NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/sci/astro/14321

Internet Message Format | 1993-01-23 | 3.2 KB

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From: ted@physics2 (Emory F. Bunn)
Newsgroups: sci.astro,sci.physics
Subject: Re: Local Expansion - Why not?
Followup-To: sci.physics
Date: 22 Jan 1993 22:41:23 GMT
Organization: Physics Department, U.C. Berkeley
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In article <[e-mail]> [e-mail] (Thomas Clarke) writes:
>Tom Van Flandern, our perennial curmudgeon, has asked why
>we don't observe Hubble expansion in the solar system.
>
>Now I know the mathematics of general relativity (GR) explains all
>this nicely, but I find my intuition lacking.
>
>Does anyone know of an intuitively satisfying explanation that
>does not require the mathematics?

As with most tricky questions in physics, there are a bunch of equivalent
ways of looking at this, each of which is more appealing to some people
than to others.  Let me give one way which I like.

We know that in a homogeneous expanding Universe, there is a number called
the critical density.  If the density of the Universe is below this
value, the Universe expands forever, and if the density is greater,
then the Universe stops expanding and recollapses.

Now there's a nice fact called Birkhoff's theorem, which says that if
you have a Universe which has spherical symmetry, then the behavior
of the part of the Universe that's within any particular spherical
shell is independent of what's outside of the shell.  Let's apply
this theorem to a simple ``toy model'' Universe:  Suppose the Universe
has some density greater than the critical density within a sphere of
radius R, and some density smaller than the critical density outside
of that sphere.  Then the region inside of the sphere will stop
expanding and recollapse after some time, by Birkhoff's theorem.
The space outside of the sphere will keep expanding, though.
(The region near, but just outside, the boundary between the overdense
and underdense regions will be complicated, but very far away from
the sphere the expansion will be almost undisturbed.)

Now our Universe doesn't look anything like this model, right?  So
why did I bother describing it?  Well, it turns out that even if
you relax the assumption of spherical symmetry, some of the qualitative
features of the Universe will be the same as in the model described
above.  Specifically, if you take an almost homogeneous big bang Universe,
and put in a small overdense region, then (if that region is
sufficiently dense), it will stop expanding and recollapse on itself,
while the rest of the Universe keeps expanding.

That's exactly what our galaxy did:  Early on it was just a big,
slightly overdense region in the expanding Universe, but because
of its higher density, it recollapsed on itself.  It didn't collapse
all the way, as the spherically symmetric region did, because
the random thermal motions of the matter in it, and the need to
conserve angular momentum, prohibited it.  But it did stop expanding,
and it hasn't been expanding ever since.

-Ted