The Elegant Universe (53 page)

Although we are still feeling the aftershocks of the second superstring revolution and absorbing the panoply of new insights that it has engendered, most string theorists agree that it will likely take a third and maybe a fourth such theoretical upheaval before the full power of string theory is unleashed and its possible role as the final theory assessed. As we have seen, string theory has already painted a remarkable new picture of how the universe works, but there are significant hurdles and loose ends that will no doubt be the primary focus of string theorists in the twenty-first century. And so, in this last chapter we will not be able to finish telling the story of humanity’s search for the deepest laws of the universe, because the search continues. Instead, let’s guide our gaze into the future of string theory by discussing five central questions string theorists will face as they continue the pursuit of the ultimate theory.

What Is the Fundamental Principle Underlying String Theory?

One overarching lesson we have learned during the past hundred years is that the known laws of physics are associated with principles of symmetry. Special relativity is based on the symmetry embodied in the principle of relativity—the symmetry between all constant-velocity vantage points. The gravitational force, as embodied in the general theory of relativity, is based on the equivalence principle—the extension of the principle of relativity to embrace all possible vantage points regardless of the complexity of their states of motion. And the strong, weak, and electromagnetic forces are based on the more abstract gauge symmetry principles.

Physicists, as we have discussed, tend to elevate symmetry principles to a place of prominence by putting them squarely on the pedestal of explanation. Gravity, in this view, exists in order that all possible observational vantage points are on completely equal footing—i.e., so that the equivalence principle holds. Similarly, the nongravitational forces exist in order that nature respect their associated gauge symmetries. Of course, this approach shifts the question of why a certain force exists to why nature respects its associated symmetry principle. But this certainly feels like progress, especially when the symmetry in question is one that seems eminently natural. For example, why should one observer’s frame of reference be treated differently from another’s? It seems far more natural for the laws of the universe to treat all observational vantage points equally; this is accomplished through the equivalence principle and the introduction of gravity into the structure of the cosmos. Although it requires some mathematical background to appreciate fully, as we indicated in Chapter 5, there is a similar rationale behind the gauge symmetries underlying the three nongravitational forces.

String theory takes us down another notch on the scale of explanatory depth because all of these symmetry principles, as well as another—supersymmetry—emerge from its structure. In fact, had history followed a different course—and had physicists come upon string theory some hundred years earlier—we can imagine that these symmetry principles would have all been discovered by studying its properties. But bear in mind that whereas the equivalence principle gives us some understanding of why gravity exists, and the gauge symmetries give us some sense of why the nongravitational forces exist, in the context of string theory these symmetries are consequences; although their importance is in no way diminished, they are part of the end product of a much larger theoretical structure.

This discussion brings the following question into sharp relief: Is string theory itself an inevitable consequence of some broader principle—possibly but not necessarily a symmetry principle—in much the same way that the equivalence principle inexorably leads to general relativity or that gauge symmetries lead to the nongravitational forces? As of this writing, no one has any insight into the answer to this question. To appreciate its importance, we need only imagine Einstein trying to formulate general relativity without having had the happy thought he experienced in the Bern patent office in 1907 that led him to the principle of equivalence. It would not have been impossible to formulate general relativity without first having this key insight, but it certainly would have been extremely difficult. The equivalence principle provides a succinct, systematic, and powerful organizational framework for analyzing the gravitational force. The description of general relativity we gave in Chapter 3, for example, relied centrally on the equivalence principle, and its role in the full mathematical formalism of the theory is even more crucial.

Currently, string theorists are in a position analogous to an Einstein bereft of the equivalence principle. Since Veneziano’s insightful guess in 1968, the theory has been pieced together, discovery by discovery, revolution by revolution. But a central organizing principle that embraces these discoveries and all other features of the theory within one overarching and systematic framework—a framework that makes the existence of each individual ingredient absolutely inevitable—is still missing. The discovery of this principle would mark a pivotal moment in the development of string theory, as it would likely expose the theory’s inner workings with unforeseen clarity There is, of course, no guarantee that such a fundamental principle exists, but the evolution of physics during the last hundred years encourages string theorists to have high hopes that it does. As we look to the next stage in the development of string theory, finding its “principle of inevitability”—that underlying idea from which the whole theory necessarily springs forth—is of the highest priority.2

What Are Space and Time, Really, and Can We Do without Them?

In many of the preceding chapters, we have freely made use of the concepts of space and of spacetime. In Chapter 2 we described Einstein’s realization that space and time are inextricably interwoven by the unexpected fact that an object’s motion through space has an influence on its passage through time. In Chapter 3, we deepened our understanding of spacetime’s role in the unfolding of the cosmos through general relativity, which shows that the detailed shape of the spacetime fabric communicates the force of gravity from one place to another. The violent quantum undulations in the microscopic structure of the fabric, as discussed in Chapters 4 and 5, established the need for a new theory, leading us to string theory. And finally, in a number of the chapters that followed, we have seen that string theory proclaims that the universe has many more dimensions than we are aware of, some of which are curled up into tiny but complicated shapes that can undergo wondrous transformations in which their fabric punctures, tears, and then repairs itself.

Through graphic representations such as Figures 3.4, 3.6, and 8.10, we have tried to illustrate these ideas by envisioning the fabric of space and spacetime as if it were somewhat like a piece of material out of which the universe is tailored. These images have considerable explanatory power; they are used regularly by physicists as a visual guide in their own technical work. Although staring at figures such as the ones just mentioned gives a gradual impression of meaning, one can still be left asking, What do we really mean by the fabric of the universe?

This is a profound question that has, in one form or another, been the subject of debate for hundreds of years. Newton declared space and time to be eternal and immutable ingredients in the makeup of the cosmos, pristine structures lying beyond the bounds of question and explanation. As he wrote in the Principia, “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external.”3 Gottfried Leibniz and others vociferously disagreed, claiming that space and time are merely bookkeeping devices for conveniently summarizing relationships between objects and events within the universe. The location of an object in space and in time has meaning only in comparison with another. Space and time are the vocabulary of these relations, but nothing more. Although Newton’s view, supported by his experimentally successful three laws of motion, held sway for more than two hundred years, Leibniz’s conception, further developed by the Austrian physicist Ernst Mach, is much closer to our current picture. As we have seen, Einstein’s special and general theories of relativity firmly did away with the concept of an absolute and universal notion of space and time. But we can still ask whether the geometrical model of spacetime that plays such a pivotal role in general relativity and in string theory is solely a convenient shorthand for the spatial and temporal relations between various locations, or whether we should view ourselves as truly being embedded in something when we refer to our immersion within the spacetime fabric.

Although we are heading into speculative territory, string theory does suggest an answer to this question. The graviton, the smallest bundle of gravitational force, is one particular pattern of string vibration. And just as an electromagnetic field such as visible light is composed of an enormous number of photons, a gravitational field is composed of an enormous number of gravitons—that is, an enormous number of strings executing the graviton vibrational pattern. Gravitational fields, in turn, are encoded in the warping of the spacetime fabric, and hence we are led to identify the fabric of spacetime itself with a colossal number of strings all undergoing the same, orderly, graviton pattern of vibration. In the language of the field, such an enormous, organized array of similarly vibrating strings is known as a coherent state of strings. It’s a rather poetic image—the strings of string theory as the threads of the spacetime fabric—but we should note that its rigorous meaning has yet to be worked out completely.

Nevertheless, describing the spacetime fabric in this string-stitched form does lead us to contemplate the following question. An ordinary piece of fabric is the end product of someone having carefully woven together individual threads, the raw material of common textiles. Similarly, we can ask ourselves whether there is a raw precursor to the fabric of spacetime—a configuration of the strings of the cosmic fabric in which they have not yet coalesced into the organized form that we recognize as spacetime. Notice that it is somewhat inaccurate to picture this state as a jumbled mass of individual vibrating strings that have yet to stitch themselves together into an ordered whole because, in our usual way of thinking, this presupposes a notion of both space and time—the space in which a string vibrates and the progression of time that allows us to follow its changes in shape from one moment to the next. But in the raw state, before the strings that make up the cosmic fabric engage in the orderly, coherent vibrational dance we are discussing, there is no realization of space or time. Even our language is too coarse to handle these ideas, for, in fact, there is even no notion of before. In a sense, it’s as if individual strings are “shards” of space and time, and only when they appropriately undergo sympathetic vibrations do the conventional notions of space and time emerge.

Imagining such a structureless, primal state of existence, one in which there is no notion of space or time as we know it, pushes most people’s powers of comprehension to their limit (it certainly pushes mine). Like the Stephen Wright one-liner about the photographer who is obsessed with getting a close-up shot of the horizon, we run up against a clash of paradigms when we try to envision a universe that is, but that somehow does not invoke the concepts of space or time. Nevertheless, it is likely that we will need to come to terms with such ideas and understand their implementation before we can fully assess string theory. The reason is that our present formulation of string theory presupposes the existence of space and time within which strings (and the other ingredients found in M-theory) move about and vibrate. This allows us to deduce the physical properties of string theory in a universe with one time dimension, a certain number of extended space dimensions (usually taken to be three), and additional dimensions that are curled up into one of the shapes allowed by the equations of the theory. But this is somewhat like assessing an artist’s creative talent by requiring that she work from a paint-by-number kit. She will, undoubtedly, add a personal flair here or there, but by so tightly constraining the format of her work, we are blinding ourselves to all but a slender view of her abilities. Similarly, since the triumph of string theory is its natural incorporation of quantum mechanics and gravity, and since gravity is bound up with the form of space and time, we should not constrain the theory by forcing it to operate within an already existing spacetime framework. Rather, just as we should allow our artist to work from a blank canvas, we should allow string theory to create its own spacetime arena by starting in a spaceless and timeless configuration.

The hope is that from this blank slate starting point—possibly in an era that existed before the big bang or the pre-big bang (if we can use temporal terms, for lack of any other linguistic framework)—the theory will describe a universe that evolves to a form in which a background of coherent string vibrations emerges, yielding the conventional notions of space and time. Such a framework, if realized, would show that space, time, and, by association, dimension are not essential defining elements of the universe. Rather, they are convenient notions that emerge from a more basic, atavistic, and primary state.

Already, cutting-edge research on aspects of M-theory, spearheaded by Stephen Shenker, Edward Witten, Tom Banks, Willy Fischler, Leonard Susskind, and others too numerous to name, has shown that something known as a zero-brane—possibly the most fundamental ingredient in M-theory, an object that behaves somewhat like a point particle at large distances but has drastically different properties at short ones—may give us a glimpse of the spaceless and timeless realm. Their work has revealed that whereas strings show us that conventional notions of space cease to have relevance below the Planck scale, the zero-branes give essentially the same conclusion but also provide a tiny window on the new unconventional framework that takes over. Studies with these zero-branes indicate that ordinary geometry is replaced by something known as noncommutative geometry, an area of mathematics developed in large part by the French mathematician Alain Connes.4 In this geometrical framework, the conventional notions of space and of distance between points melt away, leaving us in a vastly different conceptual landscape. Nevertheless, as we focus our attention on scales larger than the Planck length, physicists have shown that our conventional notion of space does re-emerge. It is likely that the framework of noncommutative geometry is still some significant steps away from the blank-slate state anticipated above, but it does give us a hint of what the more complete framework for incorporating space and time may involve.