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From: REM%IMSSS@SU-AI.ARPA (Robert Elton Maas)
Newsgroups: net.space
Subject: hyperbolic space makes for solution to Olber's paradox too
Message-ID: <8603060912.AA02064@s1-b.arpa>
Date: Thu, 6-Mar-86 04:11:31 EST
Article-I.D.: s1-b.8603060912.AA02064
Posted: Thu Mar  6 04:11:31 1986
Date-Received: Fri, 7-Mar-86 07:38:32 EST
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B> Date:         Wed, 05 Mar 86 13:05:59 EST
B> From:  ST401385%BROWNVM.BITNET@WISCVM.WISC.EDU
B> Subject:      Olber Redux
B> I don't quite understand your posting about defocussing due to
B> negative curvature being a solution to the Olber paradox.
B> The problem is with the total amount of energy;

Wrong. The problem is the density of energy. An infinite amount of
energy spread into infinite space can have any arbitrary density
depending on the fractal dimension of the generators (stars) and the
fractal dimension of space. Our null hypothesis is that space is flat
(dimension 3) and clustering of stars stops above a certain size,
being uniformly distributed in superclusters above that (dimension 3).
Dimension 3 means what we're measuring (matter or space) is C * R**3
(C a constant) inside a sphere of radius R. But having clustering
increase at higher scales causes mass to be less than dimension 3 so
that average density is zero, while having space of negative curvature
(hyperbolic) causes dimension of space to be greater than 3 and again
average density is zero. Currently we have evidence for both!! We have
not yet seen a cutoff in clustering, in fact just recently a void that
is something like a billion lightyears long has been discovered, and
for all we know the larger scale we examine the larger voids we'll
find. The inflationary-universe theory opens the possibility that on
the largest scale the universe may in fact be grossly hyperbolic.