JOSH@YKTVMH.BITNET ("Josh Knight") (03/04/86)
BH> Date: 26 Feb 86 19:55:07 GMT
BH> From: hplabs!amdahl!drivax!holloway@ucbvax.berkeley.edu (Bruce Holloway)
BH> Subject: Re: Olber's paradox
BH> Another solution (maybe): All stellar objects tend to "clump" into
BH> solar systems, galaxies, clusters, ad infinitum. So instead of spreading
BH> evenly throughout the sky, we just see light from these collections, the
BH> scope of said clumps depending on how far away the object(s) is/are.
REM> From: Robert Elton Maas <REM%IMSSS@su-ai.arpa>
REM> Subject: Many solutions to olber's paradox!! (Keep an open mind!)
REM> Of course!
...(material deleted)...
REM> I should have thought of that myself, having workd
REM> with Mandelbrot and Gosper and Farmwald and Moravec on fractal stuff
REM> at SU-AI... Indeed, if the large-scale clumping of the Universe has
REM> sufficiently small fractal dimension, then even in a static and
REM> infinite-time Universe you see only a finite amount of light from any
REM> point due to inverse-square diminuation and less than square
REM> accumulation of stars. It sounds paradoxial, after all with infinite
REM> time the density of light should increase linearily, exceeding any
REM> given level, but actually in fractal universe with increasingly large
REM> voids as you go out further you get an effect similar to a single
REM> local cluster with emptiness beyond: most of the light that is emitted
REM> goes out to fill the infinite void beyond, with the part that stays
REM> local being buonded in intensity.
From "The New Cosmos" by Albrecht Unsold (translated by W.H. McCrea,
Springer-Verlag 1969, NY), p 328:
H.W.M Olbers 1826 appears to have been one of the first astronomers
to have considered a cosmological problem from an empirical
standpoint. Olber's paradox asserts: Were the universe infinite
in time and space and (more or less) uniformly filled with stars,
then - in the absence of absorption - the whole sky would radiate
with a brightness that would match the mean surface brightness of
the stars, and thus about that of the surface of the sun.
I don't think clumping, no matter what its statistical characteristics
can avoid the paradox. Basically, if one extends one's line of sight
far enough, one finds it ending up on a star, i.e. the entire surface
is covered with star surface. At this point it is only surface brightness
that matters. Olber's paradox is "why is the night sky dark" not "why
is the sky not infinitely bright". I'm not as sure about my conclusion
if one assumes one is at the center of the universe, but I tend not
to make that assumption ;-).
As an aside, it is interesting to note that in the early part of this
century, an incorrect accounting for interstellar absorption caused many
astronomers to believe our galaxy was a small elliptical one, rather
than the large spiral it really is. Of course one of the artifacts
of this error was to place the solar system near the center of the
galaxy.
Josh Knight
IBM T.J. Watson Research Center
josh@yktvmh.BITNET, josh.yktvmh@ibm-sj.arpaethan@utastro.UUCP (Ethan Vishniac) (03/05/86)
In article <8603041333.AA12454@s1-b.arpa>, JOSH@YKTVMH.BITNET ("Josh Knight") writes: > > > I don't think clumping, no matter what its statistical characteristics > can avoid the paradox. Basically, if one extends one's line of sight > far enough, one finds it ending up on a star, i.e. the entire surface > is covered with star surface. At this point it is only surface brightness > that matters. Olber's paradox is "why is the night sky dark" not "why > is the sky not infinitely bright". The point that one`s line of sight always ends on a star is in fact sensitive to the nature of the clustering. If the clustering is arranged hierarchically, with a suitable fractal dimension, then the average line of sight *will not* end on a star. It is not a question of placing the observer at the center of the universe, any random position *in a galaxy* will have this property. Nevertheless, such models are unsatisfactory for other reasons. -- "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
desj@brahms.BERKELEY.EDU (David desJardins) (03/05/86)
In article <8603041333.AA12454@s1-b.arpa> JOSH@YKTVMH.BITNET ("Josh Knight") writes: >I don't think clumping, no matter what its statistical characteristics >can avoid the paradox. Basically, if one extends one's line of sight >far enough, one finds it ending up on a star, i.e. the entire surface >is covered with star surface. At this point it is only surface brightness >that matters. Olber's paradox is "why is the night sky dark" not "why >is the sky not infinitely bright". I'm not as sure about my conclusion >if one assumes one is at the center of the universe, but I tend not >to make that assumption ;-). Well, you may not think this, but you are wrong. If the universe is sufficiently "clumped" it is quite possible for most rays out from the Earth to never intersect a star. But this still misses the point, because even if all rays intersected stars, it would be quite possible for most of the sky to appear dark. First, because light is quantized into photons and so most of the sky would still not be omitting a photon more than occasionally, and second, because "dark" is a relative term, i.e. there is still some scattered light coming from parts of the sky that you see as "dark." -- David desJardins
desj@brahms.BERKELEY.EDU (David desJardins) (03/06/86)
JOSH@YKTVMH.BITNET ("Josh Knight") writes: >> Well, you may not think this, but you are wrong. If the universe >>is sufficiently "clumped" it is quite possible for most rays out from >>the Earth to never intersect a star. > >What I meant by "not assuming that one is at the center of the universe" >is that I assume the Universe is homogeneous and isotropic. There is no >preferred place and no preferred direction. If any distribution >satisfies this assumption, and extends infinitely in time and space, >I believe there is no way to avoid the paradox. Well, "homogeneous" = "not clumped." If the universe is clumped, then it is not homogeneous. This seems clear by definition. If the universe has an appropriate fractal dimension, it is possible for it to be infinite in every direction and yet to have *no* point from which all rays of sight terminate on a star. You essentially need only for stars to be in clumps ("galaxies"), galaxies in clumps ("clusters"), clusters in clumps, etc., and adjust the "clumping parameters" correctly. I think I can prove this with an arrangement where the fractions N1,N2,... (Ni = fraction of sky covered by cluster level i) have the property that the infinite product (1-n1)*(1-n2)*(1-n3)*... converges to a value > 0. Of course, the above seems hard to justify cosmologically. But we have accepted stranger things... -- David desJardins
franka@mmintl.UUCP (Frank Adams) (03/08/86)
In article <8603041333.AA12454@s1-b.arpa> JOSH@YKTVMH.BITNET ("Josh Knight") writes: >From "The New Cosmos" by Albrecht Unsold (translated by W.H. McCrea, >Springer-Verlag 1969, NY), p 328: > > H.W.M Olbers 1826 appears to have been one of the first astronomers > to have considered a cosmological problem from an empirical > standpoint. Olber's paradox asserts: Were the universe infinite > in time and space and (more or less) uniformly filled with stars, > then - in the absence of absorption - the whole sky would radiate > with a brightness that would match the mean surface brightness of > the stars, and thus about that of the surface of the sun. > >I don't think clumping, no matter what its statistical characteristics >can avoid the paradox. Basically, if one extends one's line of sight >far enough, one finds it ending up on a star, i.e. the entire surface >is covered with star surface. At this point it is only surface brightness >that matters. Olber's paradox is "why is the night sky dark" not "why >is the sky not infinitely bright". The assumption that extending one's line sight always leads to a star is not correct if the clumping is sufficiently pronounced. This means that every time you expand your scale of measurement, you find larger clumps, with yet larger spaces between them. This does violate the stipulation in the article quoted above that the universe be "uniformly filled with stars". 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. Frank Adams ihnp4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108
desj@brahms.BERKELEY.EDU (David desJardins) (03/11/86)
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
dbb@aicchi.UUCP (Burch) (03/17/86)
If one makes the correct assumptions about the Hubble Constant, or the age of the universe, or the shape of spacetime, you can assume an infinite universe full of stars and stuff. If the Hubble constant is high (?) enough, We cannot see them because the rate of expansion is so high that the light from these sources NEVER reaches us, or for a lower value, has not had time to reach us since the universe formed stars. If one assumes a wierd sort of structure for spacetime, one can explain that the light is dropped down some hole eventually, and never gets out. One must mistrust mind experiments; They often make some unsupportable assumptions... -- -David B. (Ben) Burch Analyst's International Corp. Chicago Branch (ihnp4!aicchi!dbb) "Argue for your limitations, and they are yours"