Olbers' paradox states that if the universe is infinite, static and homogeneous then why is the night sky dark. Of course it's been resolved but it brings up an interesting probability question:(adsbygoogle = window.adsbygoogle || []).push({});

If we model the universe with a spatial Poisson model (probability that a small element is occupied is proportional to the volume) and ignoring decay, variations in star brightness and relativistic effects etc we get

[tex]L \propto \int_r^R \tfrac{1}{s^2}dN(s)[/tex]

as the amount of light reaching your eye originating from stars between r and R units of distance away, where N(s) is a Poisson process with rate at time s proportional to s^2. Does L go to infinity as R increases?

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# Olbers' paradox - Poisson model

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