God In The Equation Read online

  But in 1929 Hubble was nowhere near those limits. By the time the first velocity-distance paper hit the press, Humason was already busy collecting more spectra at machine-gun pace. The new observations amply confirmed the linear trend of Hubble's law. In 1931, Hubble and Humason published a follow-up paper that added fifty new galaxies to the graph of redshift versus distance, including a galaxy cluster in the constellation Leo they estimated to be more than hundred million light-years from the Earth, moving away at twelve thousand miles per second. The signs were all around: the universe is expanding ecstatically, and Einstein was wrong to think he needed Lambda to hold it in place. (An inquisitive reader might well ask why the galaxy, the solar system, the living room, or this book is not caught up in this overarching expansion. The answer again lies in Einstein's equations. Gravity counteracts the stretching of space, so all these objects remain intact pretty much indefinitely. It is only in the regions between galaxies, where matter is scarce and space itself dominates, that the expansion occurs.)

  Although Hubble's empirical results spelled doom for Einstein's Lambda-dominated, immobile universe, they strongly endorsed another key aspect of his theory, the cosmological principle. Where his earlier work affirmed the uniformity of physical law throughout the universe, Hubble's later work demonstrated the uniformity of matter that Einstein's theory demanded. The farther Hubble looked, the more galaxies he saw. Everywhere the pattern was the same. Galaxies might congregate in small groups or large herds, but on the largest scale they were spread evenly through space. As his successors have surveyed greater depths of space, this distribution continues to hold. Likewise, the cosmic expansion appears pervasive; no corner is exempt. Every spot in the universe seems much like every other.

  This uniformity, which Einstein called “the cosmological principle,” has become an enshrined canon of astrophysics. It means that we do not live in a privileged location in the universe. What we see is, overall, the same as what any observer in any other spot would see. Conversely, we can extrapolate from our observations of nearby regions and assume things are generally like that everywhere else as well. In essence, this is a modern elaboration of Descartes's faith that he could trust the evidence of his senses because God would not set out to deceive him. Without the cosmological principle, Einstein could not securely apply the equations of general relativity to the universe as a whole. So while Hubble was blasting apart one detail of Einsteinian cosmology, he was vindicating its fundamental underpinnings. Although the cosmological principle greatly simplified the task of making a mathematical model of the universe, it caused headaches for Einstein's successors as they tried to reach even deeper and ask why the cosmos should be so uniform.

  But Einstein was neither celebrating nor cursing. During the 1920s, while Hubble was busy redrawing the universe, Einstein's attention was elsewhere. He searched madly for a grander version of general relativity that would unify gravity with the seemingly unrelated laws governing electromagnetism, his “unified field theory.” At the same time, he grumpily disputed the growing number of scientists who believed quantum physics proved that the world operates according to the rules of chance, not by absolute cause and effect. He also started to involve himself with the burgeoning Zionist movement.

  The task of integrating Einstein's general relativity with Hubble's zooming galaxies fell to Georges Lemaitre, the Belgian abbe who moved effortlessly between the society of clerics and that of cosmologists. He expressed faith in the simplicity and beauty of the scientific world as passionately as he pursued the possibility of finding salvation in the religious world. By the time he published his first cosmology paper in 1925, Lemaitre had already moved beyond de Sitter's idealized cosmology and started to realize that the natural state of a universe ruled by general relativity is to shrink or to grow. He thought of “solution B” not as an empty void, but as the end point of a universe that has expanded so much that its matter is diluted almost to nothingness. From his visits with Slipher and others, he knew that the spiral nebulae appear to be fleeing from us at enormous speeds. He sought to explain this motion in terms of real physical change, which is why he spoke of the “non-statistical character of de Sitter's world.”

  In 1927, Lemaitre published a paper summarizing his refined cosmological ideas. He set out to build a universe “intermediate between that of Einstein and de Sitter.” Like Einstein's, it contained matter; like de Sitter's, it explained the reddening of the nebulae. But unlike either, the Lemaitre universe was devoted to modeling physical details rather than tending to the philosophical ideals of Lambda or the mathematical abstractions of the de Sitter effect. Lemaitre spoke of galaxies, not theories of inertia or test particles. Drawing on his extensive familiarity with astronomy and thermodynamics, Lemaitre considered the effects of radiation pressure and temperature changes and regarded cosmic expansion as a true, observable consequence of the way the universe arose and evolved. “The receding velocities of the extra-galactic nebulae are a cosmical effect of the expansion of the universe,” he asserted. In his paper, he even speculated about the first cause of the expansion. Perhaps, he wrote, “the expansion has been set up by the radiation itself”—a bright, Genesis-like flash of a beginning, the first glimmer of what would later evolve into the big bang theory.

  Almost as remarkable, Lemaitre estimated the rate of expansion of the universe in his 1927 paper, two years before Hubble published his first results. How Lemaitre did so is unclear. Evidently he performed his own analysis of published and unpublished data on the distances to various galaxies whose redshifts had been measured by Slipher and others. The number that Lemaitre came up with (approximately one hundred miles per second of velocity for every million light-years of distance) was in fact very close to the value Hubble published two years later. Helge Kragh, a Norwegian historian of science who has championed Lemaitre's work, considers this good evidence that Lemaitre deserves credit for uncovering the distance-velocity relationship. “The famous Hubble law is clearly in Lemaitre's paper. It could as well have been named Lemaitre's law,” he argues.

  Unfortunately, both Lemaitre's and Hubble's early calculations of the cosmic expansion rate contained considerable error. Because of a lingering misconception in how to interpret the pulsations of Cepheid variable stars, Hubble severely underestimated the distances to galaxies. As a result, his assessment of the expansion rate—which is just velocity divided by distance—was way too high. Taken at face value, the numbers implied a universe hardly more than a billion years old, which was absurd. From studies of the decay of radioactive elements, scientists knew the Earth was at least two billion years old. Some theoretical interpretations of the dynamics of stellar clusters implied our galaxy was much more ancient still, several trillion years old. Lemaitre wasn't concerned, however, because he considered the present expansion merely a transient state of affairs. In his view, the universe had started out compact and static, resembling the Einstein model. At some point the whole became unstable, perhaps because of radiation pressure, and began to expand. The universe would then keep growing without limit until it thinned out into something resembling the de Sitter model. Thus Lemaitre managed to avoid completely contradicting his illustrious predecessors. He also nicely sidestepped, for the moment, the complicated mystical question of when the universe began.

  Lemaitre had formulated a creative, mathematically persuasive argument in favor of an expanding universe. But he ran smack into the same barrier that Friedmann had hit just a few years earlier: he had a devil of a time getting the world to notice what he had written. It didn't help that Lemaitre published his paper in the Annals of the Brussels Scientific Society, not exactly a must-read in the pews of sci/religion. Seeking to publicize his work, Lemaitre sent a copy of his paper to Arthur Eddington, but to no avail—Eddington later confessed he had either ignored the mailing or never noticed it at all. Lemaitre's cosmic solution was still largely unknown in October of 1927, when he attended the Solvay Conference in Physics in Brussels and so
ught an audience for his theory. When he approached Einstein at the conference, he received little encouragement. “Your calculations are correct, but your physics is abominable,” Einstein responded, still averse to any cosmological model that changed over time. So things stood until 1929, when Hubble let the cat out of the bag. Einstein's disciples quickly discovered that the expanding universe was not the abomination he had believed. Quite the opposite: it realized his beautiful prophecy of a unified cosmic theory.

  The exegesis of Hubble's discovery began at a January 1930 meeting of the Royal Astronomical Society. There, Eddington conferred with de Sitter to ponder the theoretical implications of the swiftly moving galaxies. Neither of the well-known cosmological models seemed compatible with the new evidence. In his book The Expanding Universe, Eddington describes the almost comically uncertain state of cosmology at the time. “Shall we put a little motion into Einstein's world of inert matter, or shall we put a little matter into de Sitter's Premium Mobile?” he wondered. Eddington, a devout Quaker with a spiritual streak a mile wide, sensed it was time to introduce some fresh thinking. He assigned a research assistant to scour the literature looking for any clever insights into the physical principles of an expanding universe. Lemaitre soon heard of Eddington's search for enlightenment and fired off a letter calling attention to his now forgotten paper. This time Eddington read it and, suitably impressed, hastened to draw attention to the Belgian priest's ideas. He quickly wrote up a semipopular summary of Lemaitre's cosmological ideas for the British journal Nature and shepherded a translated version of the 1927 paper into the Monthly Notices of the Royal Astronomical Society in 1931. Even de Sitter hailed Lemaitre's “brilliant discovery, the 'expanding universe.'”

  Lemaitre's model was still far from a straightforward picture of an outward rush of galaxies. In the latest formulation, cosmic expansion still emerged slowly from an earlier equilibrium state, which could have existed almost forever depending on the value of Lambda one plugged into the equations. Lambda also controlled how much time had passed since the beginning of the disequilibrium that sent the universe inflating into its present state. But what really mattered was that Lemaitre had stated, in scientific but quite unequivocal terms, that the universe in its present form originated at a particular moment. Einstein had declared that science could build a theory that would cover all of space, not just the corner of the universe that we can see. Now Lemaitre was claiming all of time as well.

  No scientist before him had the temerity to propose a scientific model that would reach all the way back to the origin of the universe. The idea seemed too spooky; it was a task for the people who kept track of who begat whom in the Bible. Eddington and many of the other brilliant minds grappling with the meaning of Hubble's runaway galaxies still recoiled from the obvious logical leap: if everything is moving apart now, it must have all been much closer together in the past, and at one point, it must have been all crowded together at a single point. Lemaitre made it clear that he meant his theory literally. Eddington would have none of it. Writing in the journal Nature, he stated, “Philosophically the notion of a beginning to the present order of nature is repugnant to me.”

  Lemaitre took these words as a challenge. Just weeks after Eddington's paper appeared, he started to formulate a complete picture of how the universe emerged from an initial state that he called the “primeval atom.” Such a universe would have a definite age: “A general conclusion of the theory of the expanding universe is that the time-scale of evolution is much shorter than was thought previously,” he wrote. Depending on how one adjusted the parameters—in other words, how one read the mind of God—the time of the “rupture of equilibrium” could be as far back as hundred billion years ago. In developing this model, Lemaitre countered Eddington by distinguishing the primeval atom from the universe it evolved into. The rupturing of the primeval atom gave rise to galaxies and to a spray of radiation. The moment when this formative event occurred was “a day without a yesterday,” as Lemaitre put it.

  Given Lemaitre's other life as a practicing Catholic priest, many scientists and historians have naturally assumed his cosmology was intended as a modern retelling of the Book of Genesis. The evidence points toward a distinctly different, more complicated interpretation. True, he did attempt to defend Catholicism from a direct, atheistic attack. “There is no reason to abandon the Bible because we now believe that it took perhaps ten thousand million years to create what we think is the universe,” he told The New York Times in 1933. “There is no conflict.” But rather than expanding the authority of old-time religion, Lamaitre was constricting it and, like Spinoza, rejecting the biblical conception of a willful God. He derided those who attempt to bring classical theology into their research: “Hundreds of professional and amateur scientists actually believe the Bible pretends to teach science. This is a good deal like assuming that there must be authentic religious dogma in the binomial theorem.” Years later he took pains to explain that the primeval atom “leaves the materialist free to deny any transcendental Being. . . For the believer, it removes any attempt to familiarity with God.”

  Lemaitre conceived of the primordial universe as an atom in part because he imagined that such an object would operate according to quantum rules, in which the physical state of a system can never be determined with perfect precision. “I would rather be inclined to think the present state of quantum theory suggests a beginning of the world very different from the present order of nature. . . 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,” he wrote. Thus, the state of the modern world could not be preordained from the start. Such a restriction leaves a place for God, but only a hidden God who depends on quantum physics to maintain his veil. Lemaitre may have believed in salvation, but practically speaking, his faith didn't look much different from Einstein's scientific religion, which Einstein described as “a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection.” With the primeval atom hypothesis, Lemaitre followed Einstein in the search for harmony between quantum physics and general relativity. His effort represented the spirit of Galileo more than the spirit of the church.

  All the same, Eddington objected to Lemaitre's hypothesis, which he found it “too unaesthetically abrupt.” He balked at running the clock all the way backward to an explosive beginning and preferred his own “placid theory,” based on the earlier formulation in which a semistatic universe gently slips into a state of expansion after some indefinite stretch of time. But Lemaitre was committed to his explosive primeval atom and continued to develop the idea. He pictured this atom as a giant radioactive nucleus whose decay set all the present events in motion. Some fragments of the original fireworks would survive. Lemaitre thought these might explain the existence of cosmic rays—energetic particles that shower down onto the Earth from space—which had been discovered in 1925 and were still poorly understood. At a time when the inner workings of the atom were still largely an enigma, and the atom bomb not even yet a wild conjecture, such speculations were not unreasonable. During the 1940s and 1950s, cosmologists abandoned this particular picture but found that nuclear physics is indeed indispensable for understanding conditions in the early universe; today cosmology and particle physics are inseparable partners. Before they got diverted into military matters, famed atomic researchers such as Enrico Fermi and Edward Teller lent a hand in imagining what the first moments of creation might have been like. The broad outlines of Lemaitre's primeval atom hypothesis lodged in the minds of his colleagues and became, with much modification, the modern big bang theory.

  Lemaitre's primeval atom universe consolidated the sci/religion revolution Einstein had started in 1917. Until Hubble announced a progressive pattern of velocities among distant galaxies, many astronomers (and, even more, scientists in general) r
egarded cosmology as little more than a highfalutin brand of mathematical philosophy. Now cosmology was an essential tool for explaining an otherwise baffling observation. There were a few dissenters, most notably the irascible Fritz Zwicky at Mount Wilson. But overall, the astronomical community was galvanized by the new discoveries and rapidly converted to Einstein's faith in a unified theory of the cosmos, something that had seemed so arcane and remote just a decade earlier. Lemaitre didn't say so directly, but his model also pointed to another solution to Olbers's paradox. In the Einstein model, the night sky is dark because the universe is finite in size. In the Lemaitre model, the key point is that the universe is finite in age. If ten billion years has elapsed since the atom burst and galaxies began to form, then by definition we can see only galaxies that are less than ten billion light-years away. Even if there is more universe out there, it is irrelevant to us. Its light simply will not have had time to reach us.

  While Lemaitre remained true to the spirit of Einstein's 1917 manifesto, he inverted many of its details. In addition to being dynamic, it was finite in age but potentially expanded to infinite dimensions. It retained Lambda but used it as a destabilizing rather than stabilizing force. Yet during those heady years from 1927 to 1931, Einstein did not speak up to defend his cosmology. He let his disciples carry out the search for God in cosmic dimensions, while he set off in pursuit of divine truth at the other end of the scale. Now his primary goal was to find a way to bring together gravity, which was described by general relativity, and electromagnetism, which seemed to follow the completely independent rules of quantum physics.