Re: Relativity and Theories

["Inge H. A. Pettersen" <ingep@ONLINE.NO>]

KATHERINE TODD wrote:

> This is a question that I have asked my teachers (I'm only in 10th grade),
> and of course they couldn't' answer it. I hope you can help me out, and I
> hope it isn't centered to much toward theoretical science for this list:
> In general relativity, it describes the "bending" of space-time.

At the risk of adding to the confusion I will try to make an explanation. I
think
the source of your confusion is the meaning of the word "curvature". Other
people may explain this better:
First of all I think it is more accurately from an *experimental* point of view
to say that the traces
of particles ("their world lines") - even the the particles your and my body
consist of :-) -
are bent. Within the context of general relativity deviations of world lines of
noninteracting
(OBS: in general relativity there is no "gravitational force" as in Newtons
mechanics) particles
give information about a theoretical/mathematical animal called the Riemann
tensor. *Mathematically*,
this quantity describes curvature of spacetime.

Mathematicans often talk about "extrinsic geometry" and "intrinsic geometry"
which corresponds to
different kinds of curvature. An example/analogy
might clear this up: The geometry of a 2 dimensional sphere - a basket ball -
can be described
by the geometry of the surrounding 3 dimensional space. In this case the the
curvature of the ball
as it is imbedded in 3 dimensional space is called "extrinsic curvature".
However, this is not the
curvature 2 dimensional beeings, say ants, would measure on the surface. It
turns out that there
is a "intrinsic curvature", described by the Riemann tensor, that quantify what
they measure
*within* the surface.

Going back to general relativity spacetime corresponds to 2 dimensional space
and the
theory is agnostic about the possiblility of embeddings in a higher dimensional
geometry:
The Riemann tensor is intrinsic based on what we measure in 4 dimensional
spacetime.
That is all what general relativity claims to make statements about.

Of course, as general relativity does not include quantum mechanics - in
particular
strong and electroweak interactions - we know that the theory is not complete
as a
full description of nature. Whether more dimensions need to be taken into
account
to do so, remains to be seen.

> I
> understand that concept, but then I read about "theories" about multiple
> dimensions. It seems to me that space and time would have to bend into
> something, which would make it more or less as a fact as general relativity
> that there are at least 4 spacial dimensions. Like the example with the
> surface of a beach ball, which is for all purposes in this post 2d, bends
> into the 3rd spatial dimension.
> Am I wrong, and I'm missing something, or am I right, and I just never
> realized the correlation in the theories? Please help!!
>
> I know I dont' understand it fully, but my question was just if the extra
> dimensions were implied in general relativity, but science doesn't accept
> them because it seems more like pseudo-science than actual provable facts.
> I am aware of M-theory, which is a combination of string theory and 11-D
> super gravity... it is very controversial in itself, and the outcome is
> still murky, but that was the reason I was wondering. If general relativity
> proved that M-theory really had some merit.... The answer might be beyond
> me, but I would think even if I didn't' understand the reason, I would at
> least have a "yes" or "no" answer, or even "it is still unresolved" answer.
> My only concern is that I don't really understand the math yet, but I can
> understand and visualize the concepts involved without too much difficulty.
>
> mgtodd@worldnet.att.net
> ICQ: 37233550