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: Fri, 22 Jan 1993 07:19:24 GMT


Earlier, I wrote:

>> The hypothesis that the initial explosion was an explosion of spacetime
>> and not of matter is a big bang hypothesis, not part of GR.

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

> ... Your criticism of ad hoc assumptions seems to me to come from a
> confusion between what is assumed and what is derived.  General
> relativity gives a set of field equations that determine the geometry of
> spacetime (curvature *and* expansion or contraction) from the matter
> distribution.  If you assume a homogeneous, isotropic distribution of
> matter with standard relationships between density and pressure, you
> *derive* Friedman-Robertson-Walker cosmology, with a *predicted*
> relationship between the expansion rate of the universe and the density
> of matter and radiation.

     Steve, I'm struggling to understand your words.  I don't think I'm
succeeding.  The Hubble rate appears in Einstein's Equation, but is epoch-
dependent.  Only the second derivative of scale is fixed by the matter
density, assuming no pressure.  That isn't quite what you said above, but
maybe its what you meant.  Do we agree?

> If, on the other hand, you assume an *approximately* homogeneous and
> isotropic distribution, with local areas of higher or lower density, you
> can again solve the field equations (at least in a systematic
> approximation) and look at the predictions.  In this case, you find an
> average expansion rate, but you can also look at the detailed behavior of
> regions with higher or lower densities.  I have not done these
> calculations myself, but I have no reason to doubt Ethan Vishniac's
> statement that when this is done, you find that dense enough subsystems
> do not participate in the expansion.  In any case, this is something that
> can be checked by looking at the predictions of general relativity with
> the appropriate matter distributions.  It is *not* anything new that
> needs to be brought in from the outside.

     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 (e.g., the cosmological constant), I do
not see how it is possible for local space to be neither expanding nor
contracting.  It appears obvious to me that either a) local spacetime does
not obey Einstein's Equation; or b) a compensating pressure is required to
counterbalance the universal expansion.

> I guess I don't really understand why this is confusing.  In general
> relativity, space doesn't just expand because it wants to; the expansion
> is the (predicted) response of spacetime geometry to the presence of
> matter.  If you change the matter distribution, why shouldn't you expect
> the expansion to change?

     I expect the *rate* of expansion to change, specifically to a strong
contraction, if Einstein's Equation is controlling.  Just as you say, I
also don't understand why this isn't more obvious.  When such "failures to
communicate" occur, it generally means that one of us is missing a key
piece of knowledge, and is unaware of that absence.  I'm quite prepared to
be shown that it is me, but I don't have a clue yet where my reasoning
could be going wrong.  -|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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