Free Warped Passages by Lisa Randall Page B

potentially dangerous—you wouldn’t want pieces of the universe to fall off the ends—there must be boundaries for the finite dimensions that tell them where and how to end. The question is, what happens to particles and energy when they reach these boundaries?
    The answer is that they encounter a brane. In a higher-dimensional world, branes would be the boundaries of the full higher-dimensional space, known as the bulk . Unlike a brane, the bulk extends in all directions. The bulk spans every dimension, both on and off the brane (see Figure 25). The bulk is therefore “bulky,” whereas, in comparison, the brane is flat (in some dimensions), like a pancake. If branes bordered the bulk in certain directions, some of the bulk’s dimensions would be parallel to the brane, while other dimensions would lead off it. If the brane is the boundary, the dimensions off the brane would extend only to one side.

Figure 25. A brane is a lower-dimensional surface with directions along it and directions that lead away from it, into the higher-dimensional bulk.
    To understand the nature of finite dimensions that end on branes, let us consider a very long thin pipe. Within the pipe there are three dimensions: one long and two short. To make the analogy to flat branes most straightforward, let’s imagine that our pipe has a square cross-section. An infinitely long pipe of this type would have four infinitely long straight walls. If the pipe were a universe in its ownright, it would be one with three dimensions, two of which are bounded on either side by walls and one that extends infinitely far.
    We know that a long thin pipe when viewed from afar (or with insufficient resolution) looks one-dimensional, much like the garden hose of the previous chapter. But we can also ask, as we did before with the garden-hose universe, how the pipe universe—consisting of the pipe and its interior—would appear to a conscious being living inside.
    As you might suspect, this would depend on the being’s resolution. A small fly that could move around within the square pipe would experience it as three-dimensional. Unlike the two-dimensional garden-hose example, we are assuming that the fly can move inside the pipe, and not just on its exterior. Nonetheless, as with the garden hose, the fly would experience the one long dimension differently than the other two. In one direction the fly could go arbitrarily far (assuming that our pipe is very long or infinite), whereas in the other two directions the fly could only go a short distance—the width of the pipe.
    But there is a difference between the garden-hose universe and the pipe universe, aside from the number of dimensions each has. Unlike the bug of the previous chapter, the fly in the pipe travels inside it. Thus the fly sometimes encounters walls. It can go back and forth, or up and down, and reach a boundary. The bug on the hose, on the other hand, would never reach such a boundary: instead, it would only go round and round.
    When the fly reaches the boundary of its pipe universe, there have to be rules that govern how it behaves. The walls of the pipe determine that behavior. The fly might hit the wall and splat into it; or the pipe might be reflective, so that the fly bounces off. If the pipe were a true universe bounded by branes, then the branes, which would be two-dimensional, would determine what happens when a particle, or anything else that could carry energy, reaches them.
    When things get to a boundary brane, they bounce back, just as billiard balls bounce from the edges of the table or light bounces back from a mirror. This is an example of what physicists call a reflective boundary condition . If things bounce back from a brane, energy is not lost; it doesn’t get absorbed in the branes or leak away. Nothing goes beyond the branes. The boundary branes are the “ends of the world.”

    In a multidimensional universe, branes serve the role of the boundary walls in the pipe-universe