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Olbers' Paradox

In 1826 the German astronomer Heinrich Olbers (1758-1840) published a brilliant paper in which he stated a remarkable paradox.

The brightness of the night sky is due to the light from the stars. Therefore since there is a huge number of stars spread across space and the brightness of the night sky is due to light from each one the night sky should be brilliantly bright and not dark. Wherever you look there should be a star, some close to Earth (at least four light years but still relatively close) and so far away (many millions of light years). No matter how far away they are they will all contribute to the brightness of the sky.

Now the size of a star, around three light seconds, is much less than the average distance between stars (ten light years).

Therefore if we think about the light coming from each star then it should be clear that the majority of the light from the night sky is due to the distant stars. What is different about the very distant objects in the Universe compared with those close to us? They are receding at high speeds.

This is the key to the solution of Olbers' paradox. It can be resolved by assuming that the Universe is expanding.

The expansion of the Universe implies that distant stars are receding from us and so the number of waves reaching our eyes per second is less and also the number of photons is less. This recession also means that frequency of the individual photons is less and so the energy of each photon is also smaller. (Energy = hf = hc/λ and by the Doppler effect sources receding from us will have an increase in wavelength and so a decrease in energy).

In fact the sky can be made darker by considering a larger rate of expansion.

The darkness of the sky is a way in which the Hubble constant can be estimated.

The failure to do this in 1826, some 120 years before, has been suggested by some scientists to be one of the greatest missed opportunities in Cosmology.


© Keith Gibbs 2020