"By denying scientific principles, one can maintain any paradox." -Galileo Galilei

Day and night. It seems like the simplest, most natural thing about our world, that the Sun illuminates one half of the Earth at a time.

Image credit: Public Domain Image from Desktop Wallpaper HD.

While the Earth spins on its axis, orbiting the Sun, roughly half of our lives are spent bathed in the glorious daylight provided by our parent star. The other half is spent in the dark of night, our world illuminated only by the distant stars and galaxies visible from a great distance, along with a few nearby objects that reflect our Sun's light back at us.

Image credit: Mark Unrau.

But why? Have you ever stopped to consider that there really isn't any good reason at all for the night sky to be dark?

This was first pointed out in the early 19th Century by Heinrich Olbers, who made the following argument:

The Universe is very, very large, and full of stars everywhere we look. Therefore, no matter where you look in the sky, in any direction, you'll eventually run into a star. So if all line-of-sights you can imagine eventually end on the surface of a star, why is the night sky dark, instead of illuminated everywhere?

This is known as Olbers' Paradox, and there's a beautiful illustration of it below.

Image credit: Wikimedia Commons user Kmarinas86.

As you consider objects farther and farther away, they would eventually fill-in all the dark places in the sky, and in every direction you looked, no matter how finely, there would be a photon from a distant star landing on your eye.

The immediate objection came from looking at our own Milky Way.

Image credit: Wally Pacholka.

After all, the Milky Way is full of stars: hundreds of billions of them, as we now know. Yet even on the darkest night, the perfect human eye can only see tens of thousands of individual stars, plus the galactic streak of the Milky Way itself. Of course, you'll notice there's a huge dark streak blocking out the vast majority of stars: this is neutral, light-blocking gas, known as cosmic dust.

If there's enough cosmic dust, astronomers at the time reasoned, they could block enough of the light from distant stars that the night sky would still appear dark. We see this nearby, where we are, so it stands to reason that as you go farther away, it's elsewhere, too.

Image credit: NASA and The Hubble Heritage Team (STScI/AURA) Acknowledgment: Bo Reipurth.

This argument is simple, straightforward, and demonstrably wrong. The reason Olbers' Paradox was a legitimate paradox is as follows: think about how brightness works. If the Earth were twice as far away from the Sun as it is, how much dimmer would the Sun appear? One-fourth as bright. What if it were three times as distant? The it would appear one ninth as bright. In other words, brightness falls off as one over the distance squared.

Image credit: © 2005 Lawrence Berkeley National Laboratory.

But what about the total amount of brightness? As you go farther and farther away, you can imagine that you're "seeing" more and more stars by drawing progressively larger spherical shells (hollow spheres) around your location. How much extra space are you enclosing as you add each new hollow sphere?

An amount proportional to the distance (R) squared.

So, mathematically, as you continue to consider larger and larger distances, you're adding a finite, non-decreasing amount of brightness. Which means that, if you're willing to consider arbitrarily large distances, you're considering arbitrarily large amounts of total flux. Over time, any dust that's in the way will heat up until it, too, begins to glow and shine. Meaning, once again, we'd have a night sky that looked like this.

Image credit: Wikimedia Commons user Kmarinas86.

Yet, the night sky is very clearly dark! There's a flaw in Olbers' Paradox, and you might have spotted it already if you noticed the words arbitrarily large up there.

You see, Olbers' Paradox first came up in 1823, a full 122 years before what we now know as the Big Bang model was even proposed. But we have overwhelming evidence for the Big Bang, and it teaches us a number of important truths about the Universe that contradict Olbers' (implicit) assumptions.

Image credit: ESA and the Planck collaboration.

For starters, Olbers assumed the Universe was infinite in scale. This paradox only works if you're willing to take arbitrarily large literally, and consider a Universe that's infinite in extent!

Well, our Universe is certainly big; hugely, awesomely big, and extending far beyond the part that's observable to us. But the Universe is definitely finite when it comes to its age, checking in at about 13.8 billion years. This sets a limit to how big the observable part of the Universe is to us: about 46 billion light years in radius. So that's the first resolution to Olbers' Paradox: the part of the Universe that shines for us is not infinite, and so neither is the total amount of light that's transmitted in every direction! In fact, by looking in the visible, we can see just how bright the distant Universe actually is. It's impressive, for certain, but nowhere near infinite!

Image credit: S. Beckwith & the HUDF Working Group (STScI), HST, ESA, NASA.

But there's more. You see, even if the Universe were infinite in extent, the stars in it don't live forever. (Olbers didn't necessarily know this, either.) Relying on the process of nuclear fusion to power them, stars come in a multitude of masses, sizes and colors, but they all have one thing in common: they all have a finite amount of fuel.

Image credit: NASA, ESA, and the Hubble SM4 ERO Team.

Even if the Universe were infinite in extent, the finite speed of light combined with the finite lifetime of these stars means that none of the stars that exist today will exist 100 trillion years from now. So even if the Universe went on forever, the light from a galaxy like ours, by time it reached its destination after a long enough travel-time, would have only the burned-out remnants of star systems to encounter.

But there's also one more reason the night sky is dark, and it's a reason that we're all less comfortable with: the fact that our vision, well, kind of sucks.

Image credit: Astrowiki at University of Tennessee, Knoxville.

I mean, for our everyday purposes, it's great: we're well-adapted to the light that the Sun puts out. But remember that this is only a tiny, tiny fraction (like one part in 1030) of all the electromagnetic radiation that's actually found in the Universe!

Because the Big Bang started from a hot, dense state, the relic radiation leftover from that actually does illuminate the night sky everywhere, in all directions! It's just that it illuminates the Universe at a temperature of about 2.725 Kelvin, about a factor of 1,000 too cool to be seen with our eyes.

That's exactly what the Cosmic Microwave Background is!

Image credit: NASA / COBE DMR science team.

So the reasons the night sky is dark?

The observable Universe is finite in size, age, and number of stars.

The stars that exist haven't been around forever, and won't be around forever going forward, either.

And we can't see all the different wavelengths of radiation that abound in the Universe; the Universe is dark to our eyes because of the limited amount-and-types of light that we can see.

Image credit: ESO/F. Comeron.

And that's a look into the dark depths of the Universe!