RE: Cosmology Question

From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon Feb 10 2003 - 01:55:38 MST

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    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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