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Why is the Sky Dark at Night?
A discussion of Olbers' Paradox and related issues

Copright © 1996 - 2006, P. Lutus

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Olbers' Paradox

The basic statement of Olbers' Paradox is that, in a stable, infinite universe, the night sky should blaze with the light of the stars that lie in all directions, even those far away.

Here is a small mathematical model of such a universe, with three stars about to come to life. To start "time" running, just press the button at the bottom.

This is an actual, small-scale model of heat transfer physics. For each slice of time, each cell in the model receives heat from its neighbors according to the rules of heat transfer. The "stars," of course, are sources of energy, so they do not cool off — they maintain their temperature even as they deliver energy to their environment.

If you have difficulty applying my small model to an infinite universe, here is a suggestion. First, realize that each large region of space is very much like any other — it receives some heat energy, and it radiates some also, and a typical region is in balance with its neighbors — it radiates just as much energy as it receives.

Therefore, instead of trying to imagine infinity, just imagine a large cube of space with perfect mirrors for walls. The mirrors reflect perfectly, so if you are inside and look in any direction, you see what appears to be an infinite distance.

This is what my model does — energy that reaches an edge of the square "wraps" around to the opposite edge, just as though the square was lined with mirrors. Careful thought will show that this simple method effectively mimics an infinite space.

By the way, pay attention to the changing temperatures in my small "space" as time passes. The temperatures are expressed in Kelvins, a scale in which 0 Kelvins is absolute zero — the lowest possible temperature. On this scale, room temperature is 295 Kelvins, water boils at 373 Kelvins, and steel melts at 1643 Kelvins.

One of the arguments against the classic statement of Olbers' Paradox is that there might be dust clouds that hide the light and heat of distant stars. The response to this (as you may have guessed by now) is that, over time and in a stable universe, the stars would heat the dust clouds to the stars' temperature.

Another objection is that the distant stars might be too small and far away to be seen locally. The response to this is that, at increasing distances, there are more and more stars, so their smaller apparent size is made up for by their greater numbers.
 

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