Background image: Olber’s paradox suggests that, naively, the night sky ought to be far more densely populated with starlight than in the picture.
Were the Universe to be infinite and static, any line of sight from the Earth would contain innumerable stars. Therefore, the night sky ought to appear bright, not dark. So reasoned Thomas Digges in 1576, but it was not until later work of Halley and Chasseux that it took the form of a definite paradox, for it depends critically on the fact that the fall-off in intensity of luminous sources is no faster than the inverse square. Since given an approximately uniform distribution of sources, their number at a given distance goes up as the square of that distance, the product of the two is constant, and the integral of this constant over every distance increases without bound. Given these assumptions the intensity of radiation falling on the Earth would be infinite.
The paradox is resolved given our current understanding of an expanding Big Bang universe. Not only is only a finite number of stars observable, due to the finite speed of light and the finite age of the universe, but expansion of the universe also causes light to be redshifted and its intensity to be correspondingly reduced.
This paradox is known as “Olber’s paradox” after the German astronomer Heinrich Wilhelm Olbers (1758-1840). His publication on the topic in 1823 was widely read but contributed little that was new on the subject. The paradox is also related to Seelinger’s paradox .