⚡ Dark night sky paradox

Image: The sky in visible light. Stars have a finite age and therefore a lifespan. Their source of light is too ephemeral for them to be able to saturate space with their radiance. Credit: Stellarium image

Does Olbers' paradox exist?

"Night is only night for us. It is our eyes that are dark." This citation from René Barjavel (1911-1985) in the science fiction novel "La Nuit des temps" could be the answer to the question: Why is the night black?
Each of us could simply agree that the cause of the dark night comes down to the absence of the Sun above the horizon, but that is not a good answer.
Indeed, the night is black and before the 20th century the universe is supposed to be static, infinite and populated by stars. For several centuries these two ideas will remain paradoxical!
Obviously, the night has always been dark. But if the universe were infinite in space and time, no matter which direction we looked, our line of sight would have to intersect even a very distant star. The sky should therefore appear to us everywhere as bright as the Sun. But we see that the night is essentially black!
This assertion called Olbers' paradox was studied in 1826 by Heinrich Olbers (1758-1840). However, the question had been asked since 1576 by Thomas Digges (1546-1595) in a publication where he distributed the stars randomly throughout the celestial sphere. This vision of the sky led him to ask himself the question "why did this infinity of stars not make the night sky bright?". His answer was that most of them were too far away to be seen, but that's not a good answer.
In 1610, in his letter of support to Gallileo "Dissertatio cum Nuncio Sidereo" (Conversation with the celestial messenger), Johannes Kepler (1571-1630) seems to rule out the notion of an infinite Universe.
Although many astronomers asked themselves this question, the resolution of this paradox remained unresolved for the next three centuries.
Why should an infinity of stars make the night sky shine?
Edmond Halley (1656-1742) and Jean-Philippe Loys de Chéseaux (1718-1751) will provide a mathematical answer to this question. De Chéseaux in 1744, inspired by work by Edmund Halley, imagines the sky as a series of concentric spherical layers of constant thickness centered on the observer. Thus, the number of stars in each layer is proportional to its surface, therefore to the square of its radius. In other words, at the 2d distance there are 4 times as many stars, at the 4d distance there are 16 times as many stars, and so on.
However, the luminous intensity of a star is inversely proportional to the square of its distance. In other words, if at a distance d, a star has a certain luminosity, at a distance 2d, it is 4 times less luminous. The flux of a star decreases as the inverse of the square of the distance ƒ(e)=L/4πr2 (L=luminosity).
Thus, if the universe is infinite we have an infinity of layers which have the same luminosity and the observer receives as much light energy from each layer. The total brightness should be infinite.
We know today that this assertion is incorrect because the stars have a finite lifespan.
Why not simply consider that the cosmic environment is not everywhere transparent?
Thus, light from stars could be blocked by interstellar dust and gas. This explanation is not correct either because the medium would heat up little by little while absorbing the light and would become as luminous as the surface of a star. This does not resolve Olbers' paradox.
Why not consider that the light of distant stars has not had time to reach us?
Indeed in 1848 Edgar Allan Poe (1809-1849) intuitively presented this hypothesis in his essay on the material and spiritual universe entitled "Eureka".
Indeed, the speed of light being finite (we know it at that time) it takes some time to reach us. But this assumption is not correct in an infinite and eternal Universe. If the Universe is eternal whatever the time it takes light to reach us, it should already dazzle us.
In 1901, William Thomson known as Lord Kelvin (1824-1907) demonstrated that in a transparent, uniform and static universe, uniformly filled with stars, the finite age of the stars prohibited the visibility of distant stars.
To solve this simple paradox of the dark night, we had to completely revise our conception of the Universe.
Behind the story of Olbers' paradox hid a disturbing cosmic reality from which several concepts will emerge at the end of the 20th century.
- The Universe has not always existed, it has a history and it has a finite age of 13.77 billion years.
- The speed of light (300,000 km/s) is finite and therefore the Universe has a finite size. In 13.77 billion years the photons traveled 13.77 billion light-years.
- Stars have a finite age and therefore a lifespan. Their source of light is too ephemeral for them to be able to saturate space with their radiance.
- The Universe is expanding rapidly. The sky is darker and darker because the light coming from distant galaxies is increasingly red-shifted (Doppler effect). The most distant galaxies losing more and more their brightness are extremely difficult to observe.
It is necessary to bring together all these hypotheses to solve the paradox of the dark night.

"Night is only night for us. It is our eyes that are dark."
In infrared observation, distant galaxies reveal gigantic glows that set interstellar dust ablaze. For each point in the sky, our sight crosses the infrared flux of a galaxy.
But the most original clarity is in the microwaves. This cooled fossil radiation is observed in all directions of the sky.