Natural Science Forum / Physics / Relativity / January 2005

No - they are actually an entirely different dimensions eg in general
relativity you need 4 quantities to describe the each element of the space -
hence is said to have dimension 4, in Kaluza-Klein gravity (see
http://xxx.lanl.gov/abs/gr-qc/9805018 ) you need 5 quantities - hence it is
said to have dimension 5, in string theory you need 11 - I am sure you see
the pattern.

Thanks
Bill

High school algebra doesn't address the concept
of spacetime dimension.

You're mathetically unarmed to fight the battle that
you want to fight.

We describe the 3-D world with 3 position coordinates.

To describe more dimensions, we just add more coordinates.

In string theory, the extension of spacetime in some of
the coordinate directions is very small so that we aren't
aware of it in our normal everday lives.

It's not a matter of dividing the same intervals into
smaller pieces.  It's a matter of different directions
for the intervals to go.

John Anderson

D:

 Because what they mean is that spacetime literally has more than
three spatial dimensions.

 Actually, that is not correct. Current theories suggest that at
some point there is a limit beyond which it makes no sense to
think in terms of ``smaller.''

 No. They are literally additional dimensions. The only way to try and
picture additional dimensions is to start by picturing yourself as
two-dimensional and think of what how a three-dimensional object would
appear as passed through the plane that consitutes your two-dimensional
universe and then mentally extrapolate.

Lemme give it a try...

You can orient a yardstick so that it extends in the up and down
direction.  That is, you hold it vertically so it's pointing at the
ceiling and floor.

You can also hold it so it's length is in the left and right direction,
which is the way we normally use it.

If you extend it in front of you like you're going to stab somebody
with it, then it's measuring length in the "in and out" direction.

Time is just another "direction" you could point a yardstick in, except
that the length of every line in that dimension (measured in inches) is
a negative number, so we can't point real yardsticks that way.

And if there were any yardsticks which DO point that way, we can't see
them.  We percieve this direction however, as "future" and "past".

Unlike time, the other 7 string dimensions are real "directions" you
can point at, like left/right and up/down. But the diameter of the
universe in those directions so unimaginably small that for objects as
big as yardsticks (or even atoms), it's the same as if they didn't
exist at all.

But we CAN  see the effect of energy that bounces back and forth
between these dimensions.  We percieve it as gravity, light, and the
nuclear forces, depending on which of those tiny directions the energy
is bouncing back and forth between.

====

This is my understanding of ST (except that "bouncing" isn't exactly
the word I want).

I'd appreciate corrections from anyone who understands it better.
(Note: that doesn't include you Androclese, so keep quiet).

=[ d