days to get a spectrum, while other telescopes could already do it in a few hours.

  While Humason looked for redshifts, Hubble focused on determining distances. He measured the amount of light each nebula was emitting and compared the results. From this, he could get a rough idea of how far away the objects were, comparing to his measurement of the distance of Andromeda. He then combined his measurements of distance with Slipher’s and Humason’s measurements of redshifts to look for a linear relation between the two, the telltale sign of the de Sitter effect.

  By January of 1929, Hubble and Humason had redshifts for forty-six nebulae. Of these, Hubble had distances for twenty-four, the closer ones for which Slipher had measured the redshifts. He plotted them on a graph: the x axis denoted the distances and the y axis denoted the apparent velocities determined by the observed redshifts. There was still a lot of scatter, but it looked better than Lundmark’s or Lemaître’s attempts, and there was a distinct trend: the farther away the nebulae were, the larger the redshift.

  Hubble submitted for publication, without Humason, a short paper, “A Relation Between Distance and Radial Velocity Among Extragalactic Nebulae,” plotting out his data. Lundmark had been there before him, but although Hubble mentioned Lundmark’s work in passing, he hyped the importance of his own result. In his last paragraph he wrote, “The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect, and hence the numerical data may be introduced into discussions of the general curvature of space.” In a short, modest paper submitted on the same day, Humason published his measurements of redshift and distance to a nebula that was twice as distant as all the ones that Hubble had considered in his paper. It also seemed to lie along the redshift relation that Hubble was finding. There it was, the de Sitter effect.

  Although Lundmark and Lemaître had been there before, Hubble’s discovery of the linear relationship between redshift and distance was the catalyst that brought cosmology together. In the years that followed Hubble’s seminal paper of 1929, the ideas of Einstein, de Sitter, Friedmann, and Lemaître, which had been fermenting during the previous decade or so, would finally be reconciled into one simple picture. And even though the evidence for the recession of galaxies was already sitting in Slipher’s data and Lundmark’s and Lemaître’s tentative analyses, it was Hubble’s and Humason’s papers that convinced astronomers that the de Sitter effect might be real.

  A year after Hubble’s paper was submitted, Eddington wrote up a discussion of the de Sitter effect and Hubble’s observations in The Observatory, the same journal that had published his pacifist pleas during the dark days of the Great War. The Abbé Lemaître, firmly ensconced at the University of Louvain, read Eddington’s article and was nonplussed. There was no mention of his work—his far simpler model of an expanding universe had been forgotten. Lemaître immediately sent Eddington a letter, describing his work from 1927 in which he had shown that there were other solutions to Einstein’s equations in which the universe expanded. At the end of his letter, he added, “I send you a few copies of the paper. Perhaps you may find occasion to send it to de Sitter. I sent him also at the time but probably he didn’t read it.” Eddington was mortified. His “brilliant” and “clear-sighted” student had kept him up-to-date with his forays in relativity, yet Eddington had simply dismissed and forgotten his work. He rapidly set to work promoting Lemaître’s view of the universe and convincing de Sitter to drop his own model and adopt Lemaître’s. Now it was Einstein’s turn to be won over by the expanding universe.

  Einstein’s years in the limelight had distracted him from the tumultuous progress that was being made with his theory by Friedmann and Lemaître and the observations of receding galaxies. But in the summer of 1930 he too had to recognize that something was up. During a visit to Cambridge, where he stayed with Eddington and his sister, he was infected by Eddington’s enthusiasm for Hubble’s results and Lemaître’s universe. On one of his many trips, he stopped in California and met Hubble at Mount Wilson, where they awkwardly discussed the new vision of the universe. Einstein had yet to become fluent in English and Hubble couldn’t speak German, but together they saw how the expanding universe was being adopted by physicists and astronomers alike. And so, on another trip, now to Leiden, Einstein sat down with de Sitter and embraced the new cosmology that was emerging from his theory, proposing his own version of an expanding universe. The two agreed to drop the fix that Einstein had been compelled to add to make his theory work and give him a static universe. Out went the cosmological constant that Einstein had added as an afterthought in 1917.

  After discovering the expanding universe in Einstein’s equations, Lemaître wanted to take Einstein’s general theory of relativity even further. He realized that Einstein’s theory could say something about the beginning of time. Indeed, if you accept that the universe is expanding, the next obvious question is how and why it started to do so. If you follow the universe back in time, you come to a point where the whole of spacetime was squashed into a single point. It is a bizarre state of affairs, unlike anything we see in the natural world around us. Yet that is what Friedmann’s and Lemaître’s models seemed to show: an initial moment when spacetime comes into being.

  So Lemaître proposed a completely radical idea for how the universe could have begun. It involved a true beginning to everything. In his view, the universe had emerged from a single thing: a primeval atom, or “primordial egg,” as he liked to call it. This atom would have spawned the material that fills the universe today. The atom would have decayed according the laws of quantum physics that were just beginning to be understood, just like the radioactive decay of particles that had been observed in the laboratory. The
progeny of the atom would themselves decay into more particles, and so on and so on.

  It was a simple, speculative, almost biblical model, but Lemaître was at pains to keep religion out of his proposal. As a priest, he risked more than anyone being accused of bringing his faith into what was ultimately a purely scientific hypothesis. He published a short paper in Nature with the title “The Beginning of the World From the Point of View of the Quantum Theory.” The title said everything. This wasn’t divine intervention or a theological construct. It was the practical outcome of the cold, impartial laws of physics. Nature made it that way. He summarized his view thus: “If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.”

  In January of 1931, Eddington told the audience of his presidential address at the British Mathematical Association what he thought of Lemaître’s newest idea, announcing, “The notion of a beginning of the present order of Nature is repugnant to me.” Eddington had championed Lemaître’s work on an expanding universe and had convinced Einstein to give up his static universe. Lemaître owed his international celebrity to Eddington. But this newest idea of Lemaître’s was just too much for Eddington to stomach. It pushed Einstein’s theory of spacetime beyond its valid limits, or so Eddington thought, and he let everyone know.

  Just as Einstein had dismissed the expansion of space in Friedmann’s and Lemaître’s work, Eddington refused to accept what the mathematics was telling him. Instead, he proposed another solution. With Hubble’s and Humason’s evidence for the recession of galaxies, Einstein’s static universe had been cast away, but only just. Lemaître, in an attempt to explore all the possible solutions for the universe, had shown that Einstein’s static universe had a catastrophic property that could work to Eddington’s advantage—it was unstable. If you added just a little bit of stuff to Einstein’s static universe, an extra galaxy, star, or even just an atom, it would start contracting to a point. Conversely, if you took any matter away, it would start expanding, ultimately behaving just like the universe that Friedmann and Lemaître had found. It was this instability that Eddington would retrofit to explain the expansion.