Even on the clearest winter night, with the sky studded with stars, we still see a black backdrop. However, in a static and infinite universe, the night sky should be completely bright, without dark regions or regions devoid of light. This fact had already been noticed by the brilliant Johannes Kepler in 1610, but it was the German astronomer Heinrich Wilhelm Olbers who seriously addressed the matter in 1823, formulating the paradox that bears his name.
Why is the night sky dark if there are infinite stars that would illuminate it like day?
This question was asked by astronomers of the caliber of Kepler, Halley, and Cheseaux, but they did not find a satisfactory answer. Anyone can see that during the night the sky between the stars is black, a fact that apparently contradicts the idea that the Universe is infinite. If it is, in every direction we look from Earth there should be at least one star, and the night sky should be completely bright.
As we have seen before, a paradox occurs when, using two apparently valid reasoning methods, you arrive at two opposite results. The Olbers' paradox is named after the German physicist and astronomer Heinrich Wilhelm Olbers, who wrote about this topic in 1823.
Why Is the Night Sky Black?
In all honesty, Olbers was not the first to notice the contradiction between a dark night and an infinite universe. At the beginning of the 17th century, the German astronomer Johannes Kepler used the paradox to support some of his theories. Later, in 1715, the British astronomer Edmond Halley found some especially bright areas and proposed that the sky does not shine uniformly at night because, despite the universe being infinite, the stars are not uniformly distributed.
Jean-Philippe Loys de Chéseaux, a Swiss astronomer, began to study the paradox based on Halley's earlier work. Chéseaux proposed that either the number of stars was not infinite, or the intensity of light decreased rapidly with distance, perhaps due to the presence of some kind of absorbing matter that filled space. But none of these theories satisfied the scientific community.
In 1823, when he formally stated his paradox, Olbers proposed as a solution that the sky was dark at night because “something” in space blocked most of the starlight that should reach Earth. His proposal did not differ much from Chéseaux's, and for the next hundred years the paradox was not discussed. Later it was shown that this solution was unviable. Today's scientists know that the supposed space matter that blocked light would, over time, heat up and eventually emit light with as much or more brightness than the stars.
The brightness of a sky populated by infinite stars at different distances from the observer is equal to that presented by the surface of a star. While the apparent area of a star decreases with the square of the distance separating us from it, the number of stars increases with the square of the distance, so both effects cancel out and the sky should be as bright as the Sun, which evidently does not happen.
Of course, for the stars to be “uniformly distributed” in space, they must also be uniformly distributed in time, because the farther the observed star is, the older it is. This reasoning, which projected to an infinite scale means that the universe must have an infinite age without radical changes in the nature of stars, served Kepler as an argument to postulate his model of the universe. But there is a flaw in this reasoning.
Most of the light sources in the universe are galaxies and all of them are moving away from us. This, as mentioned before, causes a decrease in the light that reaches us from them (by the inverse square law of distances) as well as a decrease in frequency (redshift). This implies, according to Planck's formula, a reduction in the energy with which light travels. In this way, photons lose energy on their journey from the stars to Earth, significantly reducing the luminous contribution of distant galaxies to the brightness of our sky.
The Age of the Universe
Another powerful argument against Olbers' paradox is the age of the Universe. It is clearly not infinite, as suggested by the Big Bang theory. This means that only the light from a finite number of stars has had time to reach us, so the paradox simply disappears. Some even see the existence of a mostly black sky as proof of the Big Bang theory.
Benoit Mandelbrot, famous for his work on fractals, proposed a different way to resolve the paradox. Mandelbrot maintains that stars are not uniformly distributed but rather they are distributed fractally, like the Cantor dust. This would explain the large dark areas observed in the sky, but studies carried out with space telescopes demonstrate that the cosmic background radiation is isotropic to 1 part in 10,000, so Mandelbrot's argument seems to be false.
The answer to Olbers' paradox is that “the universe is not infinite and has not always been the same. Otherwise, it would be uniformly occupied by the stars”, something that does not happen. There is then no place to build a Grand Hotel like the one imagined by Hilbert.
Anyway, the next time we look at a starry sky, we will remember that the existence of that black backdrop is a reminder that neither the age of the Universe nor the number of stars that compose it is infinite, something that today may seem simple to understand, but that 200 years ago made more than one astronomer sweat.
