Olbers' paradox and E.A. Poe

From: scerir (scerir@libero.it)
Date: Fri Jan 26 2001 - 02:23:43 MST

Olbers' paradox is still questionable, as you can read.

It's interesting to point out that Edgar Allan Poe
made attempts, in his "Eureka", to "solve" the paradox.
Indeed, in 1848, he stated that the blackness
of space between the stars was a glimpse of
featureless chaos before creation.

I've also got this old file (below), in my pc, about
Olbers' paradox. But I do not remember who was the writer.

Olbers' Paradox was so-named by Hermann Bondi in the 1950s,
after Heinrich Olbers who in 1823 discussed the problem:
why is the sky dark at night, indeed why do we see only the Sun by day?
If the Universe is infinite with uniform distribution of stars, every ray
sooner or later hit a star, and there would be continuous light.
Let us start from Olbers' basic assumptions:
(1) the Universe is infinite;
(2) stars are uniformly distributed throughout the Universe;
(3) the Universe does not vary with time;
(4) stars are permanent and unchanging.
Now compare a thin shell of space around the Earth with radius r and
dr containing n stars, with another shell with twice the radius.
The area of the second shell is four times the area of the first, and if
has the same thickness, the volume and number of stars in the second will
be four times those in the the first. But as the light received at Earth
diminishes by the square of the distance, the Earth receives from a star in
outer shell one quarter of the light from each star in the inner shell, but
there are four times as many stars in the outer shell, Earth receives the
amount of light from each shell.
If you go on taking shells right out to infinity, each shell gives us the
amount of light. If an outer star happens to be hidden by a nearer star, the
latter permanently receives the radiation from the outer one, and in due
equilibrium must be reached where the nearer star radiates the output from
Hence the whole sky should be as bright and as hot as the surface of the
both day and night! As this is clearly not so, one or more of the three
assumptions above, must be false. In Olbers' time, only stars were
but the argument is the same if galaxies are substituted.
Although Bondi gave Olbers the honour of pioneer, the problem had already
raised many times before him. Thomas Digges in 1576 recognized the problem,
but explained it by increasing faintness of stars with distance, which from
above discussion in not valid. Johannes Kepler, in 1610, found no problem,
because he rejected the idea of an infinite Universe, and believed that most
rays reached the boundary of the Universe without meeting a star For him,
dark night sky proved that the Universe was not infinite. In 1721, Edmund
returned to Digges' false explanation.
In 1750, the Swiss astronomer Jean-Philippe de Cheseaux, after thorough
consideration of the distribution and brightness of stars visible in his
observatory telescope, developed the geometrical argument stated above, that
decreasing luminosity of stars with distance should be exactly compensated
their increasing numbers. However, he did not abandon any of the four
but instead concluded that space must absorb radiation, so stars did fade
with distance.
This was essentially the explanation adopted by Olbers in 1823. He suggested
that interstellar clouds and dispersed gases absorb the radiation. But this
explanation fails in an infinite Universe, because the radiation absorbed by
interstellar gases does not disappear, it simply heats them up, so that in
time they radiate as much as they receive, and re-establish the searing sky.
Lord Kelvin "solved" the problem in l868 because he knew of no other source
solar or stellar energy than gravitational contraction, which was incapable
maintaining the observed energy output of the Sun for more than 100 million
years, so that any star that many light-years away would have burnt out
its initial light could reach us. This solution lapsed with the discovery of
nuclear energy.
The Hebrew, Christian, and Muslim doctrines, of course, had an adequate
in their initial divine creation, because no stars could precede the
and even if they had since been receding with the velocity of light (a
asymptote) none would yet be 6,000 light-years away, less than a twentieth
the radius of our galaxy, or a millionth of the most distant galaxies
visible by
Indeed, in 1848, the American writer, Edgar Allan Poe, stated that the
of space between the stars was a glimpse of featureless chaos before
In Ireland, sixty years later, Fournier d'Albe developed similar
Indeed, modern big bangers are really saying the same thing!
However, I pointed out a decade ago that the universal background radiation
discovered by Penzias and Wilson, far from being the relict of Gamow's
big-bang fireball, is in fact the real solution to Olbers' Paradox.
At the limit of the best telescopes (at red shift z ~ 4), there are as many
galaxies as there are stars in our Milky Way galaxy. But they are already so
faint as to be scarcely detectable, and the angle separating galaxies
only 4p x 10-14 steradians, an extremely small angle.
But they continue on beyond, until the decreasing angular separation between
them reaches the Raleigh criterion, which limits of resolution of the radio
telescopes. This depends only on focal length and aperture. (Resolution of
wavelengths of equal intensity is just possible when the maximum of one
falls on
the first diffraction minimum of the other).
Beyond this distance the images cannot be separated by the telescopes and
into a continuous field of radiation. But at this distance, the Hubble
has gone far beyond the visible spectrum into the microwave band a couple of
degrees above absolute zero. Here indeed is the universal whiteout predicted
Olbers. In the best optical telescopes, galaxies fade out before reaching
Raleigh limit of separation. Those pairs within that limit appear as single
sources, not as an Olbers continuum. Indeed, the last sources to fade would
such optically fused pairs and triplets. At progressively longer
Wien's law indicates that blackbody emission peaks at Wien's constant
(2897/T m)
that is a wavelength of about 0.2 cm.
At shorter wavelengths, the flux declines rapidly to a tenth at 0.1 cm, but
declines more slowly at longer wave-lengths. At the limit of resolution of
telescopes, Oblers' whiteout then dawns redshifted far into the microwave
(12 cm-1 cm), not far above absolute zero.
Far from implying a big bang, it would be impossible to have a Universe
such a background radiation near absolute zero. At the limit of our knowable
Universe, the redshift parameter would indeed reach infinity corresponding
absolute zero temperature, and the energy reaching us would be attenuated to

This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:56:25 MDT