Your Calculations Are Correct, but Your Physical Insight Is Abominable - Discovery - The Day We Found the Universe - Marcia Bartusiak

The Day We Found the Universe - Marcia Bartusiak (2009)


Chapter 15. Your Calculations Are Correct, but Your Physical Insight Is Abominable

Fifty-four years after its founding in 1820, the Royal Astronomical Society began to hold its monthly meetings at new headquarters in the west wing of Burlington House, a former private Palladian mansion that houses a number of British learned societies off Piccadilly in the heart of London. At the society's gathering on January 10, 1930, after a report on the current performance of two clocks at the Royal Observatory in Greenwich, the chairman called upon Willem de Sitter, then visiting England, to give an account of his latest research. De Sitter rose and spoke that evening about his own attempts to link the velocity of a galaxy to its distance. Just as Hubble had demonstrated the previous year, de Sitter too graphed a straight line through his points, making use of data obtained by Hubble, Lundmark, and Shapley. But could he explain this orderly recession of the galaxies? “I am not sure that I can,” de Sitter told his audience. The Dutch astronomer was coming to appreciate that his cosmological model was inadequate, not a good approximation of the observed universe at all. His solution depended on the cosmos being empty, but the universe was undoubtedly chock-full of matter.

In the ensuing discussion, Arthur Eddington casually wondered aloud why only two cosmological models—Einstein's and de Sitter's—had so far come out of general relativity to describe the universe. Were other solutions possible, ready for plucking within Einstein's equations? A number of respected mathematicians had been sporadically tinkering with the models, offering up modifications, but none generated wide interest. Was that the end of the road?

Einstein and de Sitter had each started with different simplifying assumptions and so arrived at different solutions. But they did have one thing in common: Both took for granted that the overall structure of space-time was static—fixed and rigid. “I suppose the trouble is that people look [only] for static solutions,” noted Eddington at the meeting. From one perspective, de Sitter's solution could be viewed as nonstatic, if you considered any matter in it as immediately flying off, “but as there isn't any matter in it that does not matter,” argued Eddington.

Much more was at stake in Eddington's question. It was easy to imagine a massive object like a star indenting space-time in a very local and specific location, but could the entire fabric of the cosmos, across the span of the universe, be changing as the eons passed? Could the universe itself be dynamic? It seemed more realistic and plausible to imagine the galaxies traveling through space rather than space-time itself varying, so everyone insisted on a cosmic space that did not move. “From the point of view of cosmologists in the 1920s,” writes science historian Helge Kragh, a dynamic universe “was a concept outside their mental framework, something not to be considered, or, if it was considered, to be resisted.” But, just in case, Eddington already had a research assistant looking into such a formulation.

What Eddington forgot was that this additional cosmological model had already been conceived and presented to him. This solution had been around for years and meshed nicely with Hubble's observations. It wasn't Einstein's universe, and it wasn't de Sitter's. Like Goldilocks and her chairs, this new cosmic model was something in between—and just right.

The novel solution was the brainchild of Eddington's former pupil, Abbé Georges Lemaître, both a physicist and Jesuit priest. A member of the faculty at the Catholic University of Louvain in Belgium, Lemaître soon read the remarks Eddington made at the London meeting, published in the latest issue of the Observatory, and quickly sent off a letter reminding Eddington of a paper he had written three years earlier, which provided the answer Eddington craved. Few had seen the article, titled “A Homogeneous Universe of Constant Mass and Increasing Radius Accounting for the Radial Velocities of Extra-Galactic Nebulae,” because for some unknown reason Lemaître had published it in an obscure Belgian journal, Annales de la Société Scientifique de Bruxelles (Annals of the Brussels Scientific Society) rather than a publication on every astronomer's must-read list. Eddington had either put Lemaître's paper aside, never getting around to reading it, or simply didn't comprehend its importance at the time. In any case, all memory of it had vanished from his mind. After receiving Lemaître's message, he was a bit shamefaced at the lapse. Looking back over the 1927 paper, he at last recognized its significance and with great enthusiasm made up for his blunder. He speedily sent de Sitter a copy of Lemaître's article, writing at the top, “This seems a complete answer to the problem we were discussing.” De Sitter as well grasped the brilliance of Lemaître's approach, calling it “ingenious” and immediately abandoning his own solution. Eddington soon arranged for Lemaître's paper to be translated and reprinted in the March 1931 issue of the Monthly Notices of the Royal Astronomical Society, where it could at last be given a proper showcase.

Originally trained in engineering, Lemaître had switched to mathematics for graduate work and upon receiving his doctorate enrolled in a seminary and was ordained a priest in 1923. Becoming fascinated with the mathematical beauty of general relativity, he went to Cambridge University for postdoctoral studies to broaden his understanding of Einstein's equations under the guidance of the eminent Eddington, who soon noticed Lemaître's talents. With his dark hair combed straight back and a cherubic face framed by round glasses, Lemaître could easily be spotted on campus because of his attire, either a black suit or an ankle-length cassock, set off by a stiff white clerical collar. Others could find him just by pursuing the sound of his full, loud laugh, which was readily aroused. Eddington told Shapley that the young Belgian, then turning thirty, was “exceptionally brilliant… quite remarkable both for his insight into physical significance of problems, and for his manipulation of intractable formulae.”

After a year in England, Lemaître traveled to the United States for further study and soon became aware of—and very interested in—the application of general relativity to cosmological questions. He made sure to attend the 1925 Washington meeting of the American Astronomical Society and was in the audience when Russell read Hubble's paper on the existence of other galaxies. While others in the room were focused on Hubble having ended the “Great Debate,” Lemaître was two jumps ahead. Though new to astronomy, he quickly realized that Hubble's discovery could also be applied to fashioning models of the universe. The newfound galaxies could be used as markers to test the condition of the universe as predicted by general relativity. Later that year, while at MIT to complete an additional PhD, he began modifying de Sitter's cosmological model. Before returning to Belgium, he visited Slipher at the Lowell Observatory, in Arizona, and also journeyed to sunny California, in order to meet Hubble and learn of the latest distance measurements of the spiral nebulae.

What Lemaître did not know during this interlude was that another researcher had already completed a similar modification. The Russian mathematician Aleksandr Friedmann had done this while Lemaître was still preparing for the priesthood. Trained in pure and applied mathematics, Friedmann specialized in the physics of the atmosphere, working at an aerological observatory and applying his expertise at the Russian front during World War I. After the war he returned to St. Petersburg to work at a geophysics observatory. There, among his diverse interests, he began investigating new solutions to Einstein's general theory of relativity, which had not been known to Russian scientists until after the war and the ensuing Russian civil strife.

The rival theories of Einstein and de Sitter were, in a way, complementary rather than competitive. In de Sitter's universe there was no matter to provide a gravitational attraction, but the cosmological repulsion allowed for movement. Einstein's universe, on the other hand, included matter, which provided enough of a gravitational force to oppose the repulsion. With enough matter, all was in perfect balance. Einstein's universe remained motionless. Friedmann blended the best aspects of these universes. He brought the two extremes under one mathematical roof, providing a model that better described the universe as we observe it: containing matter and yet also moving.

What Friedmann did most of all was introduce time into the deliberations. In papers written in 1922 and 1924 Friedmann began to play, in a sense, with Einstein's cosmological model. He wanted to see how curvatures in space-time might change over time—to “demonstrate the possibility,” as he put it. To Friedmann, this was purely a mathematical enterprise, not astronomy at all. His sole goal was to try out possible solutions to Einstein's equations when applied to the entire cosmos. Like Einstein, he too filled his model universe with matter, but this time had it rapidly moving as the eons passed. Moreover, depending on the amount of matter, this movement of space-time could be an expansion, a contraction, or even an oscillation between the two states. “We shall call this universe the periodic world,” he wrote in his report to the Zeitschrift für Physik. Friedmann even computed an age for the universe, a first in the annals of astronomy. He arrived at a figure of ten billion years, not far from today's consensus of nearly fourteen billion years, although Friedmann considered his estimate more a curiosity. He made sure to note the age could also be infinite. But, all in all, his paper was predominantly an exercise in relativistic mathematics rather than cosmology, which is why it received so little attention at the time. Friedmann made no mention of nebulae, radiation, or redshifts, nor did he promote a cosmic expansion over a contraction. The journal in fact had indexed his article under relativity theory, making no reference that it dealt with cosmology, which is why it was easily overlooked.

Einstein was certainly aware of the Russian's paper, though. He promptly dismissed the solution, thinking it had no physical significance whatsoever. In a letter to the Zeitschrift, sent off right before he went on tour in Japan, he wrote that Friedmann's results “appear to me suspicious.” Friedmann, unfortunately, had little chance to either defend or champion his intriguing idea. In 1925, he became ill with typhoid, just a month after conducting a record-breaking balloon ascent (an altitude of 4.6 miles) to make meteorological and medical observations. He soon died at the age of thirty-seven. In a way, Friedmann had offered his solution too early. At this stage, most general relativists weren't terribly interested in astronomy, and astronomers who had more at stake in this quest didn't yet make the connection, believing that such models of the universe were more like mathematical toys, fun to fiddle with but hardly attached to the real world. They didn't take them seriously.

Lemaître was the exception. From the very start of his independent calculations in the mid-1920s, he kept astronomy foremost in his mind, unlike Friedmann. De Sitter's universe could explain the redshifted nebulae but required the universe be nearly empty (which it was not). Einstein's universe could be filled with matter but couldn't account for the fleeing nebulae. Lemaître declared that his aim was to “combine the advantages of both.” Returning to Belgium and a professorship at Louvain, Lemaître continued working on the problem, at last publishing his final result in 1927. Two full years before Hubble provided the definitive observational proof, Lemaître unveiled a cosmological model in which the radius of the universe increases and galaxies surf outward on the wave. The receding galaxies, as Lemaître described it in his paper, “are a cosmical effect of the expansion of the universe.”

From our perspective, it appears that all the galaxies in the universe are rushing away from us—that we are somehow situated at the very center of the cosmic action—but in reality you would observe the same dash outward from any other galaxy in the universe. Lemaître was the first to say directly that the galaxies are fleeing from us because space-time at each and every point throughout the cosmos is continually stretching. The galaxies are not rushing through space but instead are being carried along as space-time inflates without end. The embedded galaxies are simply going along for the ride. That's why the recession occurs in a specific way: A galaxy twice as far from us recedes twice as fast; a galaxy three times farther travels three times faster, and so on. Lemaître even estimated a rate of cosmic expansion (625 kilometers per second per megaparsec, based on the galactic velocity and distance data then available) that was close to the figure of 500 that Hubble would later calculate.

This was a tremendous accomplishment and offered an astounding vision of how the universe operates. But no one noticed—no one at all. Lemaître's paper, like Friedmann's earlier, was completely ignored. It was as if the article had never been published. Lemaître traveled in Europe and the United States afterward but inexplicably did not widely discuss this latest idea with his colleagues, either in person or in letters. Throughout his deliberations, he had been in contact with astronomers who would have been tremendously interested in his new take on the universe, such as Shapley, Slipher, and Hubble. Yet he apparently kept silent. Either he still had doubts about his new cosmic model or his ardor was dampened by encounters he had with the architects of the leading cosmological models. Though outwardly an extrovert, Lemaître was still quite sensitive to the smallest slight. In October 1927, just six months after his paper came out in the Belgian journal, he met with Einstein during the Fifth Solvay Congress in Brussels, a triennial meeting of the world's top physicists, and the two had a brief chat about Lemaître's breakthrough in the city's Leopold Park. It was at this time that Lemaître first heard from Einstein about Friedmann's similar solution. By then Einstein no longer had any objection to the mathematics in either man's model (his initial rejection of Friedmann's work had been based on an error in his own calculations), but he was still repelled by the image of the cosmos that the models of both Friedmann and Lemaître conveyed. “Your calculations are correct, but your physical insight is abominable,” asserted Einstein, who could not (and would not) imagine a universe in motion. Later, while accompanying Einstein on a university lab tour, the Belgian cleric continued to press his case, talking about the latest evidence on the galaxies' speeding away from Earth. But in the end he came away from the meeting with the impression that Einstein was “not current with the astronomical facts.” Nine months later at the 1928 General Assembly of the International Astronomical Union, de Sitter was equally dismissive of the little-known priest. As one commentator noted, de Sitter seemingly had “no time for an unassuming theorist without proper international credentials.”

Georges Lemaître with Albert Einstein in 1933 at the
California Institute of Technology (Courtesy of the Archives,
California Institute of Technology)

The impasse held until Hubble and Humason verified that the galaxies were truly moving outward in a uniform way and Lemaître's model, circulated more prominently in the Monthly Notices in 1931, could at last explain it as the fabric of space-time stretching outward, carrying the galaxies ever farther apart. Now it was no longer Einstein's universe or de Sitter's universe, but the expanding universe, and Lemaître became the toast of the cosmological town for being one of its primary creators. Hubble did not really discover the expanding universe in 1929, as written up in textbooks and commonly presumed these days. That realization did not actually occur until Hubble's data could be viewed with Lemaître's model firmly in mind. Lemaître, far more than Friedmann, had linked his model with ongoing astronomical ob servations. His solution was described as a “brilliant discovery.” Top mathematical theorists began to flock to the new field of relativistic cosmology, both to extend the model and to produce variations on Lemaître's original theme of a universe in bloom. In preparing a review paper for a physics journal in the early 1930s, Princeton theorist Howard P. Robertson, himself a leading expert in this new endeavor, noted, “Imagine my surprise on being able to rustle together more than 150 references on relativistic cosmology! It seems to me that some of our highlights…are going off the deep end.”

Astronomers and theorists alike were thunderstruck by this radically new picture of the universe, which was reported as breathtaking in its grandeur and terrifying in its implications. “The theory of the expanding universe is in some respects so preposterous,” said Eddington, “that we naturally hesitate before committing ourselves to it. It contains elements apparently so incredible that I feel almost an indignation that anyone should believe in it—except myself.” That's because by then he knew that it was rooted in the most powerful idea to be introduced in the world of physics since Isaac Newton—Einstein's general theory of relativity—and test after test was proving it true.

James Jeans, a prolific writer as well as theorist, employed the iconic description of the cosmic expansion used to this day. “On the face of it,” he said, “this looks as though the whole universe were uniformly expanding, like the surface of a balloon while it is being inflated, with a speed that doubles its size every 1,400 million years… If Einstein's relativity cosmology is sound, the nebulae have no alternative—the properties of the space in which they exist compel them to scatter.” Eddington first devised this picture when he introduced his colleagues to Lemaître's solution in a 1930 paper to the Monthly Notices of the Royal Astronomical Society. Paint dots on that balloon and, as it expands, every dot will move farther from every other dot in a regular fashion. Similarly, wrote Eddington, in the expanding universe the galaxies appear to be “embedded in the surface of a balloon which is steadily inflating.” Every galaxy in the cosmos thus sees its neighbors receding into distant space.

Though Hubble left such interpretations of the velocity-distance relationship to others, he did participate in the discussions, hoping to glean what data needed to be gathered to select between competing theories. Astronomers and theorists previously resided in separate domains, but now he got them talking. Grace Hubble recalled the commotion it created in her household, shortly after Lemaître's model got wide circulation: “About every two weeks some of the men from Mount Wilson and Cal Tech came to the house in the evening…astronomers, physicists, mathematicians. They brought a blackboard from Cal Tech and put it up on the living-room wall. In the dining-room were sandwiches, beer, whiskey and sodawater; they strolled in and helped themselves. Sitting around the fire, smoking pipes, they talked over various approaches to problems, questioned, compared and contrasted their points of view. Someone would write equations on the blackboard and talk for a bit, and a discussion would follow.”

There was much to argue about. Those still skeptical of general relativity were offering other explanations for the outward march of the galaxies. British cosmologist E. Arthur Milne, for example, posited that the expansion of space-time was merely an illusion. Space was steady as a rock, but the spiral nebulae upon forming started moving in random directions and with different velocities. Over the eons, the nebulae with the fastest speeds naturally moved farther out, setting up the appearance of a cosmic expansion. It was a model that philosophically pleased Milne, who didn't believe space could possibly curve, bend, or move.

Caltech astronomer Fritz Zwicky proposed that light waves, as they traveled through space, could be interacting with matter, setting up a sort of gravitational drag. The more a light wave traveled, the more it lost energy, shifting its wavelength toward the red end of the spectrum. It resembled the de Sitter effect, only this time matter was doing the work. This could explain why the nebulae farthest out displayed the largest redshifts. Space wasn't expanding at all; the photons of light were simply getting weaker and weaker in their journey through a matter-filled cosmos. Hence, this model came to be known as the “tired photon” theory. There was no natural way to explain how this would happen; it required a new law of physics, but that didn't deter Zwicky at all. He was a legend among astronomers for his chutzpah. He felt his explanation might be pointing to a new physical phenomenon.

Hubble worked for a number of years with Caltech theorist Richard Tolman on how to test these competing models of the universe. They wanted to see which one was most compatible with the data arriving at the telescope. Their effort eventually came to naught. Given the state of astronomy at the time and the instruments available, there were simply too many uncertainties—too much guesswork—to reliably choose one cosmological model over another. Their initial data, though, seemed to better support some alternative theories, like Zwicky's “tired photon” scheme. But Hubble made the call that his data were too uncertain, which kept the expanding universe in play. “We cannot assume that our knowledge of physical principles is yet complete,” he wrote, “nevertheless, we should not replace a known, familiar principle, by an ad hoc explanation unless we are forced to that step by actual observations.” To back away from Einstein, the proof for Hubble had to be overwhelming. On the other hand, the uncertainty of it all likely reinforced his qualms at advocating any particular interpretation.

Lick astronomer C. Donald Shane, in talks with Hubble in the 1930s, actually got the impression that Hubble had “a desire to show that the red shift was not an expansion…because he seemed always to be seeking some other explanation for it.” Perusing Hubble's writings on the idea of an expanding universe, you immediately detect that he was uncomfortable with it. He acceded that theorists were “fully justified” in interpreting the galaxy redshifts as a movement outward; it was the most reasonable explanation that required no new laws of physics. But then he would invariably sneak an “on the other hand” into his script. He deemed a static and infinite universe more “plausible” and “familiar,” like a pair of old shoes he found difficult to throw out. In his Rhodes Memorial Lectures, delivered at Oxford in the autumn of 1936, Hubble reaffirmed his vacillation over the interpretation of the redshifts. Their “significance is still uncertain,” he stated. With the recent introduction of both quantum mechanics and relativity, which demonstrated quite explicitly that scientists' understanding of nature can change abruptly and in surprising ways, perhaps Hubble's caution was understandable. In his lecture Hubble went on to describe the expanding universe as a “dubious world,” though still conceding it was the more likely interpretation of the redshifts. But with alternate explanations still in play, he concluded that astronomers were in “a dilemma [whose] resolution must await improved observations or improved theory or both.”

What seemed to disturb Hubble most were the enormous velocities. The farther he and Humason extended their searches into space, the faster and faster the galaxies were retreating. Near the absolute limit of Humason's spectrograph, he recorded velocities of about 25,000 miles per second, “around the earth in a second, out to the moon in 10 seconds, out to the sun in just over an hour…the notion is rather startling,” noted Hubble.

As late as 1950, responding to a Kansas professor's written inquiry about redshifts, Hubble asserted that they “represent either actual recession (expanding universe) or some hitherto unknown principle of nature. I believe that the choice of these alternatives will be determined with the 200-inch [telescope on California's Palomar Mountain] within a few years.” Maintaining his lawyerly ways, Hubble covered all the bases when making a public statement.

Others, such as Eddington, were confounded by such equivocation. “I just don't understand this eagerness to find some other theory than the expanding universe,” he wrote in a letter to a colleague. “It arose out of difficulties … in Einstein's theory. If you do away with it, you throw back relativity theory into the infantile diseases of 25 years ago. And why the fact that the solution then found has received remarkable confirmation by observation should lead people to seek desperately for ways to avoid it, I cannot imagine.”

While Hubble remained overly cautious, Shapley came to embrace the idea of an expansion lock, stock, and cosmic barrel. It's as if the two astronomers were magnets with the same polarity, always repulsing each other to opposite sides of a question. The ultimate imprimatur, though, was provided when Einstein arrived in Pasadena in 1931 in order to consult with the high priests of cosmology at both Caltech and Mount Wilson.