Re: General Relativity

[John Denker <jsd@MONMOUTH.COM>]

At 07:05 PM 8/16/99 -0700, KATHERINE TODD wrote:
> It seems to me that space and time would have to bend into
> something. ... 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.

Short answer:  If you have an N dimensional space that is curved, it does
*not* imply the existence of an N+1 dimensional space.

You may have trouble *visualizing* such a space, but that's tough.  There's
lots of things that exist that can't be visualized.

Another answer:  Let's say additional dimensions might exist.  If you can't
visit them or interact with them in any way, then it doesn't matter whether
they exist or not.  The question of their existence is moot.  Such
questions are outside the realm of physics.

The real physics of real curved space involves questions that can be
answered *without* leaving the space.  For example, consider a tiny bug
confined to the surface of your beach ball.  The bug cannot get off the
surface, nor even see anything not on the surface.  Yet the bug can easily
determine that it is living on a curved space.  The most obvious way would
be to circumnavigate the space.  But there are other ways, which can
involve only relatively local measurements, such as the following:  The bug
would discover that for small circles, the radius equals the circumference
divided by 2pi.  But for larger circles, the radius is more than that.  The
bug can easily measure the excess radius by pacing off various circles --
and this does *not* require leaving the surface.   As far as the bug knows
or cares, there are no other dimensions.

Suggestion:  go to the bookstore or the library and grab a copy of _The
Feynman Lectures on Physics_.  In volume II, read chapter 42.