This is how things stood in the world of extra dimensions until very recently. It was thought that extra dimensions might be present but that they would be extremely small. But our expectations changed dramatically after 1995, when Joe Polchinski, of the University of California at Santa Barbara, and other theorists recognized the importance of additional objects in string theory called branes. Branes are essentially membranes—lower-dimensional objects in a higher-dimensional space. (To picture this, think of a shower curtain, virtually a two-dimensional object in a three-dimensional space.) Branes are special, particularly in the context of string theory, because there's a natural mechanism to confine particles to the brane; thus not everything need travel in the extra dimensions even if those dimensions exist. Particles confined to the brane would have momentum and motion only along the brane, like water spots on the surface of your shower curtain.

Branes allow for an entirely new set of possibilities in the physics of extra dimensions, because particles confined to the brane would look more or less as they would in a three-plus-one-dimension world; they never venture beyond it. Protons, electrons, quarks, all sorts of fundamental particles could be stuck on the brane. In that case, you may wonder why we should care about extra dimensions at all, since despite their existence the particles that make up our world do not traverse them. However, although all known standard-model particles stick to the brane, this is not true of gravity. The mechanisms for confining particles and forces mediated by the photon or electrogauge proton to the brane do not apply to gravity. Gravity, according to the theory of general relativity, must necessarily exist in the full geometry of space. Furthermore, a consistent gravitational theory requires that the graviton, the particle that mediates gravity, has to couple to any source of energy, whether that source is confined to the brane or not. Therefore, the graviton would also have to be out there in the region encompassing the full geometry of higher dimensions—a region known as the bulk—because there might be sources of energy there. Finally, there is a string-theory explanation of why the graviton is not stuck to any brane: The graviton is associated with the closed string, and only open strings can be anchored to a brane.

A scenario in which particles are confined to a brane and only gravity is sensitive to the additional dimensions permits extra dimensions that are considerably larger than previously thought. The reason is that gravity is not nearly as well tested as other forces, and if it is only gravity that experiences extra dimensions, the constraints are much more permissive. We haven't studied gravity as well as we've studied most other particles, because it's an extremely weak force and therefore more difficult to precisely test. Physicists have showed that even dimensions almost as big as a millimeter would be permitted, if it were only gravity out in the higher-dimensional bulk. This size is huge compared with the scales we've been talking about. It is a macroscopic, visible size! But because photons (which we see with) are stuck to the brane, too, the dimensions would not be visible to us, at least in the conventional ways.

Once branes are included in the picture, you can start talking about crazily large extra dimensions. If the extra dimensions are very large, that might explain why gravity is so weak. (Gravity might not seem weak to you, but it's the entire earth that's pulling you down; the result of coupling an individual graviton to an individual particle is quite small. From the point of view of particle physics, which looks at the interactions of individual particles, gravity is an extremely weak force.) This weakness of gravity is a reformulation of the so-called hierarchy problem—that is, why the huge Planck mass suppressing gravitational interactions is sixteen orders of magnitude bigger than the mass associated with particles we see. But if gravity is spread out over large extra dimensions, its force would indeed be diluted. The gravitational field would spread out in the extra dimensions and consequently be very weak on the brane—an idea recently proposed by theorists Nima Arkani Hamed, Savas Dimopoulos, and Gia Dvali. The problem with this scenario is the difficulty of explaining why the dimensions should be so large. The problem of the large ratio of masses is transmuted into the problem of the large size of curled-up dimensions.

Raman Sundrum, currently at Johns Hopkins University, and I recognized that a more natural explanation for the weakness of gravity could be the direct result of the gravitational attraction associated with the brane itself. In addition to trapping particles, branes carry energy. We showed that from the perspective of general relativity this means that the brane curves the space around it, changing gravity in its vicinity. When the energy in space is correlated with the energy on the brane so that a large flat three-dimensional brane sits in the higher-dimensional space, the graviton (the particle communicating the gravitational force) is highly attracted to the brane. Rather than spreading uniformly in an extra dimension, gravity stays localized, very close to the brane.