The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

by Brian Greene

  In Figure 7.1 we showed how the strengths of the three nongravitational couplings merge together when the temperature of the universe is high enough. How does the strength of the gravitational force fit into this picture? Before the emergence of M-theory, string theorists were able to show that with the simplest of choices for the Calabi-Yau component of space, the gravitational force almost, but not quite, merges with the other three, as shown in Figure 14.2. String theorists found that the mismatch could be avoided by carefully molding the shape of the chosen Calabi-Yau, among other tricks of the trade, but such after-the-fact fine tuning always makes a physicist uncomfortable. Since no one currently knows how to predict the precise form of the Calabi-Yau dimensions, it seems dangerous to rely upon solutions to problems that hinge so delicately on the fine details of their shape.

  Witten has shown, however, that the second superstring revolution provides a far more robust solution. By investigating how the strengths of the forces vary when the string coupling constant is not necessarily small, Witten found that the gravitational force curve can be gently nudged to merge with the other forces, as in Figure 14.2, without any special molding of the Calabi-Yau portion of space. Although it is far too early to tell, this may indicate that cosmological unity is more easily achieved by making use of the larger framework of M-theory.

  The developments discussed in this and the previous sections represent the first, somewhat tentative steps toward understanding the cosmological implications of string/M-theory. During the coming years, as the nonperturbative tools of string/M-theory are sharpened, physicists anticipate that some of the most profound insights will emerge from their application to cosmological questions.

  But without currently having methods that are sufficiently powerful to understand cosmology according to string theory fully, it is worthwhile to think about some general considerations concerning the possible role of cosmology in the search for the ultimate theory. We caution that some of these ideas are of a more speculative nature than much of what we have discussed previously, but they do raise issues that any purported final theory may one day have to address.

  Cosmological Speculation and the Ultimate Theory

  Cosmology has the ability to grab hold of us at a deep, visceral level because an understanding of how things began feels—at least to some—like the closest we may ever come to understanding why they began. That is not to say that modern science provides a connection between the question of how and the question of why—it doesn't—and it may well be that no such scientific connection is ever found. But the study of cosmology does hold the promise of giving us our most complete understanding of the arena of the why—the birth of the universe—and this at least allows for a scientifically informed view of the frame within which the questions are asked. Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.

  In the context of searching for the ultimate theory, these lofty reflections on cosmology give way to far more concrete considerations. The way things in the universe appear to us today—way on the far right-hand side of the time line in Figure 14.1—depends upon the fundamental laws of physics, to be sure, but it may also depend on aspects of cosmological evolution, from the far left-hand side of the time line, that potentially lie outside the scope of even the deepest theory.

  It's not hard to imagine how this might be. Think of what happens, for example, when you toss a ball in the air. The laws of gravity govern the ball's subsequent motion, but we can't predict where the ball will land exclusively from those laws. We must also know the velocity of the ball—its speed and direction—as it left your hand. That is, we must know the initial conditions of the ball's motion. Similarly, there are features of the universe that also have a historical contingency—the reason why a star formed here or a planet there depends upon a complicated chain of events that, at least in principle, we can imagine tracing back to some feature of how the universe was when it all began. But it is possible that even more basic features of the universe, perhaps even the properties of the fundamental matter and force particles, also have a direct dependence on historical evolution—evolution that itself is contingent upon the initial conditions of the universe.

  In fact, we've already noted one possible incarnation of this idea in string theory: As the hot, early universe evolved, the extra dimensions may have transmuted from shape to shape, ultimately settling down to one particular Calabi-Yau space once things had cooled off sufficiently. But, like a ball tossed in the air, the result of that journey through numerous Calabi-Yau shapes may well depend on details of how the journey got started in the first place. And through the influence of the resulting Calabi-Yau shape on particle masses and on properties of forces, we see that cosmological evolution and the state of the universe when it began can have a profound impact on the physics we currently observe.

  We don't know what the initial conditions of the universe were, or even the ideas, concepts, and language that should be used to describe them. We believe that the outrageous initial state of infinite energy, density, and temperature that arises in the standard and inflationary cosmological models is a signal that these theories have broken down rather than a correct description of the physical conditions that actually existed. String theory offers an improvement by showing how such infinite extremes might be avoided; nevertheless, no one has any insight on the question of how things actually did begin. In fact, our ignorance persists on an even higher plane: We don't know whether the question of determining the initial conditions is one that is even sensible to ask or whether—like asking general relativity to give insight into how hard you happened to toss a ball in the air—it is a question that lies forever beyond the grasp of any theory. Valiant attempts by physicists such as Hawking and James Hartle of the University of California at Santa Barbara have tried to bring the question of cosmological initial conditions within the umbrella of physical theory, but all such attempts remain inconclusive. In the context of string/M-theory, our cosmological understanding is, at present, just too primitive to determine whether our candidate "theory of everything" truly lives up to its name and determines its own cosmological initial conditions, thereby elevating them to the status of physical law. This is a prime question for future research.

  But even beyond the issue of initial conditions and their impact on the ensuing historical twists and turns of cosmic evolution, some recent and highly speculative proposals have argued for yet other potential limits on the explanatory power of any final theory. No one knows if these ideas are right or wrong, and certainly they currently lie on the outskirts of mainstream science. But they do highlight—albeit in a rather provocative and speculative manner—an obstacle that any proposed final theory may encounter.

  The basic idea rests upon the following possibility. Imagine that what we call the universe is actually only one tiny part of a vastly larger cosmological expanse, one of an enormous number of island universes scattered across a grand cosmological archipelago. Although this might sound rather far-fetched—and in the end it may well be—André Linde has suggested a concrete mechanism that might lead to such a gargantuan universe. Linde has found that the brief but crucial burst of inflationary expansion discussed earlier may not have been a unique, one-time event. Instead, he argues, the conditions for inflationary expansion may happen repeatedly in isolated regions peppered throughout the cosmos, which then undergo their own inflationary ballooning in size, evolving into new, separate universes. And in each of these universes, the process continues, with new universes sprouting from far-flung regions in the old, generating a never ending web of ballooning cosmic expanses. The terminology gets a little cumbersome, but let's follow fashion and call this greatly expanded notion of the universe the multiverse, with each of the constituent parts being called a universe.

  The central observation is that whereas in Chapter 7 we noted that everything we know points toward a consistent and uniform physics throughout our universe, th
is may have no bearing on the physical attributes in these other universes so long as they are separate from us, or at least so far away that their light has not had time to reach us. And so we can imagine that physics varies from one universe to another. In some, the differences may be subtle: For example, the electron mass or the strength of the strong force might be a thousandth of a percent larger or smaller than in our universe. In others, physics may differ in more pronounced ways: The up-quark might weigh ten times what it weighs in our universe, or the strength of the electromagnetic force might be ten times the value we measure, with all the profound implications that this has on stars and on life as we know it (as indicated in Chapter 1). And in other universes, physics may differ in still more dramatic ways: The list of elementary particles and forces may be completely distinct from ours, or, taking a cue from string theory, even the number of extended dimensions may differ, with some cramped universes having as few as zero or one large spatial dimension, while other expansive universes possess eight, nine, or even ten extended spatial dimensions. If we let our imaginations run free, even the laws themselves can drastically differ from universe to universe. The range of possibilities is endless.

  Here's the point. If we scan through this huge maze of universes, the vast majority will not have conditions hospitable to life, or at least to anything remotely akin to life as we know it. For drastic changes in familiar physics, this is clear: If our universe truly looked like the Garden-hose universe, life as we know it would not exist. But even rather conservative changes to physics would interfere with the formation of stars, for example, disrupting their ability to act as cosmic furnaces that synthesize complex life-supporting atoms such as carbon and oxygen that, normally, are spewed throughout the universe by supernova explosions. In light of the sensitive dependence of life on the details of physics, if we now ask, for instance, why the forces and particles of nature have the particular properties we observe, a possible answer emerges: Across the entire multiverse, these features vary widely; their properties can be different and are different in other universes. What's special about the particular combination of particle and force properties we observe is that, clearly, they allow life to form. And life, intelligent life in particular, is a prerequisite even to ask the question of why our universe has the properties it does. In plain language, things are the way they are in our universe because if they weren't, we wouldn't be here to notice. Like the winners of a mass game of Russian roulette, whose surprise at surviving is tempered by the realization that had they not won, they wouldn't have been able not to feel surprised, the multiverse hypothesis has the capacity to lessen our insistence on explaining why our universe appears as it does.

  This line of argument is a version of an idea with a long history known as the anthropic principle. As presented, it is a perspective that is diametrically opposed to the dream of a rigid, fully predictive, unified theory in which things are the way they are because the universe could not be otherwise. Rather than being the epitome of poetic grace in which everything fits together with inflexible elegance, the multiverse and the anthropic principle paint a picture of a wildly excessive collection of universes with an insatiable appetite for variety. It will be extremely hard, if not impossible, for us ever to know if the multiverse picture is true. Even if there are other universes, we can imagine that we will never come into contact with any of them. But by vastly increasing the scope of "what's out there"—in a manner that dwarfs Hubble's realization that the Milky Way is but one galaxy among many—the concept of the multiverse does at least alert us to the possibility that we may be asking too much of an ultimate theory.

  We should require that our ultimate theory give a quantum-mechanically consistent description of all forces and all matter. We should require that our ultimate theory give a cogent cosmology within our universe. However, if the multiverse picture is correct—a huge if—it may be asking too much for our theory to explain, as well, the detailed properties of the particle masses, charges, and the force strengths.

  But we must emphasize that even if we accept the speculative premise of the multiverse, the conclusion that this compromises our predictive power is far from airtight. The reason, simply put, is that if we unleash our imaginations and allow ourselves to contemplate a multiverse, we should also unleash our theoretical musings and contemplate ways in which the apparent randomness of the multiverse can be tamed. For one relatively conservative musing, we can imagine that—were the multiverse picture true—we would be able to extend our ultimate theory to its full sprawling expanse, and that our "extended ultimate theory" might tell us precisely why and how the values of the fundamental parameters are sprinkled across the constituent universes.

  A more radical musing comes from a proposal of Lee Smolin of Penn State University, who, inspired by the similarity between conditions at the big bang and at the centers of black holes—each being characterized by a colossal density of crushed matter—has suggested that every black hole is the seed for a new universe that erupts into existence through a big bang-like explosion, but is forever hidden from our view by the black hole's event horizon. Beyond proposing another mechanism for generating a multiverse, Smolin has injected a new element—a cosmic version of genetic mutation—that does an end run around the scientific limitations associated with the anthropic principle.9 Imagine, he suggests, that when a universe sprouts from the core of a black hole, its physical attributes, such as particle masses and force strengths, are close, but not identical, to those of its parent universe. Since black holes arise from extinguished stars, and star formation depends upon the precise values of the particle masses and force strengths, the fecundity of any given universe—the number of black hole progeny it can produce—depends sensitively on these parameters. Small variations in the parameters of the progeny universes will therefore lead to some that are even more optimized for black hole production than their parent universe, and have an even greater number of offspring universes of their own.10 After many "generations," the descendants of universes optimized for producing black holes will thus be so numerous that they will overwhelm the population of the multiverse. And so, rather than invoking the anthropic principle, Smolin's suggestion provides a dynamic mechanism that, on average, drives the parameters of each next-generation universe ever closer to particular values—those that are optimum for black hole production.

  This approach gives another method, even in the context of the multiverse, in which the fundamental matter and force parameters can be explained. If Smolin's theory is right, and if we are a typical member of a mature multiverse (these are big "ifs" and can be debated on many fronts, of course), the parameters of the particles and forces that we measure should be optimized for black hole production. That is, any fiddling with these parameters of our universe should make it harder for black holes to form. Physicists have begun to investigate this prediction; at present there is no consensus on its validity. But even if Smolin's specific proposal turns out to be wrong, it does present yet another shape that the ultimate theory might take. The ultimate theory may, at first sight, appear to lack rigidity. We may find that it can describe a wealth of universes, most of which have no relevance to the one we inhabit. And moreover, we can imagine that this wealth of universes may be physically realized, leading to a multiverse—something that, at first sight, forever limits our predictive power. In fact, however, this discussion illustrates that an ultimate explanation can yet be achieved, so long as we grasp not only the ultimate laws but also their implications for cosmological evolution on an unexpectedly grand scale.

  Undoubtedly, the cosmological implications of string/M-theory will be a major field of study well into the twenty-first century. Without accelerators capable of producing Planck-scale energies, we will increasingly have to rely on the cosmological accelerator of the big bang, and the relics it has left for us throughout the universe, for our experimental data. With luck and perseverance, we may finally be able to answer questions such as how the univer
se began, and why it has evolved to the form we behold in the heavens and on earth. There is, of course, much uncharted territory between where we are and where full answers to these fundamental questions lie. But the development of a quantum theory of gravity through superstring theory lends credence to the hope that we now possess theoretical tools for pushing into the vast regions of the unknown, and, no doubt after many a struggle, possibly emerging with answers to some of the deepest questions ever posed.

  Part V: Unification in the Twenty-First Century

  Chapter 15: Prospects:

  Centuries from now, superstring theory, or its evolution within M-theory, may have developed so far beyond our current formulation that it might be unrecognizable even to today's leading researchers. As we continue to seek the ultimate theory, we may well find that string theory is but one of many pivotal steps on a path toward a far grander conception of the cosmos—a conception that involves ideas that differ radically from anything we have previously encountered. The history of science teaches us that each time we think that we have it all figured out, nature has a radical surprise in store for us that requires significant and sometimes drastic changes in how we think the world works. Then again, in a bit of brash posturing, we can also imagine, as others before us have perhaps naively done, that we are living through a landmark period in humanity's history in which the search for the ultimate laws of the universe will finally draw to a close. As Edward Witten has said,

  I feel that we are so close with string theory that—in my moments of greatest optimism—I imagine that any day, the final form of the theory might drop out of the sky and land in someone's lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory than anything we have had before and that well into the twenty-first century, when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory.1