Olbers’ Paradox. Olbers’ Paradox Asks Why the Universe is Dark at Night

Olbers’ Paradox is another fundamental observation which can be made, and is possible with nothing more than the naked eye. Ask anyone to describe the night sky and the chances are that one of the first things they will tell you is that it is dark.

Kepler, whose laws of planetary motion we encountered in chapter 1, pointed out in 1610 that if the Universe is infinite, with stars scattered randomly throughout it, why is it dark at night? After all, in whatever direction one cares to look, our line of sight will, sooner or later, come to rest on the surface of a star.

Although light suffers from an inverse square reduction in its intensity based upon its distance, the further one looks into space, the more stars will appear in our line of sight, compensating for the dimming. This curious phenomenon was popularised over a century later by Heinrich Olbers, and now bears his name (see Fig. 3. 4).

Fig. 3. 4. Olbers’ Paradox asks why the Universe is dark at night. If it were infinite in extent, then our line of sight would eventually meet with the surface of a bright star. The reason the night sky is dark, therefore, is that the Universe is not infinitely large and that the redshift makes distant objects more and more faint

The most obvious solution to the problem is that stars are not distributed randomly through space: instead they form galaxies. This provides only temporary respite and the problem reappears with galaxies because, as we shall soon see, on the largest scale, galaxies and clusters of galaxies can be thought of as being spread randomly throughout space.

One solution to the problem, which gives us our first fundamental insight into the nature of the Universe, comes from a consideration of look-back time. Imagine our Galaxy and another more distant one to be plotted on a spacetime diagram. We only become aware of the other’s existence (and vice versa) when their light cone crosses our world line. If the Universe is not infinitely old, then there must be distant galaxies with light cones not yet in contact with us.

In order to resolve Olbers’ Paradox we have been forced to assume that the Universe may not be infinite in age. In doing that we have taken our first step towards the Big Bang, because it implies that at some time in the past the Universe must have been created. Another complementary resolution also exists, as will be explained in the next section.