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August 6, 2012 / who828

Olbers’ Paradox

   I have always been fascinated by Cosmos, even though we are inconsequential in terms of the vast universe the fact that we are connected to it atomically and the ability to think about this things alone opens up lot of possibilities.

Today I want to share a paradox that paved the way to modern cosmology ideas, this paradox was stated by Heinrich Wilhelm Matthias Olbers (1758 – 1840) a german astronomer. Just to be clear at the time Newton’s view of universe being infinie and fixed was  commonly accepted but Olbers’ had a problem with such views and thus he described this paradox in 1823.

So what is the Olbers’ paradox, you might ask ? It states that if the universe is static and infinitely large,  any sight line from earth in the night must end at surface of a star. Now you might argue what if its blocked by dark clouds, well in that case the dark clouds would heat up and eventually they would be as radiant as the stars.

You might also argue that intensity of light from a star depends on this equation,

I ∝ 1/R²   where I is the intensity of light, R is the distance between the observer and the star.

So in layman terms the greater the distance, the less intense the light would be and that would explain why the sky is dark at the night, right ?  Well not really Olbers’ presents a very important mathematical argument,

Olbers' mathematical argument

Here, is the distance between the shell and the earth

t is the thickness of the shell

so the surface volume of the shell would be 4ΠR²t

for N stars per volume = 4ΠR²t N

so using the intensity formula, I (intensity) = 4ΠR²t N / R², thus we get

I =  4Πt N which means distance is not effecting the intensity of light.


Now, this was for one shell for an infinite universe there would be infinite number of shells. each bigger containing the smaller one thus if we add all them for infinite number of time, e.g.

I = 4Πt N + 4Πt N + 4Πt N + …. we would get,

I = ∞

thus, at line of sight we would see a bright star and the night sky would be white instead of dark. So obviously universe is not infinite but there are other arguments need to addressed,

  1. What if if universe is not infinite but static ?

In that case, things won’t change that much as instead of infinite number of shells there would be finite amount. They would be still enough stars to light up the night sky.

2.  What if universe is infinite and static but age of stars is finite ?

Again because the universe would be infinitely old, there would be infinite amount of stars at any angular direction thus the result would remain the same.


Things that we learn from Olbers’ paradox

   The Big Bang theory explains this paradox as following,

  1. Since the universe is constantly expending (non-static) the light coming from the star’s wavelength is being expanded (because of doppler’s effect) and their frequency is lowered, thus they would be in microwave range in the spectrum and that is called “Cosmic Microwave Background Radiation” (Wherever you look in the universe there is CMBR hitting us) so while night sky is lit up even today but the light is not in the visible spectrum. Since its frequency is very low our atmosphere takes care of it.
  2.  Universe expansion might be faster than speed of light, so star going further away from us is relative faster than light coming from the star.

So, we can say there must be a time in the universe when the whole night sky would be bright (white) when it was small.



The main reason why I wrote this post because Olbers’ paradox came out in 1823, there were no big bang theories around that time but the paradox did influence astronomers, which lead to “Big Bang” theory in 1930’s which would explain the paradox almost 90 years after Olbers’ lifetime. This is one of the reason science is wonderful, things are not built upon thin air but upon ideas of previous scientist and on based those ideas we discover new things and unravel new mysteries. I feel lucky enough to learn about this magnificent things about our universe.


Learning more about the Olbers’ paradox

  1. Olbers’ Paradox Explained 
  2. Olbers’ Paradox Wiki

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