From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon Feb 10 2003 - 01:55:38 MST
Ramez writes
> From: Anders Sandberg [mailto:asa@nada.kth.se]
> > I think most cosmologists think of spatially
> > unbounded universes when they consider the open
> > universe scenario (although it is not topologically
> > required). These would have an infinite number of
> > galaxies, although I don't think this is widely
> > remarked on.
>
> Really? I'm no cosmologist, but this doesn't jive with my
> understanding. An open universe is one that will expand
> infinitely and is therefore *eventually* infinite in volume.
I'm no cosmologist either, but I think that your statement
applies to the *visible* universe---and THAT won't ever quite
be *infinite* itself: at any point t in time, it'll still
have just finite volume.
> However, an open universe has finite mass, which clearly limits the
> number of galaxies.
I don't agree, and was hoping to get confirmation along the
lines that Anders has provided. I believe that all the
confusion (when people speak of "the universe") comes from
failing to distinguish between the visible universe---only
10 to 15 billion light years in radius---from the entire
universe, which IMO is infinite in radius.
Here is why: if we assume isotropy (and whatever else it was),
then no one has center position. Therefore, even the most
remote galaxies that we see, why, they think (in terms of
their own observations) that they're in the center too. And
the most distant objects THEY can see, in the opposite
direction to us, also lie at the center of their visible
universe, and so on and so on, ad infinitum. Thus the
universe on this reading is infinite in extent.
So unless the universe has a topology that results in it having
finite volume at any time---one way is to have a closed universe,
I guess---then not only is there no boundary, but the homogeneous
material (galaxies) extend infinitely far, just as do the integers.
> Indeed, if an open universe had an infinite number of galaxies
> it would have infinite mass, which would result in a mass density
> that would guarantee collapse...
Not if the initial acceleration away from each other is great
enough!
But suppose that it is not great enough, and that there is a kind
of collapse eventually. This still hardly precludes there being
infinitely many galaxies! While we have trouble visualizing
infinitely many of anything rushing together to a "point-like"
place that has no "center", there is a trick I have found to
visualize it.
Say that right now two particular atoms are at distance apart X.
Then later, when a collapse has begun, they eventually find
themselves only X/2 distance apart. We may visualize this as
being exactly the same as if each become twice as large, but
their positions did not change. This I claim to be exactly
equivalent.
The advantage of this latter way of looking at it, is that we
can imagine each atom---in the final moments before the utter
collapse---as becoming unboundedly large. (One can easily
construct functions, such as the redoubtable y = 1/x, which
have the property of assuming infinite values at the singularity
of x=0. So think of the atom as following this course as x->0,
and assuming a size without bound.)
I personally have less problem with imagining infinitely many
atoms each over time becoming bigger and bigger without bound
than I do with infinitely much matter converging to a point.
The difficulty with the latter picture is that it appears to
leave a vast space behind where the matter used to be, which
is incorrect.
So on my contrary view, let us suppose that we can then visualize
the moment at which each atom is infinitely big and there is
no space at all between the atoms, and indeed they completely
overlap. This is the Omega point when collapse is total.
Now, by rewinding the picture from this point, we have a
way of thinking about the Big Bang that begins with infinite
mass so-called "concentrated at a point" (but which I shall
prefer to equivalently think of as just being composed of
particles infinitely large all overlapping). Then for any
positive epsilon greater than Zero (the time of the BB)
atoms have finite size yet there are infinitely many of
them---or whatever their primordial soup equivalents are.
Pat wrote
> IMHO, there are better explanations for the Hubble red
> shift and cosmic background radiation than the Big Bang.
Perhaps, but I was excluding views not held by 20 percent
or more of physicists, and I personally don't have a
problem with the BB (not that my credentials mean a damn).
Stirling writes
> At the moment, the Big Bang theory is THE theory of
> the evolution of the universe. It is also generally
> regarded as being fatally flawed in a number of different ways.
> That is, we know that, as currently stated, it's wrong.
Do you think that more than half of the professional
physics community would agree with your statement that
the Big Bang theory is wrong?
Lee
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