Number 745, September 15, 2005
by Phil Schewe and Ben Stein
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.
The tendency for certain floating things
to clump under the action of surface tension---things such as
Cheerios cereal bits in your breakfast bowl, bubbles in a glass of
beer, pepper flakes on water, even strands of hair up against a
washbasin---has important potential engineering implications, such
as for the design of self-assembling circuits and devices.
Study of
the clumping phenomenon has a long history. For example, an
excellent summary was prepared by no less than James Clerk Maxwell
for the Encyclopedia Britannica as long ago as 1875. Now a Harvard
professor, Lakshminarayanan Mahadevan, and an undergraduate student,
Dominic Vella (now a graduate student at Cambridge University),
have taken up the subject and written a pedagogical review, hoping
to rescue the subject from the obscuring algebraic complexity that
has settled around it (as Mahadevan argues) and concentrate on the
pertinent relatively simple physics principles. They emphasize that
contrary to general belief, chemical interactions are oftentimes
not paramount in determining whether clumping
occurs; instead a simple equilibrium of forces and
torques---including things such as buoyancy and surface
tension---are the deciding factors.
Even objects denser than water
can float if the geometry is right: See
this picture of a floating
thumbtack. Even more interestingly, one can control the strength
and sign of this interaction; indeed, there are indications that
insects that live on the air-water interface might even use this
effect to great advantage.
Vella and Mahadevan, American Journal
of Physics, September 2005
Contact: lm@deas.harvard.edu
Also see lab's website
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