Olber's so called paradox

Olber's paradox

The notion that the sky in an infinite universe filled with stars would be bright not dark, can be traced back to Kepler (1610). The idea was known to Halley and Cheseaux in the eighteenth century, but it was not popularized as a paradox until Olber's took up the issue in the nineteenth century.

The paradox

Suppose the universe is filled randomly with stars (galaxies) and is infinite. If this infinite universe is divided into concentric shells of some arbitrary thickness, the light received at the center from each shell is the same, since the number of stars in a shell is proportional to r² and the light intensity at the center is proportional to r^-2. The night sky is therefore bright?! Wrong. The night sky is dark. Therefore we do not live in an infinite universe that is randomly filled with stars.

Thinking again - the universe may not be infinite, but it is certainly very large. Large enough to render the night sky much brighter than it appears, hence the paradox.

Explanations

One idea that is often put forward is not correct. The suggestion is that the universe is uniform and infinite but dust and gas obscures the light from distant stars. There is dust and gas, but in an infinite universe of infinite age equilibrium would have been established, and radiation absorbed would be reradiated.

The accepted explanation takes count of two things. Firstly, light from distant stars is red-shifted. Less light energy reaches us from ever greater distances. Secondly, the Universe as we see it is not infinitely old. The Observable Universe has a radius in light years equal to the lifetime of the Universe in years. We receive radiation from no further than 13.7 billion light years (according to the latest estimate).

For a time, after Hubble discovered that the cosmological red shift, and before the Big Bang theory took center stage, Olber's paradox was presented as evidence supporting special relativity. The red shift (an SR effect) conveniently got rid of the starlight. This red-shift certainly contributes, but the finite age of the Universe is more significant.