> Our Universe Has a Topology Scale of at least 24 GPC
> Our universe has a topology scale of at least 24 Gpc, or
> about 75 billion light years, according to a new analysis
> of data from the Wilkinson Microwave Anisotropy
> Probe (WMAP).
And how many orders of magnitude is that ? Probably within about 15
orders from 1 / (h-bar) , ya think ?
> Well, yes. It is difficult to imagine how one could demonstrate
> observationally that the Universe is infinite. The best that one
> could do is show that its size was not smaller than some amount.
Quite. Particularly so when empiricism dictates that observability =
measureability, either directly or indirectly.
It is very difficult imagining how one would actually "measure"
something either infinitely long, or infinitessimally short. Almost
Even if you had a nice Peano curve sitting in your lab, how do you
actually "measure" that length ?
> Having said that, if one thinks that general relativity is the correct
> theory of gravity, the current observational data are consistent with
> a prediction from GR that the Universe is infinite in spatial extent.
I disagree precisely 1/2. Observability of length is restricted. The
universe may be infinite and open in an absolute sense, but what we
experience is finite and closed. All the experimental evidence tends to
point toward a finite universe, yet this could be due to a purely
It is finite, and also infinite, simultaneously.
Now everybody's happy.
> BK> However, some sources claim a singularity at the big bang where
> BK> the mass of the universe was contained in a point (or ring) with 0
> BK> volume. I find it hard to imagine that a 0 volume can instantly
> BK> explode to an infinite volume. Is this actually possible? Hmm, if
> BK> the singularity contained infinite matter and then expanded so
> BK> there was finite space between particles then it must become
> BK> infinitely big. Hmm, I guess, an infinitely heavy singularity
> BK> would be surrounded by an infinitely big event horizon. Could the
> BK> matter in the singularity spread over the infinite volume in the
> BK> event horizon?
> This confusion arises because people are sloppy when defining
> "singularity" and "Universe." A singularity can be more than simply a
> point. A better way of expressing what people typically say is
> something along the lines of
> If one extrapolates backward in time, one reaches a time at which
> the density and temperature of the Universe were everywhere
> infinite (the "singularity"). At this time, the radius of the
> observable Universe would have been infinitesimally small.
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