Re: Expanding Universe

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

At 02:26 PM 3/19/01 -0400, Tim O'Donnell wrote:
> My understanding is it does not expand into nothing it just
> creates space as it expands.  The questions is can it
> expand around an area/volume?  Can there be "holes" in
> space where the universe has not expanded into a
> partucular region, but has expanded into the surrounding regions?

Our universe doesn't expand "into" regions of space.  It *is* space!  You
can't speak of space expanding into a region of space.  (Our space might
expand into a previously-unused part of the *embedding* space, but since we
can't possibly know very much about the embedding space, that is almost
moot;  see below.)

The following describes a slightly-simplified model of the real universe:

My favorite analogy is the rising of raisin-bread dough.  The dough
expands.  The raisins do not expand.  Each raisin see each of the others
moving away, at a rate proportional to the distance.  You could fill a pan
with such dough, or a tub, or a swimming pool, or the entire known
universe;  the relationship between any two raisins is independent of
whatever is happening at the boundaries (if any).  We don't see any
boundaries;  every raisin we can see is expanding away from us.

In this model universe, over a wide range of timescales, to explain the
expansion, it is not necessary to invoke any physics beyond Newton's first
law of motion.  That is, if at some initial time t1 we have the property
that every raisin is moving away from every other, at a rate proportional
to separation, that property will continue to hold at subsequent
times.  Draw five world-lines on a piece of graph paper, i.e.
abscissa=distance and ordinate=time.  Let all the lines radiate from a
point at time=t0.  Choose one of lines as a reference, so we can measure
velocities and positions relative to it.  Now pick some time t1.  Look at
all the separations.  In each case, the relative separation will be
proportional to the relative velocity.  (The "constant" of proportionality
will vary with time, but at any given time a proportionality will be observed.)

=======

The raisin-bread model gives a very reasonable description of the expansion
at the current epoch, including a billion years past and future.  (If you
extrapolate it too far in either direction, additional complexities enter
the picture -- but these complexities are not worth worrying about at the
introductory level.  You have to understand the raisin-bread model before
anything fancier is worth worrying about.)

As an example of extra complexity:  you can imagine raisin-bread dough that
is (locally or globally) expanding more in some directions than
others.  This might well have happened back when the universe was very
young, and very unlike the present universe.  But you shouldn't worry about
it too much at this stage.

As another example of extra complexity:  If you want to talk about holes in
space, we first need some notion of how such a hole could be detected.  A
hole might be detected if we could circumnavigate it.  In any Euclidean
space with D>1, a circle can be continuously shrunk down to a point.  But
in a toroidal universe, there are some circles that cannot be shrunk,
because they encircle the hole or enlace the hole.  Our universe actually
does contain such holes, in the form of black holes and (allegedly)
superstrings, but these are small localized holes.  There is no reason to
believe that the current expansion of the universe involves "filling in"
any such holes.

It is much better to think in the following terms:  our space is our space,
and we don't need to worry about what (if anything) is going on in the
embedding space (if any).  The "bug on a hot plate" story explains how a
space could appear to be curved, without needing any embedding space to
curve "into" (Feynman volume II chapter 42).