Why is the Night Sky Dark?

During Olber's time, it was generally assumed that the universe was both infinite and eternal. If this were so, pondered Olber, then how can it be that one can look into the sky and see anything but a solid field of light, as if the whole of it were one continuous star?

Certainly, at greater distances from Earth, stars seem dimmer. However, with increased distance comes an increased field of view, so the two should cancel out, leaving an unbroken surface of starlight. Every line of sight must end at the surface of a star. An analogy might be that in an infinite forest, every line of sight must end at a tree trunk.

Olber himself believed that he had solved this riddle by resolving that there was dust and other matter floating about in space, which was believed to be totally empty at the time. He proposed that all this dust and debris would serve to block starlight from a sufficient distance, much like fog. Just like fog, nearby lights are clearly visible, more distant ones appear muted, and, beyond a certain point, they vanish altogether. In the forest analogy, this would be like supposing that every line of sight must end at a tree trunk, unless a leaf or something else is in the way.

A popular idea that refutes Olber's solution is that, should the universe be infinite, this dust would be heated to by the infinitude of starlight to the point that it also would shine as brightly as a star. Of course, this idea is flawed.

The mistaken assumption is that this dust would radiate in the visible spectrum. Clearly, the dust and gas would not hold on to energy merely for our benefit - it must radiate it away, and would probably do so at a wavelength well short of visibility.

Additionally, supposing that an infinitude of starlight would reach any such cloud in order to heat it to the point that it would emit in the visible spectrum ignores the absorption of energy by other clouds. Either all such clouds are absorbing energy, or none are. Thus, they are either all transparent, or not. Our best experiments, such as the surveys of the Lyman-Alpha 'forests' in some Quasar spectra, confirm that they are there, and that they do absorb energy.

The final fallacy is the notion that even if the clouds do dissipate energy via radiating it that, eventually, enough energy would build up between them to force the clouds to emit in the visible range. This supposition totally ignores Thermodynamics; the energy gradient runs in one direction only. A 100 degree source, for example, cannot heat anything to over 100 degrees. Likewise, radiation from these clouds cannot heat other clouds to a temperature higher than the cloud of the radiation's origin.

The only valid conclusion to Olber's paradox, then, is that the whole of the sky does shine as brightly as the stars - at whatever wavelength the clouds are radiating at. As it happens, in 1965 we did detect just this type of omni-directional uniform radiation: it is called the Cosmic Microwave Background, and it fills our entire sky with light at the 2mm wavelength, with a variation of only about 0.00001%. At 2mm, the sky does seem to be one flat, uniform surface of solid light.

It seems that Olber was correct after all. We live in an infinite forest of stars, where every line of sight ends at a star, or something else that is in the way.