God In The Equation Page 2
At the same time, old-time religion is losing its grip on its home the realm of ethics and morals. Traditional religious belief is growing increasingly marginal in an age when people look to thing from angels to Oprah to psychotherapists for guidance. Among many people who maintain the appearance of observance democracy and capitalism have eaten away at religion's uniform moral authority. Dietary rules fade away; patriarchal practices get watered down or discarded. These days, presidents go to professional ethicists for guidance on questions of biotechnology issues, issues that themselves seem to infringe on God's old creative domain. Creationists don't hate evolution per se. They hate the implied loss of authority of Christian values. The fact that creationists use scientific evidence to support their cause shows how far the balance has shifted. Try to imagine scientists feeling compelled to bolster their position by insisting that schools cite scriptural passages supporting the idea that the universe is governed by empirically knowable laws.
In fact, religion has been in retreat for centuries, both and before after the line of demarcation. Theologians repeatedly set out to define and defend their faith by clarifying the distinction between the earthly and the divine, but in the process they left more and more room for the empirical study of the world. Saint Augustine argued that using the human senses to study nature is a valid to explore the glory of God. The twelfth-century Jewish philosopher Moses Maimonides sought a spiritual system that was compatible with Aristotle's model of the universe, “as a means of wing some of the doubts concerning anything taught in scripture.” In the thirteenth century, Saint Thomas Aquinas folded Aristotelian physics into Christian belief, showing that the two could peacefully coexist. Baruch Spinoza, the seventeenth-century theologian, introduced the radical concept of a God that does not interfere with the operation of the world but is fully defined by His of nature.
Sci/religion has advanced to fill the void by offering its own forms of ecstasy. The most intense feelings arise when sci/religion reaches highest and farthest, striving to grasp the most remote workings of the cosmos. Aristotle proposed a fifth element to explain what keeps the sun, moon, and planets circling the Earth on their ceaseless circuit. He assumed that the heavenly element was something perfect and divine, hence removed from our flawed world. Twenty centuries later, Isaac Newton made a huge advance toward bringing the heavens within reach. He explained that all matter has an intrinsic property, inertia, which causes a moving object to keep moving. He recognized gravity as the universal attraction that controls everything from falling apples to the orbiting moon. He tethered us to heaven but still imagined that God was hidden—not in rotating spheres but in the fundamental, unmoving structure of space.
Newton's theory of gravity provided a mathematical description of how the attraction works but did not explain what gravity is. The gravitational field seemed almost magical, spreading its influence through empty vacuum. Rival scientists, and Newton himself, expressed philosophical reservations about this process of “action at a distance.” More troubling, gravity seemed to be too powerful. If everything pulls on everything else, Newton wondered, what holds the universe up? He tentatively solved the problem by assuming the universe is infinite. This was both a theological and a scientific fix. An unbounded universe could not collapse toward some central point under the spell of gravity, he believed, and the endless expanse of the stars reflected the infinite glory of his God.
Einstein took these ideas a crucial step further. In his general theory of relativity he made space an active partner with matter, giving the intangible equal status with the tangible. Matter curves space-time, and that curvature is what we feel as gravity. One kind of spookiness went away, only to be replaced by another. When he expanded these ideas to cosmic scale, Einstein became convinced that the inertia of every object is linked to the curvature of the entire universe. That linkage made sense only if the universe were finite, otherwise there would be no specific spatial background against which to measure the progress of an apple from its branch to its resting place on the ground. To explain gravity and inertia, Einstein erased Newton's infinity. But all of a sudden, gravity was out of balance. The intangible wanted to take control, making the universe collapse in on itself. This is why Einstein invented Lambda: to tame the spiritual forces and keep the sky from falling.
In Einstein's finite universe, there is no escaping the authority of science. There is no heaven where miracles can occur, no infinite space to harbor Newton's God. The old-time religions proposed that prayer and ritual observance create a link between the individual and a willful deity. Einstein presented the possibility of a cosmic connection based on an intellectual comprehension of the rules of reality. To him, these rules and God were one and the same. His gospel of sci/religion led him to the same point Spinoza had made his religious last stand. “I believe in Spinoza's God who reveals himself in the harmony of all that exists, but not in a God who concerns himself with the fate and actions of human beings,” Einstein said. Lambda represented his search for a harmonious God in his equations.
Einstein eventually renounced Lambda, but never doubted his faith in a mathematically beautiful, comprehensible universe. Lambda, meanwhile, has resurfaced again and again because of its spiritual power. It bestows exquisite balance onto today's cosmological models and so demonstrates the mystical power of sci/religion: its ability to explain the entire universe in a tidy set of mathematical concepts. Most of those touched by Lambda have never even heard of it. The total number of people who understand all the details of modern cosmology is quite small, after all. But the number of people who accept and follow Einstein's gospel is huge. The same empirical methods that conquered the most remote galaxies have also led to electric toasters, computers, and nylon panty hose. Einstein's cosmic religious sense, a feeling of “the nobility and marvelous order which are revealed in nature and in the world of thought,” has triumphed in every aspect of our lives, from the mundane to the sublime. Sci/religion is no longer only about how the heavens go. It is also about our relationship to the heavens.
Lambda expresses the Word from the great white domes on Mauna Kea. It encapsulates cosmologists' wildly optimistic belief that the universe is knowable and that we are right now on the verge of an all-encompassing understanding. Lambda's ethereal nature is integral to its inspirational appeal. The story of Lambda is the story of the secret faith that keeps sci/religion, and the human spirit, pushing ever onward.
2. HOW GOD GOT A JOB IN PHYSICS
THE GREAT PROPHET of sci/religion has an intimidating, otherworldly image. Albert Einstein's name conjures up unkempt shocks of gravity-defying grey hair framing a thought-lined brow; time travel, black holes, and other science fiction-tinged exotica; perhaps the cryptic equation E=mc2 and its explosive realization in the atomic bomb. Look more closely, however, and Einstein transforms back into a normal man driven by familiar impulses. He wanted to know where our world comes from and why it works the way it does. He wanted to understand how the remote stillness of the heavens relates to the erratic, ever-changing events here on the Earth. Above all, he wanted to know if the answers to these questions would bring him closer to God.
Einstein was far from the first to head down this path. Greek philosophers had wrestled with many of the same questions two dozen centuries earlier. They looked past the popular mythologies of the day, which attributed the inexplicable vicissitudes of weather, crops, and disease to a cantankerous community of gods. Led by the libidinous Zeus and his volatile wife, Hera—who happened to be his sister as well—these immortals ruled the world in accord with their ever-shifting moods. Mount Olympus was geographically close to the mortal realm, and the gods who lived there were likewise nearly human save for their extraordinary powers. These characters made for entertaining storytelling, but their behavior merely reflected the chaos of everyday life, it did not explain it.
More meaningful answers seemed to lie elsewhere. Like Einstein, the Greeks sought truth in the purity of mathematics and in the
heavens, where an entirely different kind of order prevailed. When the sun set, the sky glowed with innumerable pinpoints of light. It was impossible to ignore the majestic enigma of this other realm in an age when fire was the lone controllable source of nighttime illumination. The array of stars remained fixed within the vault of the heavens, unchanging from generation to generation, while the whole bowl-like firmament completed one perfect circuit each year and one somersault each day. The sun and moon wheeled their way across the star-flecked background. And a few rule breakers—the planets, literally “wanderers”—strayed across the skies in maddeningly complicated ways. Many ancient cultures sought the hidden patterns in these motions, but the Greek natural philosophers developed the uniquely creative solutions that still inspire and influence modern cosmology.
Eudoxus of Cnidos, the father of Greek mathematical astronomy, made one of the first systematic attempts to account for the irregular regularity of the heavens. His treatise, On Velocities, is long lost, but its ideas survive through his influential followers. Nearly four centuries before Jesus' birth, Eudoxus proposed that the universe consists of a series of nested, transparent shells, which carry the sun, moon, and planets as they rotate. The fixed stars sit on the outermost sphere. The Earth sat at the center of it all, but the spherical shells defined the heavens as distinct from the Earth's murky, tumultuous elements. This spherical cosmology existed to perform what historians of science call “saving the appearances”—that is, simulating the appearance of the natural world rather than explaining how it operates. But in this early era, Eudoxus already adhered to the principles of unity and simplicity that would eventually guide sci/religion to dominance.
In its basic elements, Eudoxus' model of the universe took inspiration both from Pythagoras, who had declared the sphere the perfect shape, and from Plato, who had come to embrace the idea that each component of the heavens resides on its own concentric sphere. Eudoxus reputedly bristled at the highly abstract nature of Plato's teachings—he ended up founding a rival school based on a more rigorously observational approach—but adapted these ideas to his own ends. He added additional spheres and coupled their motions, so that the whole system could explain in detail how the various bodies roamed among the stars. The resulting system was both aesthetically appealing and amenable to geometric analysis.
This was not intended as a realistic, physical model of the universe. Most likely Eudoxus regarded the spheres as useful concepts rather than real objects. It was not particularly brilliant as a predictive model, either: it required a total of twenty-seven independently moving shells, and still its inaccuracies would have been immediately evident to the naked-eye observers of the day. What Eudoxus crafted was a descriptive system that accounted for the general nature of the solar, lunar, and planetary motions. As such, it marked a small but incredibly important step toward the creation of a kind of cosmic religion, one that aspired to truth by blending philosophy and spiritualism with mathematics and observation. In Eudoxus, ancient beliefs mingle with a recognizably modern hunger for scientific certainty. “Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size, and its substance,” he swore.
Judged purely on how long it survived, Eudoxus' system of spheres would have to be considered the most successful cosmology in the history of thought. It was not fully overthrown until Johannes Kepler discovered that planets move in elliptical paths, not circles, and Galileo Galilei established observational evidence that those paths go around the sun, not around the Earth. Both of those epiphanies occurred during the first decade of the seventeenth century, roughly two thousand years after Eudoxus. Our modern big bang interpretation of cosmic history is an infant by comparison, scarcely fifty years old. Although the spheres of Eudoxus emerged from a pagan, mathematical tradition, Saint Thomas Aquinas absorbed them into church doctrine. By the time scientific knowledge finally destroyed that Earth-centered cosmology, it was so entrenched in Christian thought that the transition triggered an international religious crisis. The loss of those spheres destroyed the notion of the heavens as a physical place whose divinity increased with its distance from this flawed world, and it cast God out of His home in the firmament. It took Einstein and his second cosmological revolution to instill a new spiritual feeling by proposing that a single, monotonic line of existence runs from the Earth to the farthest star.
During their long, wildly successful tenure, the spheres of Eudoxus underwent numerous refinements, translations, and adaptations. His disciple Callippus of Cyzicus touched up some of the observational failings of the model by adding six additional spheres. But by far the most famous elaboration was carried out by one of the greatest of the Greek philosophers, Aristotle. As a student, Aristotle had studied at Plato's academy while Eudoxus was running it. Eudoxus' ideas clearly landed on fertile ground, but Aristotle added many innovations of his own. One of the hallmarks of Aristotle's philosophy was emphasis on the importance of empirical data—when it suited him, at least. Observation often seemed to serve as a justification more than as inspiration for his ideas. Bertrand Russell once quipped, “Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.” Still, Aristotle paid much more attention to the world of the senses than did Plato or Eudoxus, which led him to devise an even more complex model of the cosmos. To reconcile the general motions of the planets with a mechanically plausible, dynamic cosmos ruled by circular motion, Aristotle described a set of fifty-five crystalline spheres, rather more like a set of uncoordinated wedding gifts than the sort of economical structures one might associate with celestial harmony. In his great cosmological work On the Heavens (De Caelo), Aristotle developed a theory that would not only describe the motions in this crowded sky, but also explain them. He postulated that the heavenly realm is composed of a fifth element, called “ether.” Unlike the four elements of the human world—earth, fire, water, and air—ether naturally follows circular motion. Thus there is no problem of inertia for the cosmic spheres because the heavens, once set in motion, never run down. Ether was the essential intangible element that allowed the spheres to maintain their form and the motions. It was fundamentally unlike later scientific intangibles because it was fully cut off from the human world. Nothing like ether existed in our realm; ether functioned only on the contingency of the Creator who gave it an initial impetus. Aristotle envisioned the outermost shell of heaven, the one containing the “fixed” stars, as the edge of everything. The whole must be finite, he argued, because it clearly moved in a circle about the Earth, and an infinite sphere could not complete its rotation in a finite amount of time: “It is impossible that the infinite should move at all.” He considered the whole system eternal, in pointed contrast with earthly affairs marked by an endless series of cycles of renewal and decay. “Whatever is divine, whatever is primary and supreme, is necessarily unchangeable,” he wrote. By transforming Eudoxus' spheres into physical entities, Aristotle made an explicit connection between mathematics and God. The perfect simplicity of spherical motion both expresses and defines the divinity of the celestial world. Decoding that motion therefore becomes a stairway to heaven. As Aristotle wrote in his Metaphysica, “The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.” This exaltation of order and symmetry lives on in modern science, most visibly in the mystical extremes of particle physics and cosmology.
The Aristotelian universe, with its clear distinction between earthly and heavenly elements, established an extremely influential picture of a hierarchical universe. As he declared in On the Heavens, “We may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.” In this scheme, the Earth is at rest; the planets can move
, but in a flawed multiplicity of motions; only the “first heaven” attains the full perfection of the circle. The Catholic Church, under the philosophical guidance of Aquinas in the thirteenth century, fused this cosmological model with Christian theology, so that the celestial spheres became the literal abode of the angels. This vivid picture is still a staple of popular culture, but it has cost the church dearly—once when Copernicus and Galileo argued powerfully that the Earth is not at the center of the universe, and again when Einstein developed the first comprehensive cosmological model rooted in physics. From that point on, Aristotle's “superior glory of nature” belonged to science, not to religion.
The mechanical aspects of Aristotle's dynamic, bounded universe also proved remarkably durable. Ether calls to mind its modern counterpart, the dark energy or Lambda often invoked by cosmologists. Like ether, Lambda is an unfamiliar element whose invisible influence supposedly controls the observed heavenly motions. Einstein wanted to design a universe that was static and unchanging, an echo of the Aristotelian dictum that “that which is divine must be eternal.” But Lambda exists within the sci/religious doctrine of falsification through observation—and indeed, observation nearly killed off Lambda a decade after Einstein invoked it. Aristotle, on the other hand, was largely free to go wherever his intuition carried him. The commonsense appeal of Aristotle's cosmology also explains its longevity. His description of the spherical shape of the universe still has popular resonance because it seems so natural. Gaze up at the night sky and it looks like a dome of stars. No wonder you can still walk into a science hobbyists' store and buy a model of the sky showing the stars embedded on a spinning transparent globe. Memories of the Aristotelian spheres repeatedly surfaced in science as well. Einstein's first attempt to derive a cosmological model built around his general theory of relativity yielded a universe having a very familiar finite but unbounded shape: a sphere.