The Darkest Paradox In Astronomy

A drawing of a dark night sky dotted with stars and other celestial bodies.

“If stars are everywhere, then why isn’t the night sky as bright as the Sun?”

And no, the answer isn't that they are just far away. This is the puzzle Heinrich Wilhelm Olbers came across in 1823. It is a deceptively simple question, yet astronomers could not answer it for decades. After all, every line of sight should statistically end on a star at some point. Intuitively, one might think that it is just because most stars are so far away that we can’t see them. However, we’ll take a look into why this reasoning doesn’t work.

It’s true that the farther out you go, the dimmer each star gets. However, what many tend to forget is that the further out you go, the more stars you get as well. Imagine a spherical shell of stars at some distance from Earth. As you go farther out, each star’s light spreads thinner, dimming by a factor proportional to 1/(radius)². But at the same time, assuming that stars are approximately uniformly distributed around the universe, the number of stars in the shell grows proportional to (radius)².

1/(radius)² × (radius)² = constant (C)

These two effects cancel out, so any spherical shell of stars, regardless of its radius and the distance it extends to from Earth, contributes the same amount of light. Sum up all the possible shells in relation to Earth, and the total brightness should diverge to infinity. Thus, the sky would be impossibly bright.

∑[lower bound: k = 1; upper bound: infinity](C) = infinity

But this can’t be right, as the night sky clearly appears dark! The actual answer lies in three concepts much deeper and far more fundamental to physics and to the universe itself.

First, Expansion

A star is born right now at the farthest reaches of the universe. How long would it take for its light to reach us? Years? Centuries? Billions of Millennia? The answer is none of those. Its light will never reach Earth. Although the light is moving at the universal speed limit, something moves faster: the expansion of space. The photons from the star could be moving towards us, but since the distance between us and the star is increasing even faster, the light will never come to us. 

A good way to imagine this is walking up an escalator moving down even faster. You are doing work in one direction, but if your surroundings are moving more in the other direction, you will never reach the top of the escalator. This fact ends up eliminating a lot of stars. Since we can’t even see these “new” stars, their light doesn’t contribute to the night sky we see.

Next, Redshift

A diagram showing how the Doppler Effect works with sound, with the blue circles representing sound waves.

Even in the case that light actually does reach us, we might not be able to see it. 

Light is not fundamentally visible; rather, only a certain kind of light, called visible light, can be seen by our eyes, and it is a small range of wavelengths in the electromagnetic spectrum, ranging over about 300 nanometers (0.0000003 meters). Change this wavelength, and you leave the visible light spectrum, entering either the ultraviolet or infrared range. 

As the universe expands, the light waves traveling through it are stretched as well, causing the once visible light to fade away into an invisible form. Imagine a wailing ambulance moving towards you. As it approaches, the siren sounds higher pitched (condensed sound waves), but when it passes and moves away, the pitch of the siren drops suddenly (stretched sound waves). This effect is famously known as the Doppler Effect, and the same exact thing happens with light. The light waves drop into the invisible spectrum as they stretch, and they no longer contribute to the brightness of our night sky.

Finally, Age

If the universe existed forever, this paradox might become true. Luckily, our universe has an age. It’s old (~13,800,000,000 years old!), but it’s finite. Since light travels at a finite speed, it has only had a limited amount of time to reach Earth. Therefore, light from stars past a certain range has not yet reached us. This range is called a cosmic horizon, and it is the maximum distance from which light has had time to reach us since the Big Bang. Light is a traveler that has been travelling for billions of years, and much of it will have to travel for billions more to get to us. 

On the topic of age, it is important to note that stars themselves also have a lifespan. Stars aren’t just being formed; they are also being destroyed, meaning they will stop producing light.

What Does This Mean?

In the 1800s, the common understanding was that the universe is static, infinite, and eternal. This paradox showed that something in this statement had to be wrong. With modern technology, we found the answers. The universe isn’t infinite nor static, as in reality, it is the opposite: finite and expanding. The puzzling question Olbers had was indirect evidence that the universe had a beginning, and it set up a foundation for modern astrophysics. 

More than the actual discoveries, Olbers’ paradox teaches an important lesson: if a current theory predicts something obviously false, then the theory must change. If one sticks to theories that can’t withstand the tests of skeptics and time, then our collective knowledge may never advance.