>Hal Finney wrote:
>>
>> One problem with simplistic space
expansion models is that
>> space may be
>> infinite. In the simplest models
from general relativity, if
>> the density
>> of the universe is so small that it
will expand forever and
>> not contract,
>> that also implies that the universe,
although curved, does not "close"
>> and so goes on forever.
>>
>> You can still have an expanding
universe even if it is
>> spatially infinite.
>> It just means that distant objects
move apart, slowly at
>> first, and then
>> faster and faster.
>
>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