Why is the sky dark at night?
The question of why it is that the sky is dark at night is believed to have been first asked by Johannes Keppler in the 17th Century. However, the paradox is widely credited to the German astronomer H.W.M Olbers who presented his paper on the subject in 1823.
In order for one to appreciate the paradox, as it was then presented, one must first understand how it was that the universe was then perceived. In the 19th century the universe was believed to be both static and infinite, and described by the ordinary three-dimensional space of Euclidian Geomotetry.
However, Olbers argued that if this model of the universe were correct the sky should not be dark but rather very bright indeed. Assuming a 19th century view of the universe, as there are an infinite number of stars, if one follows any line of sight in the night sky one should eventually come to a star, which would result in the sky not only being bright, but intensely so.
An initial reaction might be to dismiss this argument, knowing that the intentisty of a star is inversely proportional to the square of the distance from the observer (r²), and that the furthest stars are therefore much dimmer to an obsever on Earth. However this effect is countered by the fact that the volume of the universe (and therefore the total number of stars) grows at a rate directly proportional to the cube of the distance from the obsever (r³).
So why is the sky dark at night?
As you will be aware, the 19th century model of the universe is now known to be inaccurate. The observable universe is neither static, nor infinite. The age of the universe is currently estimated to be 13.75 billion years old (that is 13.75 billion years since the Big Bang) and consequently we can only observe stars that are within 13.75 billion light years (that is the distance that light can travel in 13.75 billion years) of Earth. It has been calculated that within this vast but finite space there are approximately one thousand billion billion stars (10²¹).
In addition to this, the space-time of the univesre (as described by Einstein, and very different from ordinary Euclidean three-dimensional space) is continually expanding. As a consequence of this, the most distant stars in the observable universe are moving away from us at a velocity approaching the speed of light. This has the effect of further diminishing the intensity of their light, as obsevered from Earth.
It can therefore be seen that, whilst the myriad stars contribute to the glow of the night sky, it is no longer a mystery as to why it the sky remains dark at night.
It is intersting to note that Einstein's General Theory of Relativity (1916), which incorporates gravity into a fundamental description of space-time, implies that the universe is expanding. This ran contrary to the then widely accepted belief among scientists that the universe was static. Bizzare as it may seem in today's light, upon this realisation of the implication of his theory, and despite Olbers' unresolved paradox, Eistein decided to modify his theory to suit the perception of a static universe rather than modify his perception of a static universe to suit his theory, and thus resolve the paradox. It was not until the 1920's, when Edwin Hubble's observations from Mount Wilson clearly demonstrated that the universe is expanding, that the modifications to Einstein's theory were found to have been unnecessary.
So what would the night sky look like if our planet were somehow transported into a hypothetical universe which was both static and infinite?
It wouldn't; at least, not to you or I. Our planet would be obliterated by thermal radiation. The night sky would be as bright as a stellar surface, but there would be nobody left to see it.