It's been a loooong time since I exercised my astrophysical neurons, and
this seems as good a time as any...
Correct me if I'm wrong, doesn't the rate of change of the Hubble
constant indicate a limit (i.e., the speed of light) at a distance of
something like 15 billion light years? If the universe were larger than
that, anything beyond this point would have to be receding faster than
light, in apparent contradiction with relativity.
Also, I think the contraction and closure you're referring to are two
different things. A low-density universe may forever continue to expand
and yet have a finite area.
>
> Suppose space were not expanding. It is three dimensional, obviously
> (ignoring the "time dimension"). Would you demand that there exist a
> four dimensional space in which the three dimensional one was
> embedded,
> in order to give it reality? And would that four dimensional
> space have
> to be part of a larger five dimensional space, which is itself part of
> a six dimensional one, and so on?
>
> All this is conceivable, but is it really necessary? I don't
> think we need
> to assume there are higher dimensional spaces in order to give ours
> reality.
>
At the macroscopic level of reality, four dimensions seem to provide the
most useful model of spacetime. I don't see why four dimensions
necessarily implies five or six.
> Even though our space is said to be "curved", and expanding, those
> properties do not require higher dimensional spaces, either.
> Curvature is
> like a gradual internal warping of space, so that large
> enough triangles
> don't have angles that add to exactly 180 degrees. It can be fully
> described without reference to any larger embedding space.
>
> Likewise the expansion of space can be expressed soley in terms of the
> relations between objects within our universe. There is no need to
> postulate a higher dimensional universe which ours is part of.
The "internal warping of space" you describe seems isomorphic to a
four-dimensional spacetime, although the 4-D model provides (to me at
least) an easier to understand picture of things. Whether of not there
really "is" a fourth dimension doesn't seem particularly important
unless we're doing time travel. 4-D models would probably be the most
useful if one were conducting large-scale engineering projects where an
understanding of the spacetime topology were important, however.
Steven