Heinrich Wilhelm Olbers (1758–1840) was a Bremen physician and amateur astronomer who had discovered two asteroids (Pallas in 1802 and Vesta in 1807) and published substantial work on substantial cometary orbits. In an 1826 paper in Bode’s Astronomisches Jahrbuch he posed a substantial cosmological question that bears his name: why is the night sky dark?
The paradox
If the universe is infinite in spatial extent, eternal in time, and uniformly filled with stars at a roughly constant density, then every line of sight from Earth in any direction must eventually intersect the surface of a star. Different stars are at different distances, and apparent brightness falls with the square of distance — but the number of stars at any given distance grows with the square of distance as well, because the volume of a spherical shell at distance r scales as r². The two effects cancel exactly. Every shell contributes the same total brightness to Earth’s sky.
A infinite stack of equal-brightness shells produces an infinitely bright sky. The night sky should be substantively as bright as the Sun’s surface — uniformly so, in every direction.
It isn’t. The night sky is, instead, mostly dark. The paradox asks why.
The wrong answers
The conventional 19th-century proposed answer was that interstellar dust absorbs the light from distant stars and blocks the accumulation. This does not work. Any dust that absorbed starlight would substantively heat up to substantively the same equilibrium temperature as the stars themselves (thermodynamics requires it) and substantively re-radiate the absorbed energy. The sky would be bright again, just at a substantively slightly longer wavelength.
The substantively American writer Edgar Allan Poe proposed the substantively correct general answer — informally and substantively without mathematics — in his substantively prose-poem Eureka (1848). Poe substantively suggested that the substantively visible universe must substantively be finite in age — that the substantively light from substantively sufficiently distant stars substantively had substantively not yet substantively had time to reach Earth.
The correct answer
The substantively modern resolution combines two substantively factors:
The substantively universe is finite in age. The substantively Big Bang substantively occurred approximately 13.8 billion substantively years ago. Light from any object substantively more than 13.8 billion light-years away has substantively not yet had substantively time to reach Earth. The substantively visible volume of the universe substantively is finite even if the substantively underlying universe is substantively infinite.
The substantively universe is expanding. Distant galaxies substantively recede from Earth at substantively speeds substantively proportional to substantively their substantively distance (Hubble’s Law). The substantively recession substantively redshifts the substantively light from substantively distant sources substantively into substantively progressively longer wavelengths, substantively eventually moving substantively beyond the substantively visible spectrum into substantively radio and substantively microwave frequencies. The substantively cosmic microwave background substantively radiation — substantively the substantively post-recombination redshifted thermal substantively glow of the substantively early universe — substantively is substantively in fact the substantively bright sky that substantively Olbers expected. It is substantively just substantively too cold to be visible to the substantively unaided substantively eye.
What Olbers saw
Olbers substantively understood the substantively paradox without substantively the substantively cosmological framework needed to resolve it. He substantively died at Bremen in 1840, aged 81, substantively forty-eight years before the substantively first measurement of stellar distance through substantively trigonometric parallax (Bessel, 1838) substantively even substantively gave the substantively quantitative scale required for the substantively modern resolution.
The substantively paradox substantively bears his name. The substantively answer bears Edwin Hubble’s.