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

by Brian Greene

  In fact, Tom Banks of Rutgers University and Willy Fischler of the University of Texas at Austin, together with Leonard Susskind and Stephen Shenker, both now at Stanford, have formulated a version of string/M-theory in which zero-branes are the fundamental ingredients that can be combined to generate strings and the other, higher dimensional branes. This proposal, known as Matrix theory— still another possible meaning for the "M" in "M-theory"—has generated an avalanche of follow-up research, but the difficult mathematics involved has so far prevented scientists from bringing the approach to completion. Nevertheless, the calculations that physicists have managed to carry out in this framework seem to support the proposal. If Matrix theory is true, it might mean that everything—strings, branes, and perhaps even space and time themselves—is composed of appropriate aggregates of zero-branes. It's an exciting prospect, and researchers are cautiously optimistic that progress over the next few years will shed much light on its validity.

  We have so far surveyed the path string theorists have followed in the search for spacetime's ingredients, but as I mentioned, there is a second path coming from string theory's main competitor, loop quantum gravity. Loop quantum gravity dates from the mid-1980s and is another promising proposal for merging general relativity and quantum mechanics. I won't attempt a detailed description (if you're interested, take a look at Lee Smolin's excellent book Three Roads to Quantum Gravity ), but will instead mention a few key points that are particularly illuminating for our current discussion.

  String theory and loop quantum gravity both claim to have achieved the long-sought goal of providing a quantum theory of gravity, but they do so in very different ways. String theory grew out of the successful particle physics tradition that has for decades sought matter's elementary ingredients; to most early string researchers, gravity was a distant, secondary concern, at best. By contrast, loop quantum gravity grew out of a tradition tightly grounded in the general theory of relativity; to most practitioners of this approach, gravity has always been the main focus. A one-sentence comparison would hold that string theorists start with the small (quantum theory) and move to embrace the large (gravity), while adherents of loop quantum gravity start with the large (gravity) and move to embrace the small (quantum theory). 9 In fact, as we saw in Chapter 12, string theory was initially developed as a quantum theory of the strong nuclear force operating within atomic nuclei; it was realized only later, serendipitously, that the theory actually included gravity. Loop quantum gravity, on the other hand, takes Einstein's general relativity as its point of departure and seeks to incorporate quantum mechanics.

  This starting at opposite ends of the spectrum is mirrored in the ways the two theories have so far developed. To some extent, the main achievements of each prove to be the failings of the other. For example, string theory merges all forces and all matter, including gravity (a complete unification that eludes the loop approach), by describing everything in the language of vibrating strings. The particle of gravity, the graviton, is but one particular string vibrational pattern, and hence the theory naturally describes how these elemental bundles of gravity move and interact quantum mechanically. However, as just noted, the main failing of current formulations of string theory is that they presuppose a background spacetime within which strings move and vibrate. By contrast, the main achievement of loop quantum gravity—an impressive one—is that it does not assume a background spacetime. Loop quantum gravity is a background-independent framework. However, extracting ordinary space and time, as well as the familiar and successful features of general relativity when applied on large distance scales (something easily done with current formulations of string theory) from this extraordinarily unfamiliar spaceless/timeless starting point, is a far from trivial problem, which researchers are still trying to solve. Moreover, in comparison to string theory, loop quantum gravity has made far less progress in understanding the dynamics of gravitons.

  One harmonious possibility is that string enthusiasts and loop quantum gravity aficionados are actually constructing the same theory, but from vastly different starting points. That each theory involves loops—in string theory, these are string loops; in loop quantum gravity, they're harder to describe nonmathematically, but, roughly speaking, they're elementary loops of space—suggests there might be such a connection. This possibility is further supported by the fact that on the few problems accessible to both, such as black hole entropy, the two theories agree fully. 10 And, on the question of spacetime's constituents, both theories suggest that there is some kind of atomized structure. We've already seen the clues pointing toward this conclusion that arise from string theory; those coming from loop quantum gravity are compelling and even more explicit. Loop researchers have shown that numerous loops in loop quantum gravity can be interwoven, somewhat like tiny wool loops crocheted into a sweater, and produce structures that seem, on larger scales, to approximate regions of spacetime. Most convincing of all, loop researchers have calculated the allowed areas of such surfaces of space. And just as you can have one electron or two electrons or 202 electrons, but you can't have 1.6 electrons or any other fraction, the calculations show that surfaces can have areas that are one square Planck-length, or two square Planck-lengths, or 202 square Planck-lengths, but no fractions are possible. Once again, this is a strong theoretical clue that space, like electrons, comes in discrete, indivisible chunks. 11

  If I were to hazard a guess on future developments, I'd imagine that the background-independent techniques developed by the loop quantum gravity community will be adapted to string theory, paving the way for a string formulation that is background independent. And that's the spark, I suspect, that will ignite a third superstring revolution in which, I'm optimistic, many of the remaining deep mysteries will be solved. Such developments would likely also bring spacetime's long story full circle. In earlier chapters, we followed the pendulum of opinion as it swung between relationist and absolutist positions on space, time, and spacetime. We asked: Is space a something, or isn't it? Is spacetime a something, or isn't it? And, over the course of a few centuries' thought, we encountered differing views. I believe that an experimentally confirmed, background-independent union between general relativity and quantum mechanics would yield a gratifying resolution to this issue. By virtue of the background independence, the theory's ingredients might stand in some relation to one another, but with the absence of a spacetime that is inserted into the theory from the outset, there'd be no background arena in which they were themselves embedded. Only relative relationships would matter, a solution much in the spirit of relationists like Leibniz and Mach. Then, as the theory's ingredients—be they strings, branes, loops, or something else discovered in the course of future research—coalesced to produce a familiar, large-scale spacetime (either our real spacetime or hypothetical examples useful for thought experiments), its being a "something" would be recovered, much as in our earlier discussion of general relativity: in an otherwise empty, flat, infinite spacetime (one of the useful hypothetical examples), the water in Newton's spinning bucket would take on a concave shape. The essential point would be that the distinction between spacetime and more tangible material entities would largely evaporate, as they would both emerge from appropriate aggregates of more basic ingredients in a theory that's fundamentally relational, spaceless, and timeless. If this is how it turns out, Leibniz, Newton, Mach, and Einstein could all claim a share of the victory.

  Inner and Outer Space

  Speculating about the future of science is an entertaining and constructive exercise. It places our current undertakings in a broader context, and emphasizes the overarching goals toward which we are slowly and deliberately working. But when such speculation turns to the future of spacetime itself, it takes on an almost mystical quality: we're considering the fate of the very things that dominate our sense of reality. Again, there is no question that regardless of future discoveries, space and time will continue to frame our individual experience; space and time, as far a
s everyday life goes, are here to stay. What will continue to change, and likely change drastically, is our understanding of the framework they provide— the arena, that is, of experiential reality. After centuries of thought, we still can only portray space and time as the most familiar of strangers. They unabashedly wend their way through our lives, but adroitly conceal their fundamental makeup from the very perceptions they so fully inform and influence.

  Over the last century, we've become intimately acquainted with some previously hidden features of space and time through Einstein's two theories of relativity and through quantum mechanics. The slowing of time, the relativity of simultaneity, alternative slicings of spacetime, gravity as the warping and curving of space and time, the probabilistic nature of reality, and long-range quantum entanglement were not on the list of things that even the best of the world's nineteenth-century physicists would have expected to find just around the corner. And yet there they were, as attested to by both experimental results and theoretical explanations.

  In our age, we've come upon our own panoply of unexpected ideas: Dark matter and dark energy that appear to be, far and away, the dominant constituents of the universe. Gravitational waves—ripples in the fabric of spacetime—which were predicted by Einstein's general relativity and may one day allow us to peek farther back in time than ever before. A Higgs ocean, which permeates all of space and which, if confirmed, will help us to understand how particles acquire mass. Inflationary expansion, which may explain the shape of the cosmos, resolve the puzzle of why it's so uniform on large scales, and set the direction to time's arrow. String theory, which posits loops and snippets of energy in place of point particles and promises a bold version of Einstein's dream in which all particles and all forces are combined into a single theory. Extra space dimensions, emerging from the mathematics of string theory, and possibly detectable in accelerator experiments during the next decade. A braneworld, in which our three space dimensions may be but one universe among many, floating in a higher-dimensional spacetime. And perhaps even emergent spacetime, in which the very fabric of space and time is composed of more fundamental spaceless and timeless entities.

  During the next decade, ever more powerful accelerators will provide much-needed experimental input, and many physicists are confident that data gathered from the highly energetic collisions that are planned will confirm a number of these pivotal theoretical constructs. I share this enthusiasm and eagerly await the results. Until our theories make contact with observable, testable phenomena, they remain in limbo—they remain promising collections of ideas that may or may not have relevance for the real world. The new accelerators will advance the overlap between theory and experiment substantially, and, we physicists hope, will usher many of these ideas into the realm of established science.

  But there is another approach that, while more of a long shot, fills me with incomparable wonderment. In Chapter 11 we discussed how the effects of tiny quantum jitters can be seen in any clear night sky since they're stretched enormously by cosmic expansion, resulting in clumps that seed the formation of stars and galaxies. (Recall the analogy of tiny scribbles, drawn on a balloon, that are stretched across its surface when the balloon is inflated.) This realization demonstrably gives access to quantum physics through astronomical observations. Perhaps it can be pushed even further. Perhaps cosmic expansion can stretch the imprints of even shorter-scale processes or features—the physics of strings, or quantum gravity more generally, or the atomized structure of ultramicroscopic spacetime itself—and spread their influence, in some subtle but observable manner, across the heavens. Maybe, that is, the universe has already drawn out the microscopic fibers of the fabric of the cosmos and unfurled them clear across the sky, and all we need do is learn how to recognize the pattern.

  Assessing cutting-edge proposals for deep physical laws may well require the ferocious might of particle accelerators able to re-create violent conditions unseen since moments after the big bang. But for me, there would be nothing more poetic, no outcome more graceful, no unification more complete, than for us to confirm our theories of the ultrasmall—our theories about the ultramicroscopic makeup of space, time, and matter—by turning our most powerful telescopes skyward and gazing silently at the stars.

  Endnotes

  1 The terms centrifugal and centripetal force are sometimes used when describing spinning motion. But they are merely labels. Our intent is to understand why spinning motion gives rise to force.

  2 There is debate concerning Mach's precise views on the material that follows. Some of his writings are a bit ambiguous and some of the ideas attributed to him arose from subsequent interpretations of his work. Since he seems to have been aware of these interpretations and never offered corrections, some have suggested that he agreed with their conclusions. But historical accuracy might be better served if every time I write "Mach argued" or "Mach's ideas," you read it to mean "the prevailing interpretation of an approach initiated by Mach."

  3 While I like human examples because they make an immediate connection between the physics we're discussing and innate sensations, a drawback is our ability to move, volitionally, one part of our body relative to another—in effect, to use one part of our body as the benchmark for another part's motion (like someone who spins one of his arms relative to his head). I emphasize uniform spinning motion—spinning motion in which every part of the body spins together—to avoid such irrelevant complications. So, when I talk about your body's spinning, imagine that, like Newton's two rocks tied by a rope or a skater in the final moments of an Olympic routine, every part of your body spins at the same rate as every other.

  4 Like the pages in any flip book, the pages in Figure 3.3 only show representative moments of time. This may suggest to you the interesting question of whether time is discrete or infinitely divisible. We'll come back to that question later, but for now imagine that time is infinitely divisible, so our flip book really should have an infinite number of pages interpolating between those shown.

  5 It's easier to picture warped space, but because of their intimate connection, time is also warped by matter and energy. And just as a warp in space means that space is stretched or compressed, as in Figure 3.10, a warp in time means that time is stretched or compressed. That is, clocks experiencing different gravitational pulls—like one on the sun and another in deep, empty space—tick off time at different rates. In fact, it turns out that the warping of space caused by ordinary bodies like the earth and sun (as opposed to black holes) is far less pronounced than the warping they inflict on time. 15

  6 In special relativity—the special case of general relativity in which the gravitational field is zero—this idea applies unchanged: a zero gravitational field is still a field, one that can be measured and changed, and hence provides a something relative to which acceleration can be defined.

  7 To avoid linguistic complications, I'm describing the electron spins as perfectly correlated, even though the more conventional description is one in which they're perfectly anti correlated: whatever result one detector finds, the other will find the opposite. To compare with the conventional description, imagine that I've interchanged all the clockwise and counterclockwise labels on one of the detectors.

  8 Many researchers, including me, believe that Bell's argument and Aspect's experiment establish convincingly that the observed correlations between widely separated particles cannot be explained by Scully-type reasoning—reasoning that attributes the correlations to nothing more surprising than the particles' having acquired definite, correlated properties when they were (previously) together. Others have sought to evade or lessen the stunning nonlocality conclusion to which this has led us. I don't share their skepticism, but some works for general readers that discuss some of these alternatives are cited in the note section.15

  9 Pick any point in the loaf. Draw a slice that includes the point, and which intersects our current now-slice at an angle that is less than 45 degrees. This slice will represen
t the now-slice —reality— of a distant observer who was initially at rest relative to us, like Chewie, but is now moving relative to us at less than the speed of light. By design, this slice includes the (arbitrary) point in the loaf you happened to pick. 4

  10 There is an exception to this statement having to do with a certain class of exotic particles. As far as the questions discussed in this chapter are concerned, I consider this likely to be of little relevance and so won't mention this qualification further. If you are interested, it is briefly discussed in note 2.

  11 Note that time-reversal symmetry is not about time itself being reversed or "running" backward. Instead, as we've described, time-reversal symmetry is concerned with whether events that happen in time, in one particular temporal order, can also happen in the reverse order. A more appropriate phrase might be event reversal or process reversal or event order reversal, but we'll stick with the conventional term.

  12 Entropy is another example in which terminology complicates ideas. Don't worry if you have to remind yourself repeatedly that low entropy means high order and that high entropy means low order (equivalently, high disorder). I often have to.