God In The Equation Read online

  Dark matter is a generic term referring to objects that emit minimal light relative to their mass. Some of the unseen stuff might be quite unexceptional. Galaxies abound with objects that fit the bill: cool stars that shine only feebly, for instance, as well as radiation-absorbent clouds of gas and dust. Stellar corpses—collapsed remains known as white dwarfs, neutron stars, and, most extreme, black holes—have piled up steadily over the aeons since the big bang. Additional material might be hidden in brown dwarfs, failed stars that never gathered enough mass to start shining. Cosmologists needed a second variety of dark matter, however, one that would give order to the universe without showing up in the microwave background.

  Unlike Lambda, dark matter was, perhaps, verifiable: there were strong signs that at least some forms really exist. Fritz Zwicky, the terror of Mount Wilson, first realized that there is more to the cosmos than meets the eye in 1933, just a year after Einstein and de Sitter announced their new, flat cosmology. While he was studying the motions of the various members of the Coma cluster, an extensive gathering of galaxies roughly 350 million light-years away, Zwicky noticed that the galaxies in the cluster zoomed around and past one another much too quickly. Gravity must glue together the Coma cluster, or else its members would have dispersed long ago. But the galaxies in Coma were moving so rapidly that they should in fact be flying apart, assuming the visible stars and gas were the only things there. Zwicky concluded that the cluster must contain an additional component of unseen material that held everything together. In fact, he estimated that 90 percent of the Coma cluster must consist of this invisible stuff.

  Poor Zwicky. His colleagues had trained themselves so well to block out his noisy insults and wild proclamations that they missed many of his clever insights as well. They ignored his discovery, and the idea lay dormant until the early 1970s, when Peebles and his equally inquisitive Princeton colleague Jeremiah Ostriker were studying the structures of spiral galaxies and the ways that pairs of galaxies interact with one another. They found that the dynamics of the galaxies made sense only if each system had a thick halo of nonluminous matter extending far beyond the edge of the visible disk.

  At the Carnegie Institution of Washington, Vera Rubin, one of the first women to break into the men's club of cosmology, provided even more dramatic evidence that dark matter is real. She started out measuring the ways galaxies cluster together. But driven by curiosity and a frustrating lack of access to the largest telescopes, Rubin switched gears and set out to unravel how spiral galaxies rotated, an arcane subject that had produced lots of theory but few reliable observations. According to the standard assumptions of the time, the outer parts of a galaxy should turn more slowly than the inner parts because they are farther from the center of mass. Rubin found instead that stars maintain their speeds all the way to the very edge of the spiral arms. In a serious of cautious, detailed 1978 articles, she reported that she was seeing direct evidence of the dark matter halos inferred by Peebles and Ostriker. Those peripheral stars were at the edge only of the visible galaxy. A much larger, invisible galaxy provided the gravitational pull needed to keep everything moving apace at the galactic extremities.

  All at once, dark matter looked like cosmology's great savior. “The observations fit in so well, since there was already a framework, so some people embraced the observations very enthusiastically,” Rubin recalled. Researchers knew that the bright stars and galaxies do not add up to anything close to the critical density of the universe, Einstein's aesthetic goal. But if there were enough dark matter out there, it might be able to close the gap. Much to their delight, the astronomers analyzing images from the giant observatories and orbiting telescopes have since identified an abundance of dark matter everywhere they looked. X-ray telescopes reveal that groups of galaxies are surrounded by huge clouds of hot gas, apparently held together by unseen mass. Dark matter in galaxy clusters betrays itself by the way it bends starlight from more distant objects or the manner in which it draws in hapless neighboring galaxies. On the largest scales, invisible matter seems to outweigh the visible component by about twenty to one.

  For the theorists, even a twenty-to-one mix of dark matter was not enough, however. If the density of the universe has the critical value, they needed a hundred-to-one mix; a full 99 percent of the mass must be dark. And most of that dark material could not consist of conventional protons, neutrons, and electrons. The nuclear reactions deduced by Gamow, Hoyle, and their like-minded colleagues set strict limits on the amount of ordinary matter in the universe. Their model of the big bang, which so accurately predicted the composition of the cosmos and extended the reach of sci/religion, works only if the density of ordinary matter is quite low; otherwise the numbers come out all wrong. Also, too much ordinary matter would mess up the smoothness of the microwave background. So most of the dark stuff must consist of some kind of exotic material, perhaps unknown varieties of heavy subatomic particles that do not interact with the particles that make up normal matter. Current physics theories—themselves based on efforts to unify the natural forces, Einstein's old goal—predict that such particles might exist, and cosmologists dream about them happily. For now, though, these “weakly interacting massive particles,” whimsically known as “WIMPs,” are wholly hypothetical. “Most of the universe must be made from some substance that is not yet identified, and is perhaps not even known,” in the words of Alan Guth.

  No laboratory experiment has ever produced a dark matter particle; no detector has ever recorded one. In the face of this vacuum of evidence, theorists have nevertheless coined endless names for the inferred particles: axions, photinos, neutralinos. Lecturing on his motivations for the dark matter hunt, Kim Griest of the University of California, San Diego, was quite candid: “As one goes down the list of popular candidates, asking oneself which candidate is the most likely, I have to admit that 'none-of-the-above' comes to mind.” Nonetheless, the dark matter search goes on, because without dark matter our picture of the universe makes no sense. Visible matter alone cannot explain the gravitational dynamics of galaxies and clusters of galaxies. Furthermore, a universe overloaded with unseen blobs of ordinary matter would mess up the primordial reactions that Gamow, Hoyle, and company worked out so meticulously. Dark matter particles will be, by definition, difficult to detect. But the faith of the sci/religious holds that these particles will be found. A much-touted dark matter sighting at the University of Rome in 2000 now looks like the product of wishful thinking. One recent experiment gives reason for optimism, however. Physicists working on the enormous underground Super-Kamiokande experiment in Japan have uncovered evidence that neutrinos—wraithlike subatomic entities long considered massless—actually have a small mass. Neutrinos are almost imperceptible and so abundant that they could contribute a significant portion of the dark matter in the universe.

  Even the addition of dark matter did not solve the essential mysteries of the big bang; it left a gnawing spiritual hunger. The flatness problem and horizon problem remained unsolved. Nobody knew where cosmic structure comes from. Dicke discussed this unsettled state of affairs in a paper entitled “The Big Bang Cosmology—Enigmas and Nostrums,” published as part of a celebration of the centennial of Albert Einstein's birth in 1979. Although he had first warned about the flatness problem a decade earlier, the paper struck a chord within the sci/religious community. The scientific story of creation was incomplete. Einstein had wanted to know whether the laws of physics forced God to build this particular universe. Einstein's disciples still could not provide an answer. Stephen Hawking turned the question upside down and suggested it might be insoluble: “One possible answer is to say that God chose the initial configuration of the universe for reasons that we cannot hope to understand.” He did not pursue this line of thought. Hawking brought it up only to illustrate the path he refused to take. It was a testament to the authority of sci/religion that such an appeal to an old-style, unknowable God now seemed nearly absurd.

  Another, more palatab
le but nonetheless highly controversial answer comes from logical and philosophical considerations of all possible realities. We could not live in a universe whose laws preclude all the stages of development leading up to the evolution of our kind of carbon-based life, so of course we don't inhabit any of those other universes. In 1974, the British cosmologist Brandon Carter, then a neighbor of Hawking's at Cambridge University, named this somewhat circular argument “the anthropic principle.” As Carter put it, “What we can expect to observe must be restricted by the conditions necessary for our presence as observers.” This idea has become one of the most debated, reviled, and revered ideas in cosmology.

  The anthropic principle has taken on several forms. In its mildest, or weak, version it limits the number of possible physical states that cosmologists consider in their equations to those that could allow humans to exist. A startlingly speculative version proposed by John A. Wheeler of the University of Texas at Austin, the inventive physicist who first described black holes, goes much further. He averred that the time had come “to read the deeper meaning and consequences” from Einstein's cosmology. Wheeler's take on anthropic thinking, known as “the participatory anthropic principle,” states that the universe exists only if there is somebody present to observe it. In this sense, the universe must, by definition, have laws and structures that allow sentient life to exist.

  Wheeler was not the only serious scientist to follow Carter's lead. Hawking once invoked the anthropic principle to account for the overall smoothness of the universe. It could explain the flatness of the universe and the abundance of dark matter. And it could explain why the laws of physics appear precisely designed to allow this kind of universe, full of atoms and planets. Without all of these things, we never could have gotten to where we are. If the attributes of the universe were slightly different, galaxies would not form, or stars would not shine, or the whole would have collapsed before life started to evolve on Earth. A number of physicists, including Steven Weinberg, another theorist at the University of Texas at Austin, have seriously suggested that there is not one universe but an infinite number of them, each with slightly different natural laws. We merely inhabit the one that is well suited to us, our location inherently selected for us by the anthropic principle. By the late 1980s, the possibility of many universes began to find its way into mainstream cosmological theories.

  Yet many scientists view the anthropic principle as little more than an admission of defeat. “It's like throwing up your hands and saying, 'Things are the way they are because otherwise we wouldn't be here to discuss it,'” says Michael Turner of the University of Chicago, a grizzled veteran of theoretical cosmology. “My fear is that we may drift in that direction.” The anthropic principle by itself doesn't explain anything; it provides a reason for not needing to explain certain things. It offers a logical reason not to be surprised that the universe seems so finely tuned to our needs. A number of scientists—Hawking again among them—now feel bold enough to propose instead sci/religious explanations of how it all began. These are not testable theories in the conventional sense, at least not yet. But as Hawking says, “There is not much alternative, unless you are going to suppose that God is sending messages into the universe.”

  So while the anthropic principle could be used to sweep aside the flatness problem, the horizon problem, and the origin of structure in the universe, few cosmologists are willing to cede their hard-won scientific turf to what is essentially a philosophical doctrine. Most consider invoking the anthropic principle only slightly more palatable than invoking the old-style God. They have looked instead for credible hypotheses that could take sci/religion one step closer to explaining why the universe looks the way it does. These new hypotheses heralded the return of Einstein's once deposed Lambda—largely dormant since Baade and Sandage vastly increased the estimated age of the universe during the 1950s—and gave it a totally new look and mission.

  Lambda's rehabilitation initially came from the world of the very small, not the world of the very large. As early as 1916, Walter Nernst, a jovial German physical chemist who was friendly with Einstein, speculated that empty space might not be truly empty. According to newly uncovered rules of quantum physics, it could in fact be full of vibrating energy. Such energy could have a profound influence on the fate of the universe because of Einstein's equation E=mc2. Filling space with energy is equivalent to filling it with mass; if there were a large amount of energy hidden within the fabric of space, this energy would produce a huge gravitational field. Wolfgang Pauli, one of the leading quantum theorists, joked in the mid-1920s that the amount of energy predicted by the then-current models would put such a tight squeeze on the universe that it “would not even reach to the moon.”

  By the late 1940s, a pair of brash New Yorkers—Julian Schwinger at Harvard University and Richard Feynman, then working at Cornell University—gave the quantum world an even weirder spin. In their formulation, the vacuum is a boiling cauldron of activity on the subatomic scale, full of almost-but-not-quite imaginary particles that continuously pop in and out of existence. Again, the implied energy from these particles and fields was potentially overwhelming, but for a while nobody seriously considered their cosmological significance.

  Such reluctance was understandable. It was hard enough to believe that such transient, ghostlike particles really exist, much less that they might play a role in our cosmic destiny. But the quantum activity within empty space actually produces some very measurable effects. One of the most dramatic examples of these is the so-called Casimir effect, an attractive force between two closely spaced metal plates, which was predicted by the Dutch physicist Hendrick Casimir in 1948. The narrow gap between the plates limits the number of virtual particles that can appear there; the vast sea of potential particles on the outside therefore pushes the two plates together. The Casimir effect can be detected in the laboratory, and it is just one of many proofs of the reality of virtual particles. Even the fusion reactions in the centers of stars are possible only because particles that should not be able to merge, according to classical physics rules, can squeak through by borrowing energy from the turmoil of empty space. Virtual particles make the sun shine.

  It took a while to forge a link between the very smallest and very largest realms of physics research. The man who made the link between virtual particles and cosmic destiny was Yakov Zeldovich—an unfamiliar name to most Americans, but a towering figure in Soviet physics who shared credit with Andrei Sakharov as the father of that nation's hydrogen bomb. After the 1950s, Soviet authorities unshackled him from his military duties, and he chose to focus on an even bigger atomic explosion, the big bang. He saw the task of cosmology as both ridiculously ambitious and deeply romantic. “We are in a difficult position, knowing that we study directly a small part of the Universe as a whole, and knowing that yet unknown physics of very high energy is involved. One needs courage. But one needs also delicateness and precision. I would call it the Leo Tolstoy principle: a detailed courageous study of his own heart and mind helped him to understand other hearts and minds—that of Anna Karenina, that of a horse,” Zeldovich said in an address delivered shortly before his death in 1987. For security reasons, Zeldovich was not allowed to leave the Soviet bloc, but his intellectual fame was sufficient to draw the world's top physics talent, including Stephen Hawking, to his Moscow lair.

  Zeldovich was a small, intense man given to frequent and sudden brainstorms. He developed a highly influential model of how structure formed in the universe. He helped show how black holes could function as the energy sources of erupting galaxies. And in a 1967 paper he recognized the universal implications of the energy hidden within the fabric of space in the form of virtual particles. That energy, rather than bringing the heavens crashing down, could give the vacuum an elastic, springy quality, as if space were exerting an outward pressure. A large volume of space would contain more energy, and so exert more pressure, than a small volume. On a local scale, the effect of the vacuum energy
might be nearly imperceptible, but over huge distances the squirming of space could create a repulsive, antigravity effect.

  In other words, Zeldovich realized that the energy hidden within the vacuum would exactly mimic the properties of Lambda. Thus Zeldovich took a big step toward attaining one of Einstein's greatest sci/religious visions, finding a unifying link between the large world of general relativity and the tiny world of the quantum. This reincarnation of Einstein's Lambda is not quite as miraculous as it sounds. In his 1917 cosmology paper, Einstein had tried to put together the broadest possible framework for how the universe might be constructed. He therefore envisioned two general kinds of influences that could affect the dynamics of the cosmos as a whole. Gravity bends space from without, causing collapse; Lambda unbends space from within, causing expansion. The reason vacuum energy fits the description of the original Lambda is that Einstein had already left a large hole in his equations for some generic phenomenon that injects energy, and hence repulsive pressure, into the fabric of space. In fact, Fred Hoyle had already exploited this hole in much the same way with his “C-field,” the driving force behind the now discredited steady state theory. Even earlier, Lemaitre had recognized that the Lambda in his cosmology equations resembled an energy packed into the vacuum.

  The big problem came when people tried to calculate the value of Lambda associated with the vacuum energy. Making such a calculation requires a detailed understanding of all the quantum processes that produce virtual particles. Nobody has yet achieved that level of enlightenment, but physicists allowed some simplifying assumptions that reduced the problem from impossible to agonizingly difficult. After all the number crunching came the embarrassing result. Zeldovich assumed that most of the vacuum energies cancelled out, and still he got a value for Lambda that is 100 million times too large. Using the current standard quantum models, the discrepancy is far worse. The energy density of the vacuum, according to theory, should be about 120 orders of magnitude greater than is observed. A hundred and twenty orders of magnitude is 1 followed by 120 zeroes. If Lambda were actually that large, everything—you, the seat you're sitting on, the pages you're now reading—would fly apart in far less than the blink of an eye. Some missing process evidently trims Lambda to a manageable size.