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.