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Calculations performed by
Wesson and colleagues (1989) used the average rate of energy
production per unit mass of luminous matter in the Universe, the
average density of luminous matter, and the age of the Universe
as well as the speed of light to estimate the average luminous
intensity of the Universe, which was found to be 6 x 10-4
ergs/cm/sec. This is the intensity of Olbers’ light in a static
Universe without relativistic effects (Wesson, 1989).
If various forms of the
standard models for the Big Bang are incorporated into such
calculations, the expansion of the Universe only dims the light
of galaxies by one-half. In a static Universe the sky would be
dark, and the expansion of the Universe increases this darkness
by approximately a factor of two to four (Wesson, 1989, 1991).
Theoretical calculations of the extragalactic background light (EBL)
due to stars in galaxies generally agree with the EBL found from
observations, thereby establishing that the modern explanation
for Olbers’ paradox is on firm ground (Wesson, 1991). In fact,
Wesson in 1989 claimed: “This resolves Olbers’ paradox once and
for all: The night sky is dark because the universe is still
young, not because it is expanding “[italics in original].
Even if the Universe were infinite in extent and age, beyond a
certain range the intensity of galactic radiation would be so
greatly redshifted it could not be detected (Murdin, 2005).
Maddox (1991) in reflecting on
Wesson’s work stated: “In the circumstances, it hardly seems
appropriate that people should go on telling students that the
resolution of Olbers’ paradox is a relativistic effect. It is
more relevant that there was a time in the history of the
Universe when there were no galaxies of the form in which we
know them, and thus no opportunity to fill the Universe with
radiation of the kind now called visible. What happened before
then, of course, remains anybody’s guess.”
Olbers’ paradox can be
extended to other avenues of investigation. It can be applied
to the zodiacal background intensity as measured from space. If
very faint magnitude limits are examined, the increasing number
of Kuiper Belt objects (KBOs) at R magnitude < 26 implies there
should be an infinitely bright sky (Kenyon, 2001). Since such a
sky is not seen, there have to be constraints on the number and
size distribution of KBOs to match the known sky brightness at
optical and infrared wavelengths. These constraints when fully
developed can in turn be used with improved limits on measured
KBO surface brightness to yield direct estimates of the albedo,
temperature, and size distribution for small KBOs in the outer
solar system (Kenyon, 2001).
Similar work stimulated by
Olblers’ paradox is relevant for other wavelengths beside the
visible spectrum and the infrared. Solving the submillimeter
Olbers’ paradox leads to interesting constraints on the cosmic
star formation history for a wide range of assumptions about the
evolution of galaxies and star formation (Serjeant, 2005).
It has been suggested that
Olbers’ paradox is analogous to Fermi’s paradox (“if the
Universe is filled with intelligent species, where are they?”).
A seemingly simple observation and question reveals a
fundamental gap in our understanding. Where are all the
intelligent species? If we exclude purported UFO visits, we
haven’t seen any evidence for other intelligent life forms. The
reasons for this are hotly debated, and one suggestion is that
there is only a very slow migration of space-faring
civilizations (Almar, 1989).
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