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By Root 2129 0

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.

Finding the correct mathematical apparatus for formulating string theory without recourse to a pre-existing notion of space and time is one of the most important issues facing string theorists. An understanding of how space and time emerge would take us a huge step closer to answering the crucial question of which geometrical form actually does emerge.

Will String Theory Lead to a Reformulation of Quantum Mechanics?

The universe is governed by the principles of quantum mechanics to fantastic accuracy. Even so, in formulating theories over the past half century, physicists have followed a strategy that, structurally speaking, places quantum mechanics in a somewhat secondary position. In devising theories, physicists