Warped Passages - Lisa Randall [28]
There are many more familiar examples of things with restricted freedom of movement for which there are regions of space that are truly inaccessible. A charge on a wire and a bead on an abacus are both objects that live in a three-dimensional world, but travel in only one of its dimensions. There are also commonplace things that are confined to two-dimensional surfaces. Water droplets on a shower curtain travel only along the curtain’s two-dimensional surface (see Figure 26). Bacteria trapped between microscope slides also experience only two-dimensional motion. Another example is Sam Loyd’s “fifteen” game, the annoying game consisting of a little plastic tray with letters on tiles that you push around until they are correctly arranged in a square and say something like LOOK/YOUF/INIS/HED (see Figure 27). Unless you cheat, the letters stay within their plastic enclosure; they can never move in a third dimension.
Figure 26. Drops of water stuck on a two-dimensional shower curtain in a three-dimensional room.
Branes, like shower curtains and Loyd’s fifteen game, trap things on lower-dimensional surfaces. They introduce the possibility that in a world with additional dimensions, not all matter is free to travel everywhere. Just as the water droplets on the curtain are bound to a two-dimensional surface, particles or strings can be confined to a three-dimensional brane sitting inside a higher-dimensional world. But unlike the droplets on the curtain, they are truly trapped. And unlike the fifteen game, branes are not arbitrary. They are natural players in a higher-dimensional world.
Figure 27. Sam Loyd’s “fifteen” game.
Particles confined to branes are truly trapped on those branes by physical laws. Brane-bound objects never venture into the extra dimensions that extend off the brane. Not all particles will be trapped on branes; some particles might be free to travel throughout the bulk. But what distinguishes theories with branes from multidimensional theories without them are the particles on the branes—the ones that don’t travel through all the dimensions.
In principle, branes and the bulk could have any number of dimensions, so long as a brane never has more dimensions than the bulk. The dimensionality of a brane is the number of dimensions in which brane-confined particles are permitted to travel. Although there are many possibilities, the branes that will be most interesting to us later on will be the three-dimensional ones. We don’t know why three dimensions should appear to be so special. But branes with three spatial dimensions could be relevant to our world because they could extend along the three spatial dimensions we know. Such branes could appear in a bulk space with any number of dimensions that is more than three—four, five, or more dimensions.
Even if the universe does have many dimensions, if the particles and forces with which we are familiar are trapped on a brane that extends in three dimensions, they would still behave as if they lived in only three. Particles confined to branes would travel only along the brane. And if light were also stuck to the brane, light rays would spread out only along the brane. In a three-dimensional brane, light would behave exactly as it would in a truly three-dimensional universe.
Furthermore, forces trapped on a brane influence only particles confined to this same brane. The material of which we are composed, such as nuclei and electrons, and the forces through which these building blocks interact, such as the electric force, might be confined on a three-dimensional brane. Brane-bound forces would spread out only along their brane, and brane-bound particles would be exchanged and would travel solely along the dimensions of the brane.
So if you lived in such a three-dimensional brane, you would be able to travel freely along its dimensions, much as you do in three dimensions now. Anything confined within a three-dimensional