The Paradox of an Infinite Universe

Is the universe infinite? Does it have an edge? And if so, what would you see if you went there?

Today we know that the universe had a beginning 14 billion years ago and that it's been expanding ever since. But something that's expanding should also have an edge, right? Well, it sort of does. Information can’t travel faster than light. That means that we can only see parts of the universe whose light has had time to reach us in the last 14 billion years.

When we look outwards, what we see is a sphere centered on us, the observable universe. But it gets a tad more complicated – because the universe has been expanding, we know that the most far away things whose light we can see are actually 45 billion light years from us right now. So the observable universe is a sphere with a radius of 45 billion light years.

It contains around 200 billion galaxies, each with hundreds of billions of stars. So for us, there is an edge: We are looking at the past until there is just no past left. This edge is really more like an edge in time and in a sense meaningless. The real universe is for sure bigger than what we can see.

But how much? There are two options – either the universe is really big but finite, or it’s truly infinite. A finite universe means that, if you want to fill it with ice cream, you can do it. You need a lot of ice cream, but it is a finite amount. But that leads to a weird problem. Such a universe should have an edge, a cosmic wall where space ends.

And if there is an edge there should be something outside that edge. But the universe by definition is “all there is”, so how could there be stuff outside all there is? Does the idea of something outside of everything even make sense? Except of course there is a physics hack: You can have a universe that has no border, but that still could be filled with a finite amount of ice cream.

What if the universe is truly finite? Imagine an orange and a really tiny ant. The ant can only see a small piece of the skin – just as you can only see a small chunk of the universe. But if the ant starts walking, it will eventually walk around the whole orange and be back to its starting point.

So the skin of an orange is not infinite – but it doesn’t have a border. The universe is not like the skin of an orange, but it could be very similar – instead of a sphere, it could be a hypersphere, where 3D-space is curled on itself. Which is impossible for your brain to visualize unfortunately. But the point is: no borders, no outside of the hypersphere – from our human ant perspective, our whole 3D space is like the peel of the orange.

If you were aboard a spaceship flying in a straight line, you would eventually come back to Earth. How does any of this make sense? The actual physics is hard, so we have to simplify and lie a bit here. But in a nutshell it all boils down to gravity: The way it works is that mass creates gravity by bending spacetime.

This bending is the strongest where the mass is, but sort of stretches on forever, like a very mild tension in the fabric of spacetime itself. This could bend the whole universe in a way where it bends back on itself, which then makes the hypersphere. If you find this confusing, we are with you.

If the universe happens to be a hypersphere, how could we find out how big it is? On Earth we can see things disappear below the horizon and that helps us calculate how big the Earth is. Scientists tried to find some sort of “universe horizon” that would reveal the scale of the cosmic sphere – but didn’t see anything.

Which means that if the universe is a hypersphere, it needs to be so big that from our perspective it looks like we are living on a flat surface. For this to make sense, a hyperspherical universe should be at least 1,000 times bigger than our observable part. It could be a trillion times bigger for all we know, but not smaller than that.

Some scientists thought all of this is way too straightforward and came up with a wilder option: The universe could be like the frosting of a donut. A hyperdonut – also impossible to visualize for your brain. This, too, means that if you travel in a straight line, you'd get back to where you started.

But with fun complications. In a hyperdonut universe there is not the same amount of stuff in every direction. If two spaceships fly in different directions, one could get back to the start way earlier. This also means that light from faraway galaxies would do fun and confusing stuff, in a sort of cosmic hall-of-mirrors effect.

We could see far away things in two places – but not just that, but we would see it in different moments in time! Because its light would have taken much longer to travel in one direction than the other! You could see a star being born in front of you and see that same star die on the opposite side of the sky. How big would such a hyper donut universe be?

Well, because of its strange geometry, actually this is kind of the smallest possible universe – potentially just a few times bigger than the observable universe. But it could also be way, way bigger. We don’t know. Ok. So much for finite universes.

But… What if it's truly infinite and space goes on forever? What would that be like? What if the universe is truly infinite? Actually, the cosmological model used by most scientists describes an infinite universe. We mostly use it to calculate what happens inside our observable chunk, but if taken literally, it predicts an infinite universe.

An infinite universe goes on, well, forever, with no border anywhere – also impossible to visualize. Wherever you look you'll find more and more stuff in every possible direction. This kind of breaks our brain a bit for a few reasons: First of all, if the universe is infinite, is it also eternal and has been there forever? Was there a time where there was nothing everywhere and then there was something everywhere?

Well we don’t know – but we have a lot of evidence for the big bang, so it really seems like the universe started at some point in the past. But wait – since the big bang the universe has been expanding. How can an infinite thing that is everywhere become even bigger? Cosmic expansion just means that the distance between galaxies is growing with time.

Even an infinite space can become bigger. Welcome to the paradoxes of infinity. Infinity gets much weirder though. As you travel with your spaceship in a straight line, you find new galaxies, stars and planets, new wonders, new weird stuff, probably new aliens and new lifeforms stranger than you could ever imagine.

But after a long time, you might find the most special thing in the universe: Yourself. An exact copy of you watching this video right now. How can that be? Well, everything in existence is made of a finite amount of different particles. And a finite number of different particles can only be combined in a finite number of ways.

That number may be so large that it feels like infinity to our brains – but it's not really. If you have finite options to build things, but infinite space that is full of things in all directions forever, then it makes sense that by pure chance, there will likely be repetition.

Although just because something is possible, doesn't mean it will actually happen. Maybe the universe goes on forever but only the boring stuff repeats itself endlessly. Maybe there is really only one you. But if the laws of physics are the same everywhere, then far, far away gas could have given birth to stars and planets, where primitive genetic information could emerge from chemistry.

Which might have ended up in cells and animals that evolved in really unlikely ways. And eventually apes that learn how to create online videos. It happened at least once, so the chance is not 0. Even if the chance of there being an exact copy of you watching this video right now is almost zero – almost zero is still a huge number in an infinite universe.

Unfortunately you'll never meet. Because almost zero still means the chance is incredibly small. Earth as it exists right now is so unlikely, you’d have to travel incredibly far to find a second identical Earth: Some 10 to the 10 to the 29 – a 1 followed by 100 octillion zeros – times the size of the observable universe. So far that it kind of means forever far away.

Still, in a truly infinite universe, every combination of particles could reasonably not just (sighs) It's time to stop now. While these scenarios are possible on paper – we've entered science philosophy here. Currently none of these ideas are testable or provable.

If the universe is infinite we will never know. The reality is, for us the universe is finite and has an edge. And we can see the edge, the edge in time. Everything we can interact with is within the observable universe and most likely, this will stay true forever.

Even if this finite universe feels small to you, it's more than big enough to fulfill all the dreams that we and our descendants can ever come up with. Infinitely enough for all of us. While we can’t be sure whether the universe is infinite, many fascinating questions do have definitive answers in science, math, and technology - and you can learn all about them on Brilliant.org.

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