God In The Equation

by Corey S. Powell

  The true answer surely involves elements of all three explanations. The last one is certainly the one that has had the most powerful repercussions. It also hints at a tragic element in Einstein's personality. His universe extended far beyond anything yet measured by astronomers, so he could easily and correctly have argued that local measurements reveal nothing about the cosmos as a whole. His belief in a uniform distribution of matter, for instance, already contradicted the scientific understanding of the day. Einstein could have argued equally forcefully that the equations of general relativity required a dynamic universe. Had he done so, it would surely be remembered as one of his greatest insights. But the pride that served Einstein well regarding other insights, such as the bending of light, led him astray this time. He was so sure he knew how God would have created the universe that he was blinded by his own faith.

  For all its shortcomings, “On the Cosmological Considerations on the General Theory of Relativity” was a watershed paper that established Einstein as the true prophet of sci/religion. In it, he redrew the universe as utterly as Sigmund Freud had redrawn the map of the mind. He announced that science could explain the entire order of the physical world, much as Charles Darwin attempted to explain our place in the living world. Old-time religion had to give up its claims on the dark, infinite reaches of the cosmos. Einstein's cosmology was a manifesto for a new religion, one built explicitly on the joys of exploring God by exploring reality. “I am of the opinion that all the finer speculations in the realm of science spring from a deep religious feeling, and that feeling they would not be fruitful,” Einstein explained', later. But he made it clear that this religious feeling springs from the human intellect. “He believed in the power of reason to guess the laws according to which God has built the world,” said Max Born, a physicist and close friend.

  The casual ease with which Einstein created Lambda demonstrates just how ready he was to find the Lord in a set of equations. Although he soon had second thoughts about his cosmological constant, it was not because he had abandoned this spiritual path toward truth. In 1919 he distanced himself from Lambda, but only because he found it “gravely detrimental to the formal beauty of the theory.” Years later, when he reportedly denounced Lambda as his “greatest blunder,” it was because Lambda did not work as intended and improved observational evidence seemed to contradict it. Lambda was cast out of heaven, but the cosmology that replaced it was just as speculative and, in its own way, just as mystical.

  Even then Lambda lived on. In the eight decades that followed, countless other researchers have followed Einstein's lead and invoked Lambda to produce a more aesthetically appealing universe or to tinker with models that don't seem to follow the observational data. Einstein's faith and yearning for scientific ecstasy were contagious. His example emboldened many other theorists to treat questions of origin, fate, and even theology as valid territory for science, expanding and intensifying the faith of sci/religion. And his ideas gave tremendous new weight to the studies of the spiral nebulae, those still-ambiguous objects whose true nature would soon bring God's craftsmanship into much sharper view.

  4. THE NEW PRIESTS BICKER IN EUROPE AND AMERICA

  AFTER THE GREAT WAR THAT tore apart Europe, a higher-minded battle broke out in the world of cosmology. Actually it was two battles, inspired by similar spiritual yearnings but carried out in different fields. On the theoretical side, Einstein's finite but static model came under fire, as other physicists began to test the global implications of general relativity. Meanwhile, equally fierce clashes erupted among those who sought mystical truth through the eyepiece, not the equation, as astronomers debated whether our galaxy is unique or just one among a multitude. The mere existence of conflict was a sign of how far the authority of sci/religion had grown. Cosmology could now sustain its own version of Talmudic debate. Now it was possible to use mathematics to argue about the form and fate of the universe; now it was possible to place a yardstick to the heavens and disagree about the resulting measurements. The great book of nature lay open for the whole congregation to see. Everybody was eager to debate its passages, but nobody could agree on how to interpret their meaning. Einstein had started the theoretical action with his 1917 cosmology paper and his self-critical comments about Lambda, which together invited other researchers to try their hand at modeling the universe. Then he promptly went missing in action, as the stresses tearing at him—trying to do science in wartime, dissolving his marriage to Mileva, and completing general relativity—became too much to bear. In 1918 he suffered a mental breakdown and experienced chronic stomach troubles that briefly convinced him he had cancer. During this time Elsa Lowenthal, Einstein's cousin, aided him in his recovery and developed an increasingly intimate bond with him. She became his second wife after he obtained a divorce from Mileva the following year. Even after he resumed his work, Einstein was preoccupied with more tangible and testable aspects of general relativity and largely turned away from cosmology for a few years.

  While Einstein's attentions had drifted elsewhere, some of the more daring apostles of sci/religion revisited the equations of relativity, uncovering the limitations of his cosmological model. These critiques came from unlikely sources: Willem de Sitter, Einstein's friend and collaborator at the University of Leiden; Alexander Friedmann, an obscure Russian physicist with a knack for meteorology; and Georges Lemaitre, a Belgian abbe with a flair for engineering. Almost as implausible was the nature of their criticism. It was not that Einstein had gone too far, but that he had not gone far enough in exploring the ways a small set of equations could describe the destiny of the universe.

  De Sitter, a genial Dutch researcher with a firm grounding in both math and astronomy, followed a painstaking approach to research that alternately complemented and clashed with Einstein's broader, more intuitive way of thinking. As a student at University of Groningen, de Sitter had studied mathematics but found his true calling in the observational world. In 1908 he joined the Leiden observatory; he rose to the post of director and remained there until his death in 1934. At the observatory he excelled at unglamorous, highly detailed studies, such as determining the precise rotational motion of the Earth. With his tidy white goatee and eyes often lost in thought, de Sitter was the picture of the absent-minded professor—and in fact he was notorious for his good-natured forgetfulness. Far more than Einstein, de Sitter had the background and temperament to connect grand, cosmological ideas to the messy reality of the visible stars.

  Ever since the introduction of special relativity in 1905, de Sitter had been fascinated by Einstein's new physics and especially by the possibility of discerning its observable effects. Around 1913 de Sitter studied double stars to determine if the speed of light from these orbiting bodies is truly independent of their motion; when he heard about general relativity in 1916, he energetically began to calculate the astronomical implications of the theory, starting by examining how it applies to the orbits of the planets. De Sitter was already at work on an English-language popularization of general relativity when Einstein visited Leiden late in 1916. The two men met and began a fruitful collaboration, sometimes more like a competition, that drew de Sitter ever deeper into Einstein's all-encompassing worldview.

  Despite his innately practical and empirical outlook, de Sitter found himself inexorably drawn to the miraculous side of general relativity. Suddenly the universe was a plaything. Who could resist? While analyzing Einstein's equations, de Sitter found that they could be reformulated in ways that Einstein had not considered. In a trio of dense papers presented to the Royal Astronomical Society in 1917, de Sitter set out three slightly different interpretations of this discovery. In the final one, he hit on a strange but useful simplification and set the density equal to zero. This “de Sitter universe” maintained key elements of Einstein's universe—it was still uniform and it still had a tacked-on Lambda—but it contained no matter. De Sitter argued this approximation was reasonable because the density of the real universe is quite l
ow. He called the resulting cosmological model “solution B” in deference to Einstein's original “solution A.” The single voice of spiritual authority was sundered in two, like the split between the Sadducees and the Pharisees in ancient Judea.

  To Einstein, “solution B” was a serious blow. First off, de Sitter had shown that there was more than one way to interpret the cosmic implications of general relativity. Even worse, the alternate interpretation undermined some of the philosophical underpinnings of the 1917 cosmology paper. One of the primary reasons Einstein had conjured up a finite universe was to establish a reference frame of matter against which to measure inertia, but “solution B” seemed to imply that inertia could exist in a completely empty universe. Einstein had assumed that Lambda would guarantee there could be no solutions for the case in which the cosmic density is zero. He was sorely disappointed to find his equations had let him down. In a letter to de Sitter, Einstein complained that the empty universe “does not correspond to any physical possibility.” But now he clearly knew he had not attained the one and only description of reality, what he called “the true state of affairs.” The prophecy of 1917 remained to be fulfilled.

  But “solution B” was significant in another way: it seemed to produce an observable effect that could be detected and verified. In the de Sitter universe, the curvature of space-time seemed to be continuously decreasing, like the inside of an inflating balloon whose surface is continually expanding and hence growing flatter at any one spot. Because of this effect, de Sitter discovered, a clock at a great distance would appear to run more slowly than a nearby one. Consequently, a beam of light passing between the two objects would stretch in time and grow redder, with the magnitude of the effect proportional to distance. “The lines in the spectra of very distant stars or nebulae must therefore be systematically displaced towards the red, giving rise to a spurious positive radial velocity,” de Sitter wrote. As de Sitter knew, astronomers at the time were just starting to discover that many nebulae did indeed have shifts in their spectra that seemed to indicate rapid movement away from us.

  This sounds like a description of an expanding universe, but not quite. Note that de Sitter described the velocity as “spurious.” Following the lead of the great Einstein, he still regarded the universe as static and the reddening of light, then known as the “de Sitter effect,” as an illusion. In spite of his adherence to the gospel of cosmic stasis, de Sitter had taken a decisive, if unintentional, step toward setting the universe in motion. After all, space did seem to expand in the de Sitter universe. The problem was that there was no place where an observer could stand and measure the changes; it was very hard to understand what “expansion” meant in the complete absence of matter. Arthur Eddington, the British champion of relativity and a master of clarifying complicated scientific concepts, attempted to cut through the confusion by means of a simple thought experiment. He placed two particles—too small to disrupt the overall assumption of zero density—in the de Sitter universe and allowed them to move in accordance with the equations. The two particles accelerated away from each other, as if the unraveling of space were a true, physical expansion. “A number of particles initially at rest will tend to scatter,” Eddington declared. Other researchers disputed his interpretation. De Sitter, who had intended his cosmology to be static, was unsure what to think of this turn of events.

  Few scientists could make heads or tails of de Sitter's ideas. Einstein, who agreed with Descartes that space existed only in relation to objects, did not think much of a cosmological model that allowed space but not matter. He also objected that the de Sitter effect led to an absurd result. Somebody sitting in the de Sitter universe would see time growing progressively slower the farther he looked. At some great distance, the slowing would become so extreme that time would appear to stand still, creating a kind of edge of reality where the world appeared trapped in a single moment. This was most certainly not the kind of unbounded universe Einstein's God would have created. Astronomers, meanwhile, were mostly baffled by the high-minded debate over real versus imaginary motions in this strange something called “solution B.”

  In many ways, de Sitter ended up raising more questions than he answered. But by applying his stubborn curiosity to the equations of general relativity, he helped excise some of the dreamy quality from Einstein's cosmological model. If there was a second solution to the equations of general relativity, Einstein realized glumly, there might be many. Perhaps the one that described the “true state of affairs” could be found among the others. He was never entirely comfortable with the arbitrary nature of Lambda but invoked it to keep the universe eternally at rest. Now de Sitter showed that Lambda didn't even do its assigned task. The universe could appear dynamic—or at least quasi-dynamic in some funny way—even with the cosmological constant. In his final paper, de Sitter explored the possibility of jettisoning Lambda, which he disdained because he felt it “detracts from the symmetry and elegance of Einstein's original theory.” By exposing possible observable effects of a cosmology built around general relativity, de Sitter reminded Einstein that he, like Copernicus before him, needed hard evidence to support his revolutionary view of the universe. Good sermons alone don't get at God's secrets; scientific prophecy proves its power only when witnesses can testify to its truth.

  Coaxed along by these thoughts, Einstein began the slow process of disowning Lambda. More than a decade later, he joined with de Sitter to deal with this problem and try once again to fashion a single, conceptually beautiful model of the universe. By then astronomers had reported shocking news that forced Einstein to abandon completely his ideal of a static universe. Until then, however, neither he nor de Sitter was prepared to confront the full physical implications of a universe ruled by general relativity. That monumental task fell to Alexander Friedmann, a largely forgotten visionary who was the leading disciple of sci/religion—the first person to break with thousands of years of tradition and set the universe in motion.

  Friedmann's brief life was full of dramatic, improbable twists. He was born in St. Petersburg, Russia, to parents whose bent was artistic, not scientific. His mother was a pianist, his father a ballet dancer and composer. When Friedmann was nine years old, his parents divorced and he ended up in the custody of his father; he did not see his mother again for twenty-four years. Notwithstanding the domestic turmoil, Alexander shot to the top of his class at the St. Petersburg Gymnasium, where he was promptly caught up in another kind of unrest. The “Bloody Sunday” massacre of 1905 outside the czar's palace triggered widespread protests and student uprisings, which Friedmann joined. By the end of the year, Czar Nicholas II created a reformist constitutional monarchy that lasted until the revolutions of 1917 that brought the Communists to power. While Russia lapsed into relative calm, Friedmann studied math and physics at the University of St. Petersburg. There he worked under Paul Ehrenfest, the Austrian-born physicist and animated free thinker who later struck up a close friendship with Einstein. Ehrenfest introduced the young Friedmann to relativity, quantum theory, and other new ideas sweeping physics. While continuing his graduate education, Friedmann also lectured at the university's Mining Institute, which contributed to his unusual brew of expertise in math, physics, aeronautics, and meteorology.

  Friedmann's academic progress again halted abruptly, this time because of World War I. He enlisted as an aviator, lectured on aeronautics to Russia's fledgling air force, and buried himself in math theory between bombing raids. “Sometimes I get sick of the war. . . and yet the spirit is still strong, and if I get used to studying here, then probably, by the end of the war, I will have finished my dissertation,” he wrote to his mathematician friend Vladimir Steklov. Although his letters frequently display a similar effort to keep his spirits high during war, Friedmann emerged from the conflict depressed and in poor health. He returned to St. Petersburg University—now Petrograd University, reflecting the revolution that engulfed Russia in civil war and ended with the triumph of the Bolsheviks unde
r V. I. Lenin. (For a brief time, Russia had a leader who was also interested in the latest science: Lenin's library in the Kremlin included two dozen books on relativity theory.) Amazingly, Friedmann persevered through the changes and managed to finish his master's and secure a number of academic appointments in Petrograd. One of his students at Petrograd University was George Gamow, who later developed the idea of the expanding universe into a detailed model of the parable of creation.

  After the end of World War I, word of Einstein's new theory finally filtered into Soviet Russia and into the underfunded, often unheated halls of Petrograd University. Friedmann immediately immersed himself in a detailed study of general relativity. Given the endlessly difficult circumstances of his life, no wonder Friedmann was so drawn to cosmology. Imagine his mathematical mind soaring above the warfare and petty bureaucracies that had made his life miserable, as he wrote in 1922, “The surest and deepest way to study the geometry of the world and the structure of our universe with the help of Einstein theory consists in the application of this theory to the whole world and in the use of astronomical research.” Archival photographs from those years show Friedmann as a thin, bespectacled man, his receding hairline weakly offset by a limp mustache. Behind his watery eyes and introspective expression, however, a grand panoply of possibilities was unfolding.