Re: expansion of the universe

["John S. Denker" <jsd@MONMOUTH.COM>]

Tucker Hiatt wrote:
...
> The universe-as-cylinder model is consistent with the notion of a
> zero-volume creation event, the big bang.

Consistent with, but not necessarily requiring such an event.

> But the cylindrical universe is "closed," isn't it?

Ha!  I was sneaky about that.  Note that my cylinder has
zero intrinsic curvature, so the ants have no idea that it
is a cylinder at all (unless they manage to circumnavitate
it).  I didn't say anything about the size of the cylinder.
So I hereby declare it to be a googolplex light-years in
circumference, and infinite in the axial direction.

> That means that it -- like the
> spherical universe -- contains a finite amount of space.

Not really.  It has definitely infinite total space, and
there's no upper bound on the size of the "small" direction;
I could have chosen a number bigger than a googolplex.

> Current measurements indicate that the universe is probably not
> closed.

We should be careful, even if the astronomers aren't.
They often say "closed" when they really mean "positive
curvature".

> Rather, it is "critical" or "open".

Again:  "critical" probably means zero intrinsic curvature.
"open" probably means negative intrinsic curvature.

My cylinder is techically closed in one direction (but
this is irrelevant to the physics) and in any case has
zero intrinsic curvature.

> In either of these
> cases, the universe has an infinite amount of space AND ALWAYS HAS
> HAD AN INFINTE AMOUNT OF SPACE, no?

This is tricky business.  Suppose the balloon is very,
very old, but for the last dozen-or-so years I've been
adding air to it so that it is expanding with a Hubble
constant with the value
        H = c / 10 light-years

When the ants look out the window, they can't see
anything more than 10 ly away.  Things near that
distance have been redshifted right down to DC.

This does !!not!! mean that the universe is 10 ly
across, nor that it is 10 years old, nor that it
has a curvature of (10 ly)^-1.  These are !!four!!
different concepts:
 -- diameter of cylinder (googolplex)
 -- age of balloon  (large but unspecified)
 -- Hubble parameter (.1 y^-1)
 -- curvature (zero)

> Here's the question:  HOW IS A UNIVERSE WITH AN INFINITE AMOUNT OF
> SPACE CONSISTENT WITH A BIG BANG?  I.e., can we possibly envision how
> an infinite amount of space undergoes creation?

I have trouble envisioning anything being infinite under
any conditions.  Once I envision such a thing, getting it
to expand is the easy part :-)