Why Do We Reside in a Three-Dimensional Universe?

Andreas Karch (University of Washington) and Lisa Randall (Harvard) propose to explain why we live in three dimensions and not some other number. Currently, the popular string theory of matter holds that our universe is actually ten-dimensional, including, first of all, the dimension of time, then the three "large" dimensions we perceive as "space," plus six more dimensions that are difficult to see, perhaps because they are hidden in some way. There is reason to believe, therefore, that our common 3D space is but a portion of some membrane or "brane" within a much more complicated higher-dimensional reality. Specifically, Karch and Randall address themselves to the behavior of three-dimensional force laws, including the force of gravity. Having several dimensions rolled up is one way to explain why gravity if so weak.

Another view, pioneered by Randall and Raman Sundrum, holds that if gravity is localized on a 3D defect in the larger multi-dimensional universe and if spacetime is sufficiently warped, then the other spatial dimensions might be large after all. But why is our "local gravity" apparently a 3D defect in a 10D universe? Why not a 4D defect or some other dimensionality?

In the present paper, Karch (karch@feynman.phys.washington.edu) and Randall show that the cosmic evolution of the 10D universe, involving a steady dilution of matter, results in spacetime being populated chiefly by 3D and 7D branes. Several versions of string theories require the existence of 3D and 7D branes; indeed, the particles that constitute matter---such as quarks and electrons---can be considered open strings with one end planted on a 3D brane and the other end planted on a 7D brane.

Karch and Randall, Physical Review Letters, upcoming article