🚀 go-pugleaf

Thomas Clarke asks:

>My intuition goes something like this.  Imagine two small particles
>in empty space.  According to GR as applied to the big-bang (BB)
>cosmology [steady-state cosmology too, I would dare say], two
>observers using electromagnetic means (are there any other) would
>observe a steadily increasing seperation as the universe expands.
>
>Now insert a large gravitating body between the two observers, and put
>them into orbit around the body.  Their observations will now show
>no increase in seperation.
>
>Why?  My intution (and TVF's apparently) says there should be no
>difference between the two cases.  Let the body's mass go to zero,
>continuity then implies there should then be no expansion even with 
>the body absent.

Actually, this is a good example and helps make everything clear.
If space is really empty then there are two (equally valid) descriptions
of the universe.  One is Minkowski space and one is the zero density
BB model.  They are related by a simple transformation given
(among many other places) in the Problem Book in Relativity and
Gravitation by Lightman, Press, Price, and Teukolsky.  The
BB model is the future lightcone of a single event in empty
space, with the surface of the lightcone corresponding to the
initial singularity in the BB model.

Now if I put two particles down I have to specify their
initial velocities with respect to each other.  If they
are at rest in the BB model, then they are moving apart
in the Minkowski metric.  If they are at rest in the
Minkowski metric, then they are falling together in
the BB metric, just fast enough to cancel the 
"expansion of space".  If they are tied together by rubber
bands, tractor beams, nuclear forces etc. then in Minkowski
space this looks totally unremarkable, but in BB model it
is 'nonlinear small scale structure defying the expansion
of the universe'.  Of course, either description is equally
good, but the result is perhaps more obvious in the Minkowski
metric.

The point this illustrates is the 'expansion of space' in 
the BB models is a consequence of initial conditions rather
than some long range mysterious force due to the rest of
the universe.  In fact, as a consequence of Birkhoff's theorem
we can see that no such force exists.  The expansion of the
universe is due to its initial expansion and can be reversed
locally without residual effects.

-- 
"Quis tamen tale studium, quo ad primam omnium rerum causam evehimur,
tamquam inutile aut contemnendum detractare ac deprimere ausit?"-Bridel
Ethan T. Vishniac, Dept. of Astronomy, The University of Texas at Austin
Austin, Texas, 78712                   ethan@astro.as.utexas.edu