(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.
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
(email@example.com) 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,