God In The Equation Read online

  To Newton, the concept of an expanding or contracting universe was unthinkable. Cosmic order was a manifest expression of God's flawless creation. Yet the disruptive reality of gravity was evident everywhere. In the solar system, for instance, the planets all pull at one another, distorting the elliptical orbits with messy secondary motions that he feared could make the whole setup unstable. (In recent years, a number of scientists have shown that many solar system motions are indeed chaotic, fundamentally unpredictable over long periods of time. Fortunately Newton wasn't around to hear.) For the planets, Newton speculated that God might step in from time to time and clean up any discordant motions. But it seemed absurd that God would have created an entire unstable universe.

  As far as Newton had moved past Aristotle, he still could not conceive of the universe as a dynamic whole. But Aristotle had the luxury of simply invoking the Divine in his claims about the ether. Newton had to figure out how to squeeze God into his testable equations. The basic problem was that gravity attracts everything to the center of mass, he decided. We are drawn to the Earth's center and hence weigh a little less on a mountaintop than at the seashore. The Earth in turn is drawn to the sun's center, and so on. As long as the universe has a center, it seemed, everything would be drawn toward that point and there could be no rest.

  Newton was hardly the only scientist to reject the possibility of an evolving cosmos. Philosophers had imagined the universe as finite or infinite. In the eighteenth century, the British theologian and amateur astronomer Thomas Wright even imagined the possibility that our galaxy is just one of many island universes floating in the immensity of space. But prior to the second decade of the twentieth century, nobody had ever considered the possibility of an expanding or contracting universe. Such change seemed heretical, for either direction implies a beginning or an end. Although the Book of Genesis tells of a moment of creation, the idea of a literal beginning of time or an ultimate end was philosophically unappealing even to theologians such as Saint Augustine, who imagined God as timeless. An eternal cosmos is inherently more attractive. People may be weak and mortal, but there is some solace in believing the universe is indestructible and eternal.

  In a series of letters with his friend, a young clergyman named Richard Bentley, Newton devised a cunning escape from this cosmic predicament. He abandoned his original picture of the cluster universe and proposed instead an infinite universe in which mass is uniformly distributed throughout. At any point, a mass would be drawn in all directions equally. The universe could not collapse toward its center, because it has no center. Instead it would gather in clumps to form stars, “scattered at great distances from one another through all that infinite space.” The unstoppable nature of gravity created the problem. So Newton appealed to one intangible, the infinite extent of space, to undo the mischief created by another, the infinite reach of the strange force called gravity.

  This argument is the direct predecessor of Einstein's Lambda, which also created an equilibrium that was supposed to counter the destructive pull of gravity. It is a clever way to build a static, eternal universe. Newton considered infinity a natural attribute of God and probably thought, incorrectly, that appealing to infinity would get him out of his bind. Alan Guth at the Massachusetts Institute of Technology, whose theoretical innovations helped reinvigorate the big bang model in the 1980s, sympathizes with Newton's error. Guth added a major new spiritual element into cosmology—an early episode of rapid expansion called “inflation”—to introduce a necessary balance into the big bang. “The failure of Newton's reasoning is an illustration of how careful one has to be in thinking about infinity,” he writes, but then adds sternly, “From the modern viewpoint, an infinite distribution of matter under the influence of Newtonian gravity would unquestionably collapse.” This turnabout was caused not by new discoveries but by new ways of looking at infinity and, by extension, new ways of looking for God.

  In an infinite universe, the whole thing can collapse even without having a central point. Every part would fall toward every other part, from every direction, at an ever-accelerating pace. Ironically, what Newton conjured up was a system that would be the exact opposite of the real universe as we now know it, in which galaxies are fleeing in every direction without a center to the action. An unfortunate soul trapped in Newton's universe instead would see the galaxies rushing inward from all directions. The farther away a galaxy is, the faster it would approach, as the whole headed for a catastrophic crash-up. It would surely be a spectacular, terrifying sight. But it is one we will never witness. Newton's attempt to find a solution in infinity, like Einstein's later reliance on Lambda, was the wrong solution, even though it ended up nudging sci/religion toward a far more powerful, all-encompassing one.

  Ever shrewd, Newton recognized the precarious nature of his solution. As long as the stars were distributed evenly throughout his infinite cosmos, he might imagine that the equal gravitational attractions in all directions would cancel out one another. The motion of even a single star would disrupt the balance, however. Einstein ran into a very similar problem trying to stabilize his model of the universe with Lambda. Newton ultimately evaded his predicament with a weak appeal to the Creator, who had thoughtfully placed the stars far apart, “lest the systems of the fixed Stars should, by their gravity, fall on each other mutually.”

  Newton had no other way out. Abandoning his phenomenally successful theory of gravity would have been absurd. Given his theology, however, abandoning the idea of an eternal, static universe would have been equally mad. What kind of Creator would bring the universe into existence only to fling it apart or dash it to bits? When infinity proved insufficient to rescue this model, Newton called upon the ultimate savior. The terms of the appeal reflected something new: Science was starting to dictate to God. Even though he unshakably regarded God as the ruler of the universe, Newton found himself in the position of specifying the placement of the stars so that his theory of gravitation would not be compromised. He thought he was being true to the old-time religion, yet Newton was sowing the seeds for the sci/religion that would replace it.

  The great and terrible thing about looking to science for spiritual satisfaction is that its ideas are constantly open to criticism and contention. There is no guarded dogma available for protection. Newton had set down his best description of the cosmic laws of gravitation and started to treat the extent of the universe as a mathematical problem. Now it was possible for others to debate his solutions and question his views on cosmic divinity. With this disruptive freedom came a new kind of joy. Science promises that its practitioners will attain a precious, progressive kind of revelation: an ever closer approximation to the true nature of physical reality. This spiritual journey can proceed painfully slowly. Newton's ideas regarding the universal effects of gravity remained largely unchallenged until the early twentieth century. But when they arrived, Einstein's general theory of relativity and the discovery of the expanding universe elevated the scientific spiritualism to a whole new plane.

  One of the most powerful objections to Newton's infinite, eternal cosmos centered not on delicate interpretations of gravitational stability, but on a question so simple that it sounds almost idiotic: Why is the sky dark at night? In an unbounded universe, the sky would be filled with an infinite number of stars and so should be awash with light. Yet every evening, the sun sets and the night is as black as ever. Edmund Halley, champion of the Principia, rushed to craft a plausible explanation. In a pair of papers presented in 1721, he proposed a variety of solutions, primarily arguing that the light from the most distant stars is so feeble that it would “vanish even in the nicest Telescopes, by reason of their extreme minuteness.” Halley considered this paradox important enough that he discussed it at a meeting of the British Royal Society, where the elderly Newton was in the audience. The stakes were high. Here was simple way to judge the magnitude of God's handiwork and evaluate Newton's belief that the glory of the Lord should be reflected in the infinite e
xpanse of the universe.

  Despite Halley's arguments, the question of the dark sky resurfaced from time to time in the following decades. It again came to the fore in the 1820s, when Heinrich Wilhelm Olbers, a German physician turned astronomer, revisited and popularized this astronomical mystery; as a result, it is now usually known as Olbers's paradox. Olbers exposed a gaping flaw in Halley's logic. If every line of sight eventually meets the surface of a star, it doesn't matter whether some of those stars are extremely far away. Every speck of the sky will be filled with starlight, and the whole should appear as bright as a hundred thousand suns. Olbers still believed in Newton's universe—“Is it conceivable that the almighty Creator should have left this infinite space empty?”—so he looked for a loophole and found one. Starlight adds up only if it passes freely through space. “This absolute transparency of space is not only wholly un-proven, but also quite improbable,” he wrote. Dark intervening clouds or interstellar mist must block the light from the most distant stars, he concluded happily, rendering them invisible.

  As physicists came to understand the nature of radiant energy, however, they realized the futility of Olbers's solution. Energy from the most distant stars would not vanish. It would be absorbed and become a part of the obscuring clouds. If the universe were endlessly old, the energy accumulating in those clouds would cause them to grow hotter and hotter until they too glowed white hot, again as brilliant as the surface of the sun. We should be blinded and fried by an onslaught of infinite starlight, yet all is calm. The paradox stands unless one of Newton's infinites is wrong: the universe cannot be both infinitely old and infinitely abundant with stars. Finally, in the twentieth century, astronomers discarded both infinities in response to Einstein's equations and the discovery of the expanding universe. In this way they solved one set of philosophical issues but created others, most notably how it all began and how it all will end.

  The solution to Olbers's paradox emerged slowly from efforts to move beyond Newton's vague description of stars scattered evenly throughout an infinite expanse and to develop a more concrete picture of the scale and organization of the heavens. Even in Newton's day, it was clear that his model was a broad simplification of reality. The shimmering band of the Milky Way slices the heavens in two, blatant evidence of cosmic asymmetry. When Galileo trained his spyglass on the Milky Way, he saw right away that it appears packed full of faint stars, like the lights of a distant port descried from far offshore. This gathering clearly betrayed an organized pattern to the universe, but it took scientists more than three centuries to understand fully what that pattern is.

  Newton's theory of gravity, which explained how a conglomeration of stars could hold together by their mutual attraction, might plausibly have led him to conclude that the Milky Way is just such a starry swarm. In reality, Newton was a big-picture spiritual thinker who didn't get involved in fussy matters of astronomical cartography, much like Einstein after him. The first person to knit observation and logic into a coherent picture of our home galaxy was a man who knew a lot about logical thinking, Immanuel Kant. These days he is better remembered for philosophical innovations like the categorical imperative, but the lines between science and philosophy were not as clearly drawn in the eighteenth century as they are today. Kant started thinking about the structure of the Milky Way after reading (and slightly misunderstanding) a review of a book by Thomas Wright, in which Wright discusses the possibility that we live in an enormous disk of stars. Kant grew enamored of this notion and developed it far beyond Wright's brief and rather speculative description.

  In his Universal Natural History and Theory of the Heavens of 1755, Kant argued that such a structure naturally arises from Newton's laws: “The influence of the fixed stars, as of so many suns. . . are striving to approach each other on account of this mutual attraction. . . sooner or later each implodes in a single clump, unless this cataclysm is prevented, as it is with the spheres of our planetary system, by the action of centrifugal forces.” Extrapolating from the mechanics of the solar system, where the planets all orbit the sun in more or less the same plane, Kant deduced that the centrifugal forces would similarly arrange the spinning mass of stars into an enormous disk—an idea that he generously, even excessively, credited to Wright. When we look perpendicular to the disk, Kant explained, the sky appears dark and we see only occasional, scattered stars. But when we look along the disk, viewing it edge-on from within, we see all of the distant stars more or less lined up. The glow of the Milky Way in the sky is “a densely illuminated belt of innumerable stars aligned like the greatest of great circles.”

  Then Kant stripped back another layer of cosmic mystery by combining his analysis with the astronomers' increasingly complete census of the sky. Telescopic observations had revealed dozens of fuzzy patches of light, known generically as nebulae (Latin for “clouds”), dotting the sky. These nebulae, he proposed, might be other systems like our own, scattered through the tremendous depths of space. “Their shape, which is just what it ought to be according to our theory; the feebleness of their light, which demands an assumption of infinite distance—all these correspond perfectly with the assertion that these elliptical figures are just such world systems and, so to speak, Milky Ways, whose structure we have just unfolded,” he wrote. From Newton's laws Kant understood, in at least a general way, that these systems should exhibit collective circular motions like the orbiting of the planets. Many of the nebulae have a whirlpool-like appearance, which Kant took, quite correctly, as a sign of that motion. His conclusion that the Milky Way is but one among innumerable galaxies allowed him to return to an unbounded, Newtonian cosmology in which “the whole infinite extent of its greatness is everywhere systematic and interrelated.”

  Intrigued by these ideas, the masterful German British astronomer William Herschel set out to determine if Kant's fanciful musings could survive a good thrashing from the scientific doctrine of falsification through observation. Using giant telescopes of his own design, Herschel performed a detailed census of the sky and attained vastly improved views of the enigmatic nebulae. Herschel was a tireless worker who kept careful records as he picked over every degree of the heavens. His efforts paid off spectacularly with the 1781 discovery of Uranus. This triumph, the first addition to the solar system since antiquity, delighted King George III, who soon after made Herschel the royal astronomer. (This was during the American Revolutionary War, when George III could use some good news, and before the full progression of his porphyria, the hereditary blood disease that tainted the king with a lasting reputation as an irascible eccentric.) With this newfound support, Herschel set off to map the “Construction of the Heavens.” He made the first stab at measuring the Milky Way by searching for the faintest stars that must lie at its edge. This overly ambitious task never yielded the answer he sought, but it did confirm Kant's notions about our galaxy's disk-like form.

  During his long hours at the eyepiece of the world's most powerful telescope, a forty-foot-long brute with a forty-eight-inch metal mirror at its heart, Herschel familiarized himself with the different kinds of nebulae and recognized that they vary tremendously. At first he believed all of them were composed of stars. But by 1791 he had changed his mind and realized correctly that the nebulae fall into two broad categories: those that are gatherings of stars so remote that they all blend together, and those that are truly gaseous or, using his terminology, composed of “luminous fluid.” This fluid might “produce a star by its condensation,” he speculated, introducing the idea that celestial bodies might evolve even if the universe as a whole is immortal. Herschel also recognized objects such as the Andromeda nebula for what they truly are, distant galaxies as imposing as our own. Their feeble glow hinted at the tremendous extent of space between them and us. Herschel affirmed the Newtonian belief in “the indefinite extent of the sidereal heavens, which must produce a balance that will effectually secure all the great parts of the whole from approaching to each other,” but he added a tremendous ap
preciation for the complexity of how these parts are arranged.

  Despite his best efforts, Herschel could not quantify the dimensions of the whole. He could only guess, because nobody had yet found a way to measure the most basic unit of the cosmic yardstick, the distance to the nearest stars. Herschel died twenty-six years before the problem was solved by Friedrich Wilhelm Bessel, a German astronomer who had studied under none other than Heinrich Wilhelm Olbers. Bessel took Aristotle's old argument in favor of an immobile Earth and stood it on its head. As the Earth circles the sun, its changing position must make nearby stars appear to shift back and forth against the more distant stellar backdrop. This perspective effect, called “parallax,” is an essential part of our depth perception. Place a vertical finger in front of your face and close first one eye, then the other. The way your finger jumps relative to the background is parallax, and it works exactly the same for stars as for fingers. If you know how much the Earth's location changes over the course of the year and how much the apparent position of a star has changed over the same time, high school trigonometry will give you the star's true distance. Because nobody had succeeded in observing such a parallax, Bessel knew the size of this motion had to be extremely small. He sifted through data on fifty thousand stars, searching for the most promising one to study. Finally he settled on 61 Cygni, a yellow orange double star barely visible to the eye in the constellation Cygnus, which he correctly deduced must lie relatively nearby. His first set of observations in 1815 went nowhere. Two decades later he tried again, armed with a vastly superior measuring telescope known as a heliometer. Over a year and a half Bessel watched 61 Cygni, and this time he clearly saw the star shift back and forth by one-third of an arc second—about the apparent angular size of a quarter seen at a distance often miles. In 1838, Bessel announced that the distance to 61 Cygni is “657,700 mean distances of the earth from the sun,” or 10.3 light-years, very close to the modern value of 11.4 light-years. One light-year is about six trillion miles, so outer space is huge and unfathomably empty. Whereas great thinkers had formerly resorted to counting up crystalline spheres, astronomers now had a ruler with which to measure the heavens.