The Fabric of the Cosmos: Space, Time, and the Texture of Reality (62 page)

Throughout this book we have periodically alluded to the ultramicroscopic constituents of spacetime, but although we've given indirect arguments for their existence we've yet to say anything about what these constituents might actually be. And for good reason. We really have no idea what they are. Or, perhaps I should say, when it comes to identifying spacetime's elemental ingredients, we have no ideas about which we're really confident. This is a major gap in our understanding, but it's worthwhile to see the problem in its historical context.

Were you to have polled scientists in the late nineteenth century about their views on matter's elementary constituents, you wouldn't have found universal agreement. A mere century ago, the atomic hypothesis was controversial; there were well-known scientists—Ernst Mach was one—who thought it wrong. Moreover, ever since the atomic hypothesis received widespread acceptance in the early part of the twentieth century, scientists have been continuously updating the picture it supplies with what are believed to be ever more elementary ingredients (for example, first protons and neutrons, then quarks). String theory is the latest step along this path, but because it has yet to be confirmed experimentally (and even if it were, that wouldn't preclude the existence of a yet more refined theory awaiting development), we must forthrightly acknowledge that the search for nature's basic material constituents continues.

The incorporation of space and time into a modern scientific context goes back to Newton in the 1600s, but serious thought regarding their microscopic makeup required the twentieth-century discoveries of general relativity and quantum mechanics. Thus, on historical time scales, we've really only just begun to analyze spacetime, so the lack of a definitive proposal for its "atoms"—spacetime's most elementary constituents— is not a black mark on the subject. Far from it. That we've gotten as far as we have—that we've revealed numerous features of space and time vastly beyond common experience—attests to progress unfathomable a century ago. The search for the most fundamental of nature's ingredients, whether of matter or of spacetime, is a formidable challenge that will likely occupy us for some time to come.

For spacetime, there are currently two promising directions in the search for elementary constituents. One proposal comes from string theory and the other from a theory known as
loop quantum gravity.

String theory's proposal, depending on how hard you think about it, is either intuitively pleasing or thoroughly baffling. Since we speak of the "fabric" of spacetime, the suggestion goes, maybe spacetime is stitched out of strings much as a shirt is stitched out of thread. That is, much as joining numerous threads together in an appropriate pattern produces a shirt's fabric, maybe joining numerous strings together in an appropriate pattern produces what we commonly call spacetime's fabric. Matter, like you and me, would then amount to additional agglomerations of vibrating strings—like sonorous music played over a muted din, or an elaborate pattern embroidered on a plain piece of material—moving within the context stitched together by the strings of spacetime.

I find this an attractive and compelling proposal, but as yet no one has turned these words into a precise mathematical statement. As far as I can tell, the obstacles to doing so are far from trifling. For instance, if your shirt completely unraveled you'd be left with a pile of thread—an outcome that, depending on circumstances, you might find embarrassing or irritating, although probably not deeply mysterious. But it thoroughly taxes the mind (my mind, at least) to think about the analogous situation with strings—the threads of spacetime in this proposal. What would we make of a "pile" of strings that had unraveled from the spacetime fabric or, perhaps more to the point, had not yet even joined together to produce the spacetime fabric? The temptation might be to think of them much as we do the shirt's thread—as raw material that needs to be stitched together—but that glosses over an absolutely essential subtlety. We picture strings as vibrating in space and through time, but without the spacetime fabric that the strings are themselves imagined to yield through their orderly union,
there is no space or time.
In this proposal, the concepts of space and time fail to have meaning until innumerable strings weave together to produce them.

Thus, to make sense of this proposal, we would need a framework for describing strings that does not assume from the get-go that they are vibrating in a preexisting spacetime. We would need a fully spaceless and timeless formulation of string theory, in which spacetime emerges from the collective behavior of strings.

Although there has been progress toward this goal, no one has yet come up with such a spaceless and timeless formulation of string theory—something that physicists call a
background-independent
formulation (the term comes from the loose notion of spacetime as a backdrop against which physical phenomena take place). Instead, essentially all approaches envision strings as moving and vibrating through a spacetime that is inserted into the theory "by hand"; spacetime does not emerge from the theory, as physicists imagine it would in a background-independent framework, but is supplied to the theory by the theorist. Many researchers consider the development of a background-independent formulation to be the single greatest unsolved problem facing string theory. Not only would it give insight into the origin of spacetime, but a background-independent framework would likely be instrumental in resolving the major hang-up encountered at the end of Chapter 12—the theory's current inability to select the geometrical form of the extra dimensions. Once its basic mathematical formalism is disentangled from any particular spacetime, the reasoning goes, string theory should have the capacity to survey all possibilities and perhaps adjudicate among them.

Another difficulty facing the strings-as-threads-of-spacetime proposal is that, as we learned in Chapter 13, string theory has other ingredients besides strings. What role do these other components play in spacetime's fundamental makeup? This question is brought into especially sharp relief by the braneworld scenario. If the three-dimensional space we experience is a three-brane, is the brane itself indecomposable or is it made from combining the theory's other ingredients? Are branes, for example, made from strings, or are branes and strings both elementary? Or should we consider yet another possibility, that branes and strings might be made from some yet finer ingredients? These questions are at the forefront of current research, but since this final chapter is about hints and clues, let me note one relevant insight that has garnered much attention.

Earlier, we talked about the various branes one finds in string/M-THEORY: one-branes, two-branes, three-branes, four-branes, and so on. Although I didn't stress it earlier, the theory also contains
zero-branes—
ingredients that have no spatial extent, much like point particles. This might seem counter to the whole spirit of string/M-theory, which moved away from the point-particle framework in an effort to tame the wild undulations of quantum gravity. However, the zero-branes, just like their higher dimensional cousins in Figure 13.2, come with strings attached, literally, and hence their interactions are governed by strings. Not surprisingly, then, zero-branes behave very differently from conventional point particles, and, most important, they participate fully in the spreading out and lessening of ultramicroscopic spacetime jitters; zero-branes do not reintroduce the fatal flaws afflicting point-particle schemes that attempt to merge quantum mechanics and general relativity.

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.