Re: Cosmology

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

At 04:57 PM 2/11/01 -0600, cliff parker asked:
> what it means to have a universe that is stretching the fabric of
> space-time as we speak but somehow the patch of fabric that we occupy
> remains unchanged.

That's an important question.

See if this helps:  One standard metaphor is a balloon, which is being
inflated by adding air to the inside in the usual way.  Attached to the
outside are pennies.  The rubber of the balloon expands.  The pennies do not.

So it is with the universe.  Atoms have a certain size, because of the
physics of electrons and suchlike.  Molecules are built of
atoms.  Measuring sticks are built of molecules.  All these things have a
definite size.

Similarly, galaxies have a size set by their kinetic energy, their
potential energy, and suchlike.

The space between measuring sticks can expand, leaving each stick
unchanged.  The space between galaxies can expand, leaving each galaxy
unchanged.

At the next level of detail:  consider the prototypical gravity-wave
detector, consisting of two beads sliding on a stick.  A gravity wave comes
by.  It changes the metric tensor in the vicinity.  But does it change the
distance between the beads?  It takes a bit of training to understand the
answer, but the answer is no.  The distance is defined by the stick.  The
gravity wave causes the beads to "fall" toward each other, and that's just
what they do.  The gravity wave also acts on the molecules of the
stick.  They _would_ fall toward each other if they were free to do so, but
they don't because they are constrained by the other molecules in the
stick.  Result:  the beads move relative to the stick.  You can observe
this as an indication of the passage of the gravity wave.

Note that the stick _does_ stretch by some small bounded amount;  it has to
stretch a little, by Hooke's law if nothing else, in order to develop a
force to oppose the "tidal" force from the gravity wave.  But this reaction
is very different from the motion of the beads, which start moving and keep
on moving.

====

BTW note that if everything expanded together, nobody would notice
anything;  the expanded space would be measured with expanded sticks, and
the answer would come out the same.