Perhaps Chris can delete the above anonymous clone of my following post...
As a "starter", I can recommend reading ziggy's and my post in
Apparently, my "Help! My Unicorn run away" thread has meanwhile managed to run away
both from CelestiaUsers and the Purgatory;-). Let's see where it will end...
Since, after redemption of the 'Unicorn' from Purgatory
, the above angel turned out to have obviously male gender, I preferred to rank a little plant around his waist in order not to endanger our many very young readers;-)
Contemplations on Extra Dimensions
Let us get back to this most basic question of extra dimensions, but forget about the specific framework within string theory that I touched upon further up in this thread...
There exists a "lore" that convinces us that we live in
3 space + 1 time = 4 dimensions.
We also believe that these 4 dimensions are "non-compact".
: While an infinite
line is a simple "non-compact"
manifold, we may simply arrive at its compactified
its +infinity and -infinity ends such as to make a
of it! So the simplest "role models" for compact
spaces are always n-dimensional spheres, starting with the circle]
Once we are ready to contemplate about more than 4 spacetime
dimensions, we should be immediately overwhelmed by some most basic,
Why on earth, are we then living in 4=3+1 and not in
5, 6 or 8 dimensions?? Is perhaps our very existence intrinsically
coupled to the number of dimensions being exactly 4? Why does there
only seem to be one time
and not perhaps two or more? [ In relativity,
the time dimension is treated on exactly the same footing as space dimensions]
The answers to all those most fundamental questions are still pending,
but the quest for them makes people work very hard indeed...Recently
we might have seen some "light at the end of tunnel" though...
Normal matter that we describe within the so-called Standard Model of
strong, electromagnetic and weak interactions, cannot propagate a
large distance in possible extra dimensions without conflict with
observations. It has been recently recognized, however, that this
conflict can be avoided if the Standard Model is confined
some mechanism to act only in a (3+1)-dimensional subspace
, embedded in a higher dimensional
environment (the so-called "bulk")!
are extended p-dimensional objects
that derive their name from being higher-dimensional generalizations
of "membranes"; we are thus said to live on "brane-worlds" in the
However, this 3-brane trick for the Standard Model forces will not
work for gravity
which necessarily propagates in all
, since it is the dynamics of spacetime itself!
The outstanding experimental success of Newton's 1/r^2 law (=>
) and general relativity would therefore seem to imply
four non-compact dimensions. n extra compact dimensions of size R would modify
Newton's law into a 1/r^(2+n) behaviour at distances r<<R. At large
distances r>>R the gravitational flux lines cannot penetrate anymore
in the extra dimensions and the familiar 1/r^2 law is always recovered!
About 5 years ago it was realized by some theorists from Stanford and
Trieste that tests of Newton's law did not exist at distances
smaller than about 1mm!
. So in view of the above said, a huge
new 'fashion' took off, since suddenly there was the exciting possibility
extra dimensions of order ~1mm were "just next door"
and could be hunted for via deviations from Newton's law!
Let me stop [or break] here in order not to overdo;-)