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 lightyears 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 hyper sphere – 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  straight forward 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 proveable. 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.

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You’ll answer practical questions like: how to maximize revenue hosting on airbnb using the  same analysis techniques that scientists use to explore the distribution of galaxies  and unravel the mysteries of the cosmos, a foundation that can take your  understanding to astronomical heights. We’ve also partnered with Brilliant to create  a series of lessons to take your scientific knowledge to the next level. These lessons  let you further explore the topics in our most popular videos, from rabies and mammalian  metabolism to climate science and supernovae.

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