From: schinder@leprss.gsfc.nasa.gov (Paul J. Schinder)
Newsgroups: alt.atheism
Subject: Re: In the Infinite Universe
Date: 26 Aug 92 14:14:24 GMT
Reply-To: schinder@leprss.gsfc.nasa.gov
Organization: Goddard Space Flight Center

In <92238.152617EXG106@psuvm.psu.edu> <EXG106@psuvm.psu.edu> writes:

>According to the Bing Bang theory, there are three possible  "futures" for this
> universe of ours.  Assuming that enough mass exists in the universe and a big
>Crunch results (I personally would like to believe that this senario will occur
>), space would be in a sense, infinite.  Consider this: you draw dots on the su
>rface of a balloon.  Each of those dots represents a galaxy (or a cluster or su
>per-cluster: irrelevent).  As you inflate the balloon the space between the bal
>loons expands.  If you start at one point and begin moving in a straight line (
> which in this case would be restricted to the surface of the balloon, so it wo
>uld actually be a curved line which would be the shortest distance between two
>points: non-euclidean geometry), you would go on forever, hence infinity.  Now
>just imagine that on a three dimensional scale. (good luck)
>:)

OK, let's go through a quick primer on the Big Bang theory, neglecting
such visual aids as balloons.  In standard big bang theory, the
universe is assumed to be filled with a "fluid" with the same (time
changing) energy density and temperature everywhere.  Crank the
Einstein equations, and out pop three solutions depending on the value
of the density compared to a critical density (the ratio of the actual
density to the critical density is called \Omega in TeX notation).
The three are: 1) a closed, finite universe that eventually
recollapses (\Omega > 1), 2) a flat universe where \Omega = 1, which
expands forever and is infinite, 3) an open universe with \Omega < 1,
which expands forever and is infinite (the difference between 2) and
3) is in the geometry of the spacetime).  In this context "infinite"
means given a point I can always find another point in the universe
arbitrarily far away, "closed" means that given a point in the
universe I can't do that (there's a maximum distance).  The expansion
of the universe merely means that given two points, the distance
between them increases with time.  (Of course, terms like "distance"
have specific meanings as well in relativity; two oldish but still
good books on the Big Bang are Misner, Thorne and Wheeler's
"Gravitation", and Weinberg's "Gravitation and Cosmology".  Neither of
these has anything on inflationary cosmologies, however.)

It's important to lose the commonplace, but wrong, picture of the big
bang as a "cosmic egg" exploding into a pre-existing space.  The big
bang theory says, based on the Einstein equations, that there was a
spacelike singularity a finite time in the past, where the density was
infinite. At that singularity, space-time and all the stuff in it
began. (To be more precise, we lack the theory necessary to describe
events at or shortly after the singularity.  That will take a theory
of quantum gravity.).  If the universe is open, then it was *always*
spatially infinite, even though the distance between any two given
points was smaller the farther back in the past you go (and approaches
zero as you approach the singularity).
--
--------
Paul J. Schinder
NASA Goddard Space Flight Center
schinder@leprss.gsfc.nasa.gov