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Astro Concepts

Olbers' Paradox

Paul Kohlmiller

The comedian George Carlin used to do a bit where he was the hippy-dippy weather man. "And the weather tonight is ... dark, man." But he didn't ask the question, why is it dark? Once you get past the flippant answer "duh, because it's night time" you see why it is an interesting question. If there are an infinite number of stars, shouldn't the sky be bright. Since the sky is not that bright, why not? Today we call this question Olbers' Paradox. Johann Kepler considered this question but he argued that the universe must be finite. Otherwise the total flux from all the stars would make the night sky "as luminous as the sun." Isaac Newton preferred the idea of an infinite universe because Newton's theory of gravity would seem to require either an infinite universe or one that would eventually collapse on itself. According to Newton, a finite universe would "fall down into the middle of the whole space, and there compose one great spherical mass." Swiss astronomer Jean Phillipe Loys de Cheseaux (1718-1751) studied this paradox in the 18th century and gave it some mathematical background. Cheseaux considered the sky to be a series of concentric shells. He came up with shells up to a distance of 3 quadrillion light years. At that point the number of stars is enough to fully cover the sky -- 1046 stars. Cheseaux's answer (in 1744) was that something must be attenuating the stellar light. Otherwise, since the sky covers 180,000 times more area than the sun does and since there should be sun like stars in every part of the sky, there would 180,000 times more light hitting the earth from the stars than from the sun. If that was so we would be toast, literally. Enter Heinrich Wilhelm Olbers (1758-1840), a retired physician. Olbers' name sticks to this paradox for two reasons: 1. He gave the question it's most succinct phrasing: if the universe is infinite then wherever you look your gaze should hit upon a star. 2. He put forth his study in a paper and Cheseaux put his in an appendix of a book about comets. But it is not the case that Olbers came up with a new and better solution. He was much like Cheseaux; the dust in the interstellar medium must be attenuating the light. Olbers presented his study in 1826 . Olbers again started with the idea of concentric spheres although, instead of summing up the star light, he summed up the area of visible stellar disks. Halley and Cheseaux assumed that the stars are uniformly distributed. Olbers did not but he determined that it wouldn't make much difference. Neither Cheseaux nor Olbers took into account that some foreground stars would block (occult) background stars but that would mean they need even more stars. In 1848, the attenuating dust answer was blown out of the water by John Herschel. If you have that much radiation hitting dust, that dust must have absorbed so much radiation that it must reradiate it back into space. Thus, if the sky isn't filled with the light of stars, it would be filled with the light of irradiated dust. Another possibility is that stars are not distributed equally. For example, fractals have been shown to mimic nature's distribution capabilities. A fractal distribution of stars might result in a lot of gaps which causes the sky to be mostly dark. In fact, the latest detailed pictures of the CMB look like they might be a fractal. This possible solution was put forward by the person most closely associated with fractals, Benoit Mandelbrot. The idea that it is the expansion of the universe that answers Olbers was promulgated by Hermann Bondi's reformulation of the Olbers' paradox. From 1948-1965 it was widely held that the universe was in a steady state. After Hubble demonstrated the universe is expanding, the steady state proponents saw this as a possible answer to Olbers' Paradox: if there is a major systematic motion in the Universe, namely Hubble's expansion, then some of Olbers' assumptions are not correct. According to Wesson, this made some sense before the big-bang theory but not so much after it. Wesson says that the expansion answer was "uncritically repeated in research work and ... textbooks" because there was "no account of the relative importance of the expansion and finite-age factors". Wesson used a computer model to compare these two possible answers to this paradox: expansion versus the finite age of the universe. His program was based on principles of General Relativity. One key point of GR is that the light from sources moving away from us is still traveling at the speed of light regardless of the speed of the source. Using input data such as the age of the galaxies and the rate of expansion it calculates the extragalactic background light. Then Wesson ran the model again setting the rate of expansion to zero. The result in both cases was exactly what we see: a dark sky. But setting the rate of expansion to zero only made it slightly darker. Most astronomers now agree that the finite age of the universe is the primary answer to the paradox. And consider the answer to Olbers' when thinking about Fermi's Paradox -- they haven't had time to reach us yet.

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