Monday, August 15, 2022

Why is the sky dark at night? What does this simple fact teach us about the universe we live in?

—Why, the sky is dark at night because the Sun is illuminating the other side of the Earth! What does this have to do with the entirety of the universe we live in?” one might quite properly argue.

But if the universe is infinite and has infinite stars and galaxies, there will certainly be a star in any direction we look. The area that the Sun occupies in the sky is 180,000 times smaller than the area of ​​the entire sky. So we should expect the sky to shine with the intensity of 180,000 suns, even at night! It would be impossible for us to live inside such an extraordinary furnace!

Therefore, the question becomes perfectly reasonable: “—Why is the sky, in a universe infinite in extension and with infinite stars, dark at night?”


The darkness of the night sky, in terms of the previous paragraph, is known in the scientific literature as the “Olbers paradox”. This name is due to the German physician and astronomer Heinrich Olbers (1758-1840), who in 1823 called attention to the question, and presented a possible solution - which soon proved to be flawed.


The problem is older, however. Olbers was not the first to raise the issue. Worthy of mention is the great astronomer Johannes Kepler (1571-1630), probably the first to pose this problem. Galileo Galilei (1564-1642), the great Italian astronomer, first pointed the newly invented telescope at the sky in 1609. Among other great discoveries, he soon found that the Milky Way was, in fact, made up of large number of stars. Kepler, who believed in a finite universe, then argued that the darkness of the night sky was evidence that he was right, that is, the universe was indeed finite. We will see below that Kepler was also wrong. The solution of the “Olbers paradox” does not exclude the possibility of an infinite universe.


Figure. Hubble Space Telescope image of a region of the Messier 4 globular cluster. The sky is not completely covered by stars, even in this densely populated region (Image: NASA and H. Richer/University of British Columbia, Canada)

At this point in the discussion it is quite helpful to use an analogy. Let us suppose an observer in the middle of an extensive forest. Each tree has an average diameter equal to “d” — 20 cm for example. And the trees are separated from each other by an average distance “L” — 2 meters, for example. A tree will therefore occupy a total average area “A”, equal to L times L. The observer will not be able to see anything beyond a distance “D” equal to A/d.


We will have, therefore, in our example above, that, beyond a distance of 4/0.20=20 meters, our vision will be obstructed by what we can call a “wall” of tree trunks. This distance is called the “coverage distance”, or, “background boundary”. Theoretical prediction can easily be verified in a real forest! It works!

In the case of the cosmos, we have instead of an area “A”, an average volume “V”, occupied by a star. Each star presents to the observer a disk of average area “s”. We can then calculate the “coverage distance” for this case as well. And that will represent the distance at which we would see a covered sky, with the luminous intensity of the solar disk. This distance is, similarly to the forest example, V/s.


The Englishman Edward Harrison (1919-2007), who was professor emeritus of Physics and Astronomy at the University of Massachusetts, in the United States, was responsible for presenting the definitive solution to the enigma of the darkness of the night sky. In a remarkable book, entitled “The darkness of the night: an enigma of the universe”, written in 1987 and published in Portuguese, in 1995, by Jorge Zahar Editor Ltda., he presents all the historical details of the problem, and discusses the proposed solutions. — a total of 15! The fifteenth is the solution he presents, and the definitive one. His solution represents a synthesis of what is correct in some of the solutions presented.

Among the proponents of solutions to the riddle are the aforementioned Kepler and Olbers, the English physicist William Thomson (1824-1907) — Lord Kelvin — and, surprisingly, a poet and prose writer, the American Edgar Allan Poe (1809-1907). 1849).


Poe, also an amateur scientist, published in 1848, a year before his death, an essay entitled “Eureka: A Prose Poem”, where, among other things, he presents the idea – correct – that the night sky is not bright. because the distance of the background stars is so great that their light has not yet had time to reach us, due to the finite speed of light.


Lord Kelvin went further. Essentially, he agrees with Poe. His important contribution is scientific in nature. Unlike Poe, whose arguments are speculative in character, he showed, through detailed calculations, that not only was the finite speed of light an important ingredient in solving the riddle, but that the finite existence of stars was also fundamental.


Harrison calculated the background limit for the entire universe using up-to-date astronomical data and found a distance of 100 billion trillion light years! Even if this distance is so great, the universe could be bigger, and we could have a sky “infernally” covered with light. Why, after all, doesn't this happen? As the average age of stars is on the order of 10 billion years — which, incidentally, is the predicted “lifetime” of the Sun — it follows that before its light reaches us, that is,  after traveling 10 billion light years, they simply stop emitting light, as they reach the end of their evolutionary cycle.


 Harrison's final conclusion, which summarizes Kelvin's calculations quite simply, is that there is not enough energy in the universe for the sky to appear excessively bright.


Good for us humans and for all life on the planet!


Johannes Kleper


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