Why is it dark at night?

It seems like a trivial question: Why is it dark at night and why do we see individual stars against a dark background?

The dark silhouettes of single trees, seen from below, with the starry sky behind.
Starry Sky above a forest.

The German astronomer Heinrich Wilhelm Olbers, born in 1758, pondered exactly this question and conducted a thought experiment: At that time, it was believed that the universe was infinitely large and infinitely old, with stars homogeneously distributed within it. Under these assumptions, the light from stars in every direction should have reached us by now, and therefore, the sky should appear at least as bright as the surface of a star at every point. Even considering that the intensity of light on Earth decreases with the square of the distance to the light source (star), the number of visible stars at a certain distance would increase with the square of the distance. If one imagines the stars distributed on spherical shells around the Earth, the area of each of these hypothetical spherical shells also increases with the square of the distance. Both effects would thus cancel each other out, and in an infinitely large universe with evenly distributed stars, the sky should shine brightly everywhere. However, this is clearly not the case based on common experience.

The reason for this is that one of the assumptions underlying this thought experiment—that the universe is infinitely old—does not correspond to reality. However, this was not known during Olbers' time. It wasn't until the 20th century that it was discovered that the universe, although old, is not infinitely old—specifically, it is only 13.8 billion years old. Stars have formed and disappeared since then. This means that there hasn't been enough time for the light from infinitely many stars to reach us. Whether the universe is spatially infinite is unknown. However, what we do know is that the observable universe is finite, and its size can be estimated. Therefore, the number of stars from which we can receive light is also limited by spatial constraints.

Modern astronomy (1) has found even more reasons to fully resolve Olbers' paradox.

The theory of the beginning of the universe states that besides the visible light from galaxies and stars, there is another type of radiation, invisible to the eye, that we receive from all directions with radio telescopes. This is the cosmic background radiation, the „oldest“ form of radiation that reaches Earth. Put poetically, it is the still visible „flicker“ of the Big Bang. Approximately 400,000 years after the beginning of the universe, when the universe—initially an unimaginably hot entity—had cooled to about 3750 Kelvin, the previously free, unbound electrons and protons could aggregate into hydrogen atoms. With the atoms, the matter we know today was formed. The free electrons and protons had previously scattered all electromagnetic radiation, making the universe appear like an opaque fog. But from then on, the scattering ceased, and the universe became transparent. Due to its temperature of 3750 Kelvin, it must have emitted thermal radiation that we should be able to observe to this day. (2)

As a consequence, we should be able to perceive warmer light in the visible spectrum uniformly distributed across the entire sky at night. The reason this is not the case is that—as we now know—the universe itself, meaning space, has been expanding since its inception, causing the background radiation to be "redshifted." This shift to longer wavelengths corresponds to lower radiation energy and temperature. What we can measure today as background radiation is „cold“ microwave radiation coming uniformly from all directions, which the human eye cannot perceive. Therefore, the night sky is dark and only speckled with many, but separated, points of light.

The expansion of the universe is not to be understood as galaxies moving away from each other in space, but rather as an expansion of space itself—according to the theory of General Relativity. Since the recession velocity of galaxies increases with distance (3), beyond a certain distance, galaxies move away from us faster than the speed of light.

In space, nothing can move faster than the speed of light, but space itself can expand so rapidly that objects move away from each other faster than light. In such cases, no information can be transmitted between these objects through space. Therefore, astronomers speak of the observable universe: For any location in the universe, such as Earth, there is a horizon that defines the part of the universe from which light has been able to reach that location since the Big Bang. This horizon is referred to as particle horizon. The radius of the particle horizon is currently about 46 billion light-years, as the universe has been expanding since its inception 13.8 billion years ago (and will continue to grow in the future). This means that we can see light today from objects that was emitted shortly after the Big Bang, more than 13 billion years ago. However, due to the expansion of the universe, these objects are now much farther away from us than they were at the time of their light emission, namely 46 billion light-years.

To be a bit more precise: The particle horizon describes the region of the universe around a location from within which light could have reached that location since the Big Bang. However, this does not mean that we will ever be able to see the light that any object within this horizon emits today. This introduces two additional concepts: the „Hubble radius“ and the „event horizon“. The Hubble radius is the distance from a location at which objects (galaxies) are receding from this location at exactly the speed of light due to the expansion of space. This radius is approximately 14 billion light-years. One might assume that light within this radius could, in principle, reach the location (Earth) at some point in the distant future. Due to the uneven expansion rate of the universe over its history, the horizon beyond which information can ever reach Earth is slightly larger and is called the event horizon, with a radius of approximately 16 billion light-years. Light emitted today by a star at the edge of the particle horizon, say about 40 billion light-years away, will never be able to reach Earth. However, light emitted today within the event horizon will be able to.

Yet even within the limited „bubble“ of the observable universe, the number of galaxies is unimaginably large. A rough estimate yields 10 to 100 trillion stars. (4)

For the experience of the night sky on Earth, it is essentially the stars of our own galaxy—the Milky Way—that play a role. All the stars we can resolve as individual points with the naked eye are located in our immediate cosmic neighborhood, at most a few hundred to a few thousand light-years away. What we see on clear nights as a luminous band in the sky, commonly referred to as the „Milky Way“, is the projection of the main disk of our galaxy, where most of the stars are concentrated, onto our celestial sphere. The stars that we can no longer perceive individually with the naked eye are mostly very far from us; the center of the Milky Way is about 26,000 light-years away. Other galaxies, on the other hand, are at distances of several million to billions of light-years. The Andromeda Galaxy, our neighboring galaxy, is about 2.5 million light-years away.

The following photo was taken in Cantal in the French Massif Central. It shows the band of the Milky Way, whose brightest section can be seen from Europe in the south on summer nights. In this photo, artificial light sources played virtually no role. Visible is the center of our galaxy, partially obscured by dark interstellar dust clouds. The mountain silhouette on the right belongs to the 1,783-meter-high Puy Mary, and the distinctive notch on the mountainside to the left is the rock furrow „Breche Rollande“. This panorama is composed of several individual shots taken consecutively with the same exposure time.

A dark mountain silhouette at night with the starry sky above. 
                The bright band of the Milky Way is clearly seen in the center of the image 
                 as it rises perpendicular into the sky.
Milky Way above the Cantal, France

The following photograph shows a nighty scene at a remote lake in the Black Forest, Germany. Shooting stars are clearly visible (top right in the image), while the two shorter streaks in the center of the image are from airplanes. The photo was taken at Wildsee in the high moor near Kaltenbronn in the northern Black Forest.

A night in the forest with trees partly covering the starry sky. In the background a lake which reflects the sky. At the upper right corner, three shooting stars are visible next to each other, following nearly the same direction.
Shooting stars above a lake in the Black Forest, Germany.