Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.BERKELEY.EDU
Path: utzoo!watmath!clyde!burl!ulysses!bellcore!decvax!ittatc!dcdwest!sdcsvax!ucbvax!brahms!desj
From: desj@brahms.BERKELEY.EDU (David desJardins)
Newsgroups: net.space
Subject: Re: Clumping doesn't fix Olber's paradox
Message-ID: <12331@ucbvax.BERKELEY.EDU>
Date: Tue, 11-Mar-86 05:20:04 EST
Article-I.D.: ucbvax.12331
Posted: Tue Mar 11 05:20:04 1986
Date-Received: Thu, 13-Mar-86 07:44:16 EST
References: <8603041333.AA12454@s1-b.arpa> <1189@mmintl.UUCP>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: desj@brahms.UUCP (David desJardins)
Organization: University of California, Berkeley
Lines: 18

In article <1189@mmintl.UUCP> franka@mmintl.UUCP (Frank Adams) writes:
>
>What is not obvious to me is whether the stars can have a finite density
>in the universe as a whole if such clumping is present.  One must add the
>requirement that there be a finite upper bound on the density of stars
>in any finite region, of course -- a condition which is unlikely to be
>violated.

   If by finite you mean nonzero (a common misstatement by physicists),
then I think it is clear that this is impossible.  If the mean density
of stars on arbitrarily large spheres is above a nonzero threshold for
an infinite sequence of radii tending to infinity (which I think is the
appropriate definition of "finite density in the universe as a whole"),
then each of these spheres must block out a fixed fraction of the rays
from the Earth, and so together they will block any given ray with
probability one.

   -- David desJardins