Re: Creation (long)

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Jim Green wrote:
> Yes this is what I was referring to -- and I don't know what lay language to
> use -- Folks help me out here.  As the rubber sheet expands the distance
> between the ants grows, but the ants are walking too -- such that if the
> expansion were to slow or stop, the ant-ant distance would still increase.

If the stretching of the rubber sheet stopped and the ants continued to
walk, then the mean distance between the ants would remain the *same* as
some of the ants wandered toward some other ants and away from other ants.
If the rubber sheet is not stretching the distribution of ants remains
constant with only local concentration fluctuations as the ants wander
around haphazardly.  The same is true for the galaxies.  Local
intergalactic motions are distributed in all directions with some galaxies
approaching and others receding.  If there were no underlying Hubble
expansion of space the mean density of galaxies would remain the same with
only local density fluctuations which average out to uniformity on the
largest length scales.  The thinning of the mean matter density in the
universe is due solely to the Hubble expansion of space. The local motions
of the individual galaxies and their clusters average out to zero wrt the
comoving coordinates fixed to the 'fabric' of space.  In the ant analogy
the ants wander in *all directions* at random.  Without the sheet expanding
there would be no place for the ants to go which would reduce their
mean density.  If they thin out in some places then they will clump up in
other ones.  Remember the distribution of ants (and galaxies) is *uniform*
on the largest length scales throughout all of the whole sheet (i.e. all
space).

> But there is still a problem in my head:
>
> You say that as the Universe expands that what ever "stuff" was at the rim
> of the Universe shortly after the BB has always remained relatively close to
> that "rim" (whether we are talking about balloons or rubber sheets of what
> ever dimension)  -- eg your ants stay close to the "edge" .

I said *nothing* about a "rim of the universe" and have no idea what you
mean by this notion or the idea of the "ants being close to the edge".
I did mention gas molecules in the cylinder being at opposite ends of the
cylinder, but I emphasized that those cylinder boundaries were not a valid
part of the analogy.  I only wanted to consider those gas molecules because
they were widely separated, and as the piston was withdrawn their
separation increased at a rate proportional to their separation (which just
happened to be maximum at the opposite cylinder boundaries), *not* because
they had anything to do with an "edge".  I did say that a 2-d *analogy* of
our 3-d space was *like* a rubber sheet or the surface of a balloon.  But
this is a *lower dimensional analogy*.  If the universe is finite and
spherical-like then it is like the 3-d 'hypersurface' of a 4-d balloon.
IOW the whole 3-d of space is the 3-d 'edge' of a 4-d sphere and none of
the universe has any extent or thickness along the 4th 'radial' direction.
If the universe is infinite it is like an infinite rubber sheet (except it
extends in 3-dimensions instead of 2 as in the analogy).  Maybe a better
view is to suppose that the universe is like the inside of an *infinite*
3-d rubber eraser which is stretching outward in all directions.  All of
the infinite eraser is filled with ants (or galaxies).  A problem with the
3-d example is that if the ants are embedded in the rubber they get stuck
and cannot wander around randomly in the rubber matrix.  Since Helium
balloons quickly go flat because tiny inert Helium atoms can easily diffuse
through the pores in the rubber, maybe we should imagine our infinite
rubber eraser as saturated with Helium atoms instead of ants.  The
individual helium atoms wander around through the rubber but the overall
Helium concentration remains constant as long as the whole eraser is not
being stretched.  If it *is* being stretched then the mean Helium
concentration becomes more rarified with time.  If the rubber is being
shrunk then the helium concentration increases with time.

>                                                             But didn't the
> Universe "expansion" initially proceed at a rate >c?  The "stuff" even
> photons can't travel at >c.

The stuff gets carried along for the ride as it is carried along by the
rubber fabric.  If two distant parts of the sheet are being pulled away
from each other faster than c then the stuff on the sheet will separate
faster than c.  The stuff does *not* move faster than c wrt the fabric
or wrt adjacent neighboring stuff.  In fact the stuff is nearly at rest
wrt the rubber sheet and its local motions are haphazard anyway.  The
photons do move at speed c wrt any local frame including the comoving frame
in which the fabric where the photon is at some instant is locally at rest.
But two different photons at very distant parts of the sheet will
separate from each other faster than c since the underlying sheet is
carrying them along with it faster than c.  Remember the Hubble recession
velocity due to the stretching to the 'fabric' is proportional to the
separation in space.  The farther the separation the faster the recession
speed.  At sufficiently remote separations one part of the fabric pulls
away from another part of the fabric faster than c.  For example, suppose
that the universe is 10^10 yr old and is infinite in extent.  Then the
parts of the universe that are 10^100 ly away from us are receding at a
speed of some ~10^90 * c.  These parts are *not* part of our observable 
universe since we are outrunning any causal influences that they may be
propagating toward us.  These places are just too far from us for them to
be able to influence us in any way.

>                              I am confused.  In my head the "rim" traveled
> faster than the stuff and later (I don't know what "later" might mean) this
> expansion slowed down to <c (at least in some scenarios) such that the
> photons are "catching up" to the "rim". And if the expansion slows to <<<c
> even the galaxies would "catch up"
>
> Where have I gone wrong?

You have gone wrong by assuming that there is a rim, edge or some sort of
a shock wave or expansion from the big bang.  Let me repeat.  The BB is NOT
an expansion of matter INTO a previously empty space from a small subregion
of that space.  It is NOT like an ordinary explosion.  Rather the
whole space is ALWAYS FILLED UP with stuff at all times (since the BB
singularity at the beginning of time).  It is the SPACE ITSELF that is
stretching and *that* is what thins out the preeexisting stuff in that
space more or less uniformly everywhere as time goes on.  The stuff in
the space is locally more or less carried along for the ride as the
space expands and this causes the stuff in different regions of space to
separate from each other at large length scales (at a rate proportional to
their separation).

> Tom, this is just fine and it surely makes the point to a lay person well
> enough,  But I think I misunderstand something -- even if the balloon were
> to stop growing, the dots still flee from each other.  NO???  Help me out
> here.  I am waiting for Dave Bowman to chime in here.  Where are you???

The dots do *not* still flee each other if the balloon were to stop
growing.  The dots are carried along for the ride of the expansion of the
balloon.  If the dots were ants then the ants may continue to mill around
aimlessly, but they would *not* flee each other on the average.

Consider me to have chimed in again.  I do have other things to do besides
write large phys-l opera, so be patient.

David Bowman
dbowman@gtc.georgetown.ky.us