REM%IMSSS@SU-AI.ARPA (Robert Elton Maas) (03/06/86)
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.
ethan@utastro.UUCP (Ethan Vishniac) (03/06/86)
First, let me just point out that fractal models of clustering have
the following problems:
1) Deep counts of galaxy numbers, usually done in a number of
small areas scattered across the sky, show only small variations.
[One has to be careful about this. Different observers use
slightly different techniques so a given data sample should include
only the work of one group at a time.] In one sample I happen to
have on hand (Tyson, Jarvis, Valdes or some permutation of those
names) the total counts vary by less than 10% on the average.
Moreover, some fraction of this variation (or all of it) may be
due to absorption by gas clouds in our galaxy. Presumably this
could be checked by using IRAS data.
2) No *dynamical* model of such a universe has ever been constructed.
That is, one that includes the general expansion and includes
reasonable evolution of the clustering.
3) The microwave background is isotropic to at least a few parts in
10^5. If its origin is cosmological, the most likely interpretation,
then the limits this sets on gravitational fluctuations in the
universe is quite severe on very large scales.
4) Lastly, the theory of cosmological nucleosynthesis gives results
which are nicely consistent with a nearly homogeneous big bang model.
It is not apparent how this could be preserved in a model with
fractal clustering.
It is certainly true that the fractal model takes care of the night
sky.
>
> 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.
The first comment might be possible if galaxies are not a good tracer
of mass in the universe, except that an indefinite extension of teh
clustering hierarchy would violate point #1. The second is somewhat
mysterious to me. The inflationary hypothesis suggests that on the
largest scale the geometry of the universe could be nearly anything,
but on visible scales (billions of light years) should be close to
a flat Friedman model.
This seems more like net.astro than net.space. I am cross listing it.
Perhaps discussion should continue there.
--
"Ma, I've been to another Ethan Vishniac
planet!" {charm,ut-sally,ut-ngp,noao}!utastro!ethan
ethan@astro.UTEXAS.EDU
Department of Astronomy
University of Texas