Warped Passages - Lisa Randall [27]
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 example above. Like walls, such branes would have lower dimension than the full space; a boundary always has a lower dimension than the object it bounds. That is as true for the boundary of space as it is for the crust that is the boundary of a loaf of bread. It is also true for the walls in your house, which have one lower dimension than the room they enclose: the room is three-dimensional, whereas any individual wall (when we ignore its thickness) spans only two dimensions.
Although so far in this section I have concentrated on branes that sit at boundaries, branes don’t always sit at the edge of the bulk. They could conceivably exist anywhere in space. In particular, branes might sit somewhere away from the boundary, inside of space. If a boundary brane is like a thin heel at the end of a loaf of bread, such a non-boundary brane would be like a thin slice of bread within the loaf. A non-boundary brane would still be a lower-dimensional object, like the ones we have already considered. But non-boundary branes would have higher-dimensional bulk space on either side.
In the next section, we’ll see that whatever the number of dimensions of the bulk or of the brane, and no matter whether branes are inside a space or at a boundary, branes can trap particles and forces along them. This makes the region of space they occupy very special.
Trapped on Branes
It is very unlikely that you will explore all the space available to you. There are probably places that you wish you had visited and voyages you’ll never take—into outer space or the depths of the sea, for example. You haven’t been to these places, but, in principle, you could go. There is no physical law that makes it impossible.
If, however, you lived inside a black hole, your travel opportunities would be far more severely constrained, more restricted even than those of women in Saudi Arabia. The black hole (until it decayed