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Astronomy — Why does it get dark at night?

We have all noticed that the night sky is dark.  However, reasonable assumptions about the geometry of the universe can lead us to the conclusion that the night sky should glow as brightly as a star’s surface.  This conflict between observation and theory is call Olbers’ paradox after Heinrich Olbers, a Viennese physician and astronomer who discussed the paradox in 1826.  However, Olber’s paradox is not Olbers’.  The problem of the dark night sky was first discussed in 1576 and was further analyzed by such astronomer as Johannes Kepler in 1610 and Edmond Halley in 1721.  Olbers gets the credit through an accident of scholarship on the part of modern cosmologists who did not know of previous discussions.  What’s more, Olbers’ paradox is not a paradox.  We will be able to understand why the night sky is dark by revising our assumptions about the nature of the universe.

To begin, let’s state the so-called paradox.  Suppose the universe is static, infinite, eternal, and uniformly filled with stars.  If we look in any direction, our line of sight must eventually reach the surface of a star.  Consequently, every point on the surface of the sky should be as bright as the surface of a star, and it should not get dark at night.  Of course, the most distant stars would be much fainter than the nearer stars, but here would be a greater number of distant stars than nearer stars.  The intensity of the light from a star decreases according to the inverse square law, so distant stars would not contribute much light.  However, the farther we look in space, the large the volume we survey.  Thus the number of stars we see at any given distance increases as the square of the distance.  The two effects cancel out, and the stars at any given distance contribute as much total light as the stars at any other distance.  Then given our assumptions, every spot on the sky must be occupied by the surface of a star, and it should not get dark at night.

Imagine the entire sky glowing with the brightness of the surface of the sun.  The glare would be overpowering.  In fact, the radiation would rapidly heat the earth and all other celestial objects to the average temperature of the surface of the stars, at least 1000 degrees Kelvin.  Thus we can pose Olbers’ paradox in another way: “Why is the universe so cold?”  Olbers assumed the sky was dark because clouds of matter in space absorb the radiation from distant stars.  But this interstellar medium would gradually heat up to the average surface temperature of the stars, and the gas and dust clouds would glow as brightly as the stars.  Today’s cosmologists believe they understand why the sky is dark.  Olber’s paradox makes the incorrect prediction that the sky should be bright because it is based on two incorrect assumptions.  The universe is neither static nor infinitely old.

The galaxies are receding from us.  The distant stars in these galaxies are receding from the earth at high velocity, and their light is Doppler-shifted to long wavelengths.  We can’t see the light from these stars because their light is red-shifted, and the energy of the photons is reduced to levels we cannot detect.  Expressed in another way, the universe is cold because the photons from very distant stars arrive with such low energy they cannot heat up objects.  Although this explains part of the problem, the red shifts of the distant galaxies are not enough to make the sky as dark as it appears.

The second part of the explanation was first stated by Edgar Allan Poe in 1848.  He proposed that the night sky was dark because the universe was not infinitely old but had been created at sometime in the past.  The more distant stars are so far away that light from them has not reached us yet.  That is, if we look far enough, the look-back time is greater than the age of the universe, and we look back to a time before stars began to shine.  Thus the night sky is dark because the universe is not infinitely old.  This is a powerful idea because it clearly illustrates the difference between the universe and the observable universe.  The universe is everything that exists, and it could be infinite.  But the observable universe is the part that we can see.  It is estimated that the universe is 15 to 20 billion year old.  In that case, the observable universe has a radius of 15 to 20 billion light-years.  Do not confuse the observable universe, which is finite, with the universe as a whole, which could be infinite.  The assumptions that we made when we described Olbers’ paradox were at least partially in error.  This illustrates the importance of assumptions in cosmology and serves as a warning that our commonsense expectations are not dependable.  All of astronomy is reasonably unreasonable — that is, reasonable assumptions often lead to unreasonable results.  That is especially true in cosmology, so we must examine our assumptions with special care.

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