Olber's Paradox

The night sky is black. When we look up at the night sky in a random direction, almost certainly our eyes will not rest on a star. This seems in contradiction with the first truly scientific models of the Universe that modelled the Universe as static, uniform an infinite, since these three imply that whichever direction we look in the night sky, our line of sight should rest on the surface of a star, and hence that the whole night sky should be bright. The paradox is not resolved by thinking that the further away a star is, the dimmer it should be. If stars are distributed in space with density %rho , a spherical shell of radius r and thickness dr contains 4 %pi r^2 %rho dr stars and and doubling the radius gives 4%pi 4 r^2 %rho dr. Using the inverse square law gives the amount of light from the second one as equal to the amount of light from the first one.

We can find the brightness of the night sky by adding up the contributions from all the shells. Since the Universe is assumed to be infinite, there should be an infinite number of shells and the night sky should be infinitely bright. It makes no difference that some stars will be blocked from our view by other stars, because the stars are randomly distributed with uniform average density in space, so every line of sight should end on a star.

Possible Solutions

The Universe is not infinite. It has a definite finite size. Then looking outwards in some directions will be looking past the furthermost star.

The Universe has a finite age. In this case we are only able to see the light from those stars that take less than the age of the Universe to reach us.

The light is absorbed before it gets to us. However, whatever has absorbed the light will warm up and eventually re - radiate the light eventually, so this does not resolve the paradox.

The Universe is not static. If the Universe is expanding then stars are receding from us and their light will undergo a redshift, possibly to infinite wavelength or zero energy.

The Universe is not static. Not all the light shells will contribute the same amount of light – light from the most distant shells will take longer to reach us. Since stars are known to have a finite lifetime, we cannot assume they have been around forever.

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