From: metares@well.sf.ca.us (Tom Van Flandern)
Subject: Re: "Modeling" the Expanding Universe? (was Re: That Great Pulsar Timing Flame War)
Organization: Whole Earth 'Lectronic Link
Date: Tue, 26 Jan 1993 07:33:14 GMT


Earlier, I wrote:

>> Given that high-enough matter density will always eventually convert an
>> expansion into a contraction, and that a non-expanding, non-contracting
>> space is unstable without pressure, I do not see how it is possible for
>> local space to be neither expanding nor contracting.

and carlip@landau.ucdavis.edu (Steve Carlip) replied:

> I'm still not sure why this is confusing, but here's a guess.  I think
> you're looking at properties of *a* solution of the Einstein equations
> with a *particular* matter distribution, and trying to treat these as
> universal characteristics.  You are correct in saying that a high enough
> *homogeneous, isotropic* matter density will eventually convert expansion
> to contraction.  But on the other hand, there are certainly solutions to
> the field equations, such as the Schwarzschild solution, in which the
> scale factor is constant.  The geometry of spacetime depends on the
> details of the matter distribution, not just on averages  ...  the field
> equations are a complicated set of nonlinear partial differential
> equations, for which intuition is not to be trusted.

     Well, I agree up to a point.  But we mustn't throw reason out the
window.  If solutions do not give reasonable physical behavior, then
something is wrong.

     We agree that if the matter distribution is homogeneous and isotropic,
all of space can expand or contract.  Now consider a homogeneous, isotropic
universe plus a single locality in it with an abnormally high matter
density.  Let that abnormal matter density approach infinity.  [I consider
20 orders of magnitude, as in the case of the solar system, as an
approximation of infinity.]

     Now as I understand it, the Einstein's Equation is supposed to have
solutions that will allow the nearly infinite matter density locality to
halt a general expansion and remain flat.  But the condition of local
spacetime depends only on the matter distribution in the universe, not on
its motion.  Therefore we can make the same statement if the universe is in
a state of general contraction: a nearly infinite matter density locality
must halt the general contraction and remain flat!  I submit that goes
beyond counter-intuitive into the unimaginable.

> I realize that this is essentially a negative response --- I'm telling
> you why your intuition here is wrong, but not suggesting an alternative.

     I sincerely appreciate your efforts.  I'm content to give this
argument up if a good explanation arises.  You see all the elements of my
argument -- which one is wrong?  You've made the best effort yet at
addressing my question using my own language and concepts.  But because of
the picture I drew above, I'm starting to suspect that there may be no way
out of this dilemma despite your valiant efforts.  I'm still open to
suggestions.  -|Tom|-

-- 
Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
Meta Research was founded to foster research into ideas not otherwise
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