From: Chris Ho-Stuart <>
Newsgroups: aus.religion.christian,aus.religion,nz.soc.religion
Subject: Re: Some hard questions for Able
Date: 16 Mar 1999 01:40:27 GMT

In aus.religion.christian Edward Ruvinski <> wrote:
> Chris Ho-Stuart wrote:
>
> > > Actually, it makes very little difference whether at Event One
> > > the universe was 0.00000 units in size, 0.001 units in size,
> > > 1.001 units in size or 100,000 units in size.
> >
> > This is still incorrect.
> >
> > In discussions of the size of the universe, sometimes people refer to
> > the size of the observable universe
>
> What was it that made you believe I was doing such a thing?

I did not so assume... I was being careful for readers who
may check my comments from other sources.

> > The present rate of expansion is known aproximately. The rates of
> > expansion in the past may have included a period of "exponential"
> > expansion (inflationary epoch), but was never infinite. In any
> > case, the rate of expansion does not address the finiteness or
> > infiniteness of the universe.
>
> Yes it can.
>
> Let us assume for the purposes of illustration that the
> expansion rate of the universe could attain infinite velocity.
> Let's call this universe Universe-1.  Let us now assume that the
> this velocity could only be achieved for what we humans would
> recognise as one second.  Hey, presto!  An infinitely-sized
> universe (I was, originally, going to write "What would be
> the diamater of  the universe?" but realised that the question
> becomes meaningless).

An infinite velocity is an undefined velocity. The term "singularity"
is used to denote situations where analytic descriptions become
undefined. The singularity at the origin of the unviverse, at
the center of a black hole, and at the Schwartzchild radius of a
black hole are all singularities. The latter can be handled by
a suitable co-ordinate transform. The two former examples are
intrinsic and indicate a failure of the particular analytic model
to capture or define the state. At the initial singularity, size
is also undefined.  There is no initial zero size. There is either
a finite space which which decreases without limit in the past, or
there is an infinite space which varies in curvature without limit,
but is always infinite.

I repeat: the rate of expansion was never infinite (undefined)
although in the limit it approaches a singularity (increases
without bound). There is no notion of going from a finite size
to an infinite size.

> In Universe-2, let's assume the exact same conditions as before, except that
> the infinite velocity would be achieved for what we would describe as two
> seconds.  Would Universe-2 be larger than Universe-1?  No, it would not.
>
> Now, let's assume that prior to the New Inflationary Epoch of infinite
> velocity, Universe-1 was twice the diamater of Universe-2 and both universes
> would experience an infinite expansion rate for what we would call one
> second.  After the epoch, both universes would be infinite in size.

The inflatioary epoch does not involve infinite velocities. It
involves an exponentionally increasing rate of expansion. The
duration of this epoch is postulated to be very short (perhaps 10^-10
seconds). Inflationary expansion means that a given region doubles
in size in a fixed very short amount of time. The inflationary
epoch lasted long enough for a finite number of such doublings.
There is no transition from finite to infinite.

> Therefore, it would be impossible to ascertain the initial conditions of a
> universe prior to an epoch of infinite velocity.
>
> > What is significant is the relation between expansion and density. (The
> critical density question.)
>
> Are you refering here to the critical density of the universe?

Yes. The critical density is actually critical for a given rate of
exansion. Since we can measure the present rate of expansion, we
know the critical density. In the past, the density of the nuiverse
was greater but so was the rate of expansion. What is critical is
really the ratio. Note that this does not apply to an inflationary
universe, where expansion is driven by a vaccum energy density. The
universe is not presently in such a state.

Cheers -- Chris