The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

  "Oh, right, that time-dilation thing of special relativity," Lisa agrees. "Cool. Anyway, I want to get home in time for dinner, so climb through the wormhole, because we've got to hurry." "Okay," Bart says, crawling through the wormhole. He buys a Butterfinger from Apu, and he and Lisa head home.

  Notice that although Bart's passage through the wormhole took him but a moment, it transported him 6 million years back in time. He and his ship and the wormhole mouth had landed far into earth's future. Had he gotten out, spoken with people, and checked the newspaper, everything would have confirmed this. Yet, when he passed through the wormhole and rejoined Lisa, he found himself back in the present. The same holds true for anyone else who might follow Bart through the wormhole mouth: he would also travel 6 million years back in time. Similarly, anyone who climbs into the wormhole mouth at the Kwik-E-Mart, and out of the mouth Bart left in his ship, would travel 6 million years into the future. The important point is that Bart did not just take one of the wormhole mouths on a journey through space. His journey also transported the wormhole mouth through time. Bart's voyage took him and the wormhole'smouth into earth's future. In short, Bart transformed a tunnel through space into a tunnel through time; he turned a wormhole into a time machine.

  A rough way to visualize what's going on is depicted in Figure 15.5. In Figure 15.5a we see a wormhole connecting one spatial location with another, with the wormhole configuration drawn so as to emphasize that it lies outside of ordinary space. In Figure 15.5b, we show the time evolution of this wormhole, assuming both its mouths are kept stationary. (The time slices are those of a stationary observer.) In Figure 15.5c, we show what happens when one wormhole mouth is loaded onto a spaceship and taken on a round-trip journey. Time for the moving mouth, just like time on a moving clock, slows down, so that the moving mouth is transported to the future. (If an hour elapses on a moving clock but a thousand years elapse on stationary clocks, the moving clock will have jumped into the stationary clocks' future.) Thus, instead of the stationary wormhole mouth's connecting, via the wormhole tunnel, to a mouth on the same time slice, it connects to a mouth on a future time slice, as in Figure 15.5c. Unless the wormhole mouths are moved further, the time difference between them will remain locked in. At any moment, should you enter one mouth and exit the other, you will have become a time traveler.

  Building a Wormhole Time Machine

  One blueprint for building a time machine is now clear. Step 1: find or create a wormhole wide enough for you, or anything you want to send through time, to pass. Step 2: establish a time difference between the wormhole mouths—say, by moving one relative to the other. That's it. In principle.

  Figure 15.5 (a) A wormhole, created at some moment in time, connects one location in space with another. (b) If the wormhole mouths do not move relative to one another, they "pass" through time at the same rate, so the tunnel connects the two regions at the same time. (c) If one wormhole mouth is taken on a round-trip journey (not shown), less time will elapse for that mouth, and hence the tunnel will connect the two regions of space at different moments of time. The wormhole has become a time machine.

  How about in practice? Well, as I mentioned at the outset, no one knows whether wormholes even exist. Some physicists have suggested that tiny wormholes might be plentiful in the microscopic makeup of the spatial fabric, being continually produced by quantum fluctuations of the gravitational field. If so, the challenge would be to enlarge one to macroscopic size. Proposals have been made for how this might be done, but they're barely beyond theoretical flights of fancy. Other physicists have envisioned the creation of large wormholes as an engineering project in applied general relativity. We know that space responds to the distribution of matter and energy, so with sufficient control over matter and energy, we might cause a region of space to spawn a wormhole. This approach presents an additional complication, because just as we must tear open the side of a mountain to attach the mouth of a tunnel, we must tear open the fabric of space to attach the mouth of a wormhole. 12 No one knows whether such tears in space are allowed by the laws of physics. Work with which I've been involved in string theory (see page 386) has shown that certain kinds of spatial tears are possible, but so far we have no idea whether these rips might be relevant to the creation of wormholes. The bottom line is that intentional acquisition of a macroscopic wormhole is a fantasy that, at best, is a very long way from being realized.

  Morever, even if we somehow managed to get our hands on a macroscopic wormhole, we wouldn't be done; we'd still face a couple of significant obstacles. First, in the 1960s, Wheeler and Robert Fuller showed, using the equations of general relativity, that wormholes are unstable. Their walls tend to collapse inward in a fraction of a second, which eliminates their utility for any kind of travel. More recently, though, physicists (including Thorne and Morris, and also Matt Visser) have found a potential way around the collapse problem. If the wormhole is not empty, but instead contains material—so-called exotic matter— that can exert an outward push on its walls, then it might be possible to keep the wormhole open and stable. Although similar in its effect to a cosmological constant, exotic matter would generate outward-pushing repulsive gravity by virtue of having negative energy (not just the negative pressure characteristic of a cosmological constant 13 ). Under highly specialized conditions, quantum mechanics allows for negative energy, 14 but it would be a monumental challenge to generate enough exotic matter to hold a macroscopic wormhole open. (For example, Visser has calculated that the amount of negative energy needed to keep open a one-meter-wide wormhole is roughly equal in magnitude to the total energy produced by the sun over about 10 billion years. 15 )

  Second, even if we somehow found or created a macroscopic wormhole, and even if we somehow were able to buttress its walls against immediate collapse, and even if we were able to induce a time difference between the wormhole mouths (say, by flying one mouth around at high speed), there would remain another hurdle to acquiring a time machine. A number of physicists, including Stephen Hawking, have raised the possibility that vacuum fluctuations—the jitters arising from the quantum uncertainty experienced by all fields, even in empty space, discussed in Chapter 12—might destroy a wormhole just as it was getting into position to be a time machine. The reason is that, just at the moment when time travel through the wormhole becomes possible, a devastating feedback mechanism, somewhat like the screeching noise generated when microphone and speaker levels in a sound system are not adjusted appropriately, may come into play. Vacuum fluctuations from the future can travel through the wormhole to the past, where they can then travel through ordinary space and time to the future, enter the wormhole, and travel back to the past again, creating an endless cycle through the wormhole and filling it with ever-increasing energy. Presumably, such an intense energy buildup would destroy the wormhole. Theoretical research suggests this as a real possibility, but the necessary calculations strain our current understanding of general relativity and quantum mechanics in curved spacetime, so there is no conclusive proof.

  The challenges to building a wormhole time machine are clearly immense. But the final word won't be given until our facility with quantum mechanics and gravity is refined further, perhaps through advances in superstring theory. Although at an intuitive level physicists generally agree that time travel to the past is impossible, as of today the question has yet to be fully closed.

  Cosmic Rubbernecking

  In thinking about time travel, Hawking has raised an interesting point. Why, he asks, if time travel is possible, haven't we been inundated with visitors from the future? Well, you might answer, maybe we have. And you might go further and say we've put so many time travelers in locked wards that most of the others don't dare identify themselves. Of course, Hawking is half joking, and so am I, but he does raise a serious question. If you believe, as I do, that we have not been visited from the future, is that tantamount to believing time travel impossible? Surely, if people succeed in building time machines
in the future, some historian is bound to get a grant to study, up close and personal, the building of the first atomic bomb, or the first voyage to the moon, or the first foray into reality television. So, if we believe no one has visited us from the future, perhaps we are implicitly saying that we believe no such time machine will ever be built.

  Actually, though, this is not a necessary conclusion. The time machines that have thus far been proposed do not allow travel to a time prior to the construction of the first time machine itself. For the wormhole time machine, this is easy to see by examining Figure 15.5. Although there is a time difference between the wormhole mouths, and although that difference allows travel forward and backward in time, you can't reach a time before the time difference was established. The wormhole itself does not exist on the far left of the spacetime loaf, so there is no way you can use it to get there. Thus, if the first time machine is built, say, 10,000 years from now, that moment will no doubt attract many time-traveling tourists, but all previous times, such as ours, will remain inaccessible.

  I find it curious and compelling that our current understanding of nature's laws not only suggests how to avoid the seeming paradoxes of time travel but also offers proposals for how time travel might actually be accomplished. Don't get me wrong: I count myself among the sober physicists who feel intuitively that we will one day rule out time travel to the past. But until there's definitive proof, I think it justified and appropriate to keep an open mind. At the very least, researchers focusing on these issues are substantially deepening our understanding of space and time in extreme circumstances. At the very best, they may be taking the first critical steps toward integrating us into the spacetime superhighway. After all, every moment that goes by without our having succeeded in building a time machine is a moment that will be forever beyond our reach and the reach of all who follow.

  16 - The Future of an Allusion

  PROSPECTS FOR SPACE AND TIME

  Physicists spend a large part of their lives in a state of confusion. It's an occupational hazard. To excel in physics is to embrace doubt while walking the winding road to clarity. The tantalizing discomfort of perplexity is what inspires otherwise ordinary men and women to extraordinary feats of ingenuity and creativity; nothing quite focuses the mind like dissonant details awaiting harmonious resolution. But en route to explanation—during their search for new frameworks to address outstanding questions—theorists must tread with considered step through the jungle of bewilderment, guided mostly by hunches, inklings, clues, and calculations. And as the majority of researchers have a tendency to cover their tracks, discoveries often bear little evidence of the arduous terrain that's been covered. But don't lose sight of the fact that nothing comes easily. Nature does not give up her secrets lightly.

  In this book we've looked at numerous chapters in the story of our species' attempt to understand space and time. And although we have encountered some deep and astonishing insights, we've yet to reach that ultimate eureka moment when all confusion abates and total clarity prevails. We are, most definitely, still wandering in the jungle. So, where from here? What is the next chapter in spacetime's story? Of course, no one knows for sure. But in recent years a number of clues have come to light, and although they've yet to be integrated into a coherent picture, many physicists believe they are hinting at the next big upheaval in our understanding of the cosmos. In due course, space and time as currently conceived may be recognized as mere allusions to more subtle, more profound, and more fundamental principles underlying physical reality. In the final chapter of this account, let's consider some of these clues and catch a glimpse of where we may be headed in our continuing quest to grasp the fabric of the cosmos.

  Are Space and Time Fundamental Concepts?

  The German philosopher Immanuel Kant suggested that it would be not merely difficult to do away with space and time when thinking about and describing the universe, it would be downright impossible. Frankly, I can see where Kant was coming from. Whenever I sit, close my eyes, and try to think about things while somehow not depicting them as occupying space or experiencing the passage of time, I fall short. Way short. Space, through context, or time, through change, always manages to seep in. Ironically, the closest I come to ridding my thoughts of a direct spacetime association is when I'm immersed in a mathematical calculation (often having to do with spacetime!), because the nature of the exercise seems able to engulf my thoughts, if only momentarily, in an abstract setting that seems devoid of space and time. But the thoughts themselves and the body in which they take place are, all the same, very much part of familiar space and time. Truly eluding space and time makes escaping your shadow a cakewalk.

  Nevertheless, many of today's leading physicists suspect that space and time, although pervasive, may not be truly fundamental. Just as the hardness of a cannonball emerges from the collective properties of its atoms, and just as the smell of a rose emerges from the collective properties of its molecules, and just as the swiftness of a cheetah emerges from the collective properties of its muscles, nerves, and bones, so too, the properties of space and time—our preoccupation for much of this book— may also emerge from the collective behavior of some other, more fundamental constituents, which we've yet to identify.

  Physicists sometimes sum up this possibility by saying that spacetime may be an illusion—a provocative depiction, but one whose meaning requires proper interpretation. After all, if you were to be hit by a speeding cannonball, or inhale the alluring fragrance of a rose, or catch sight of a blisteringly fast cheetah, you wouldn't deny their existence simply because each is composed of finer, more basic entities. To the contrary, I think most of us would agree that these agglomerations of matter exist, and moreover, that there is much to be learned from studying how their familiar characteristics emerge from their atomic constituents. But because they are composites, what we wouldn't try to do is build a theory of the universe based on cannonballs, roses, or cheetahs. Similarly, if space and time turn out to be composite entities, it wouldn't mean that their familiar manifestations, from Newton's bucket to Einstein's gravity, are illusory; there is little doubt that space and time will retain their all-embracing positions in experiential reality, regardless of future developments in our understanding. Instead, composite spacetime would mean that an even more elemental description of the universe—one that is spaceless and timeless—has yet to be discovered. The illusion, then, would be one of our own making: the erroneous belief that the deepest understanding of the cosmos would bring space and time into the sharpest possible focus. Just as the hardness of a cannonball, the smell of the rose, and the speed of the cheetah disappear when you examine matter at the atomic and subatomic level, space and time may similarly dissolve when scrutinized with the most fundamental formulation of nature's laws.

  That spacetime may not be among the fundamental cosmic ingredients may strike you as somewhat far-fetched. And you may well be right. But rumors of spacetime's impending departure from deep physical law are not born of zany theorizing. Instead, this idea is strongly suggested by a number of well-reasoned considerations. Let's take a look at some of the most prominent.

  Quantum Averaging

  In Chapter 12 we discussed how the fabric of space, much like everything else in our quantum universe, is subject to the jitters of quantum uncertainty. It is these fluctuations, you'll recall, that run roughshod over point-particle theories, preventing them from providing a sensible quantum theory of gravity. By replacing point particles with loops and snippets, string theory spreads out the fluctuations—substantially reducing their magnitude—and this is how it yields a successful unification of quantum mechanics and general relativity. Nevertheless, the diminished spacetime fluctuations certainly still exist (as illustrated in the next-to-last level of magnification in Figure 12.2), and within them we can find important clues regarding the fate of spacetime.

  First, we learn that the familiar space and time that suffuse our thoughts and support our equations em
erge from a kind of averaging process. Think of the pixelated image you see when your face is a few inches from a television screen. This image is very different from what you see at a more comfortable distance, because once you can no longer resolve individual pixels, your eyes combine them into an average that looks smooth. But notice that it's only through the averaging process that the pixels produce a familiar, continuous image. In a similar vein, the microscopic structure of spacetime is riddled with random undulations, but we aren't directly aware of them because we lack the ability to resolve spacetime on such minute scales. Instead, our eyes, and even our most powerful equipment, combine the undulations into an average, much like what happens with television pixels. Because the undulations are random, there are typically as many "up" undulations in a small region as there are "down," so when averaged they tend to cancel out, yielding a placid spacetime. But, as in the television analogy, it's only because of the averaging process that a smooth and tranquil form for spacetime emerges.

  Quantum averaging provides a down-to-earth interpretation of the assertion that familiar spacetime may be illusory. Averages are useful for many purposes but, by design, they do not provide a sharp picture of underlying details. Although the average family in the U.S. has 2.2 children, you'd be in a bind were I to ask to visit such a family. And although the national average price for a gallon of milk is $2.783, you're unlikely to find a store selling it for exactly this price. So, too, familiar spacetime, itself the result of an averaging process, may not describe the details of something we'd want to call fundamental. Space and time may only be approximate, collective conceptions, extremely useful in analyzing the universe on all but ultramicroscopic scales, yet as illusory as a family with 2.2 children.