The Paradox of an Infinite Universe

Is the

universe

infinite

? Does it have any advantages? 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 has been expanding ever since. But something that is expanding should also have an advantage, right? Well, in a way it does. Information cannot travel faster than light. That means 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 outward, what we see is a sphere centered on us, the observable universe. But it gets a little more complicated: Because the universe has been expanding, we know that the farthest things whose light we can see are actually 45 billion light years away from us right now.

So the observable universe is a sphere with a radius of 45 billion light years. It contains about 200 billion galaxies, each containing hundreds of billions of stars. So, for us there is an advantage: we look at the past until there is no past left. In reality, this advantage is more like a time advantage and, in a sense, is meaningless. Without a doubt, the real universe is larger than what we can see. But how much? There are two options: either the universe is really large but finite, or it is truly

infinite

. A finite universe means that if you want to fill it with ice cream, you can.

You need a lot of ice cream, but it's a finite amount. But that leads to a strange 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 “everything that exists,” so how could there be things outside of everything that exists? Does the idea of ​​something outside of everything make sense? Except, of course, there's a physics trick: you can have a universe that has no boundaries, but could still be filled with a finite amount of ice cream.

What if the universe was truly finite? Imagine an orange and a really small ant. The ant can only see a small piece of skin, just as you can only see a small piece of the universe. But if the ant starts walking, it will eventually go around the entire orange and return to its starting point. So the skin of an orange is not infinite, but it also has no edge. The universe is not like the peel of an orange, but it could be very similar: instead of a sphere, it could be a hypersphere, where three-dimensional space is curled around itself.

Which, unfortunately, is impossible for your brain to visualize. But the point is: there are no borders, there is no outside the hypersphere; From our human ant perspective, our entire 3D space is like the peel of an orange. If you were aboard a spaceship flying in a straight line, you would eventually return to Earth. How does all this make sense? Real physics is hard, so we have to simplify and lie to ourselves a little here. But in a nutshell, it all comes down to gravity: the way it works is that mass creates gravity by bending spacetime. This curvature is strongest where the mass is, but in some ways it goes on forever, like a very slight tension in the fabric of space-time itself.

This could bend the entire universe in a way that would fold in on itself, which would then form the hypersphere. If this is confusing to you, we're with you. If the universe were a hypersphere, how could we know its size? On Earth we can see things disappear below the horizon and that helps us calculate the size of the Earth. Scientists tried to find some kind of "universal horizon" that would reveal the scale of the cosmic sphere, but they saw nothing. Which means that if the universe is a hypersphere, it has to be so big that, from our perspective, it looks like we live on a flat surface.

For this to make sense, a hyperspherical universe would have to be at least 1,000 times larger than our observable part. For all we know, it could be a trillion times larger, but no smaller than that. Some scientists thought this was all too simple and came up with a crazier option: the universe could be like the icing on a donut. A hyperdona, also impossible for your brain to visualize. This also means that if you travel in a straight line, you will return to the starting point. But with fun complications. In a hyperdonut universe there are not the same amount of things in all directions.

If two spacecraft fly in different directions, one could return to the starting point much sooner. This also means that light from distant galaxies would produce fun and confusing things, in a sort of cosmic hall-of-mirrors effect. We could see distant things in two places, but not only that, we would see them at 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 born in front of you and see that same star die on the opposite side of the sky. How big would such a hyperdonut universe be?

Well, due to its strange geometry, this is actually the smallest possible universe, potentially a few times larger than the observable universe. But it could also be much bigger. We do not know. OK. So much for the finite universes. But... What if it is truly infinite and space lasts forever? What would that be like? What if the universe was truly infinite? In reality, the cosmological model used by most scientists describes an infinite universe. We mainly use it to calculate what happens inside our observable fragment, but if taken literally, it predicts an infinite universe. An infinite universe continues, well, forever, with no boundaries anywhere and impossible to visualize.

Everywhere you look you will find more and more things in every possible direction. This breaks our brains a bit for several reasons: First, if the universe is infinite, is it also eternal and has it been there forever? Was there a time when there was nothing everywhere and then there was something everywhere? Well, we don't know, but we have a lot of evidence from the big bang, so it really looks like the universe began 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 simply means that the distance between galaxies increases over time. Even infinite space can become larger. Welcome to the

paradox

es of infinity. However, infinity gets much stranger. As you travel with your spaceship in a straight line, you encounter new galaxies, stars and planets, new wonders, new strange things, probably new aliens and new life forms stranger than you can 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 it be? Well, everything that exists is made of a finite number 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 seems infinite to our brain, but in reality it is not. If you have finite options for building things, but an infinite space that is filled with things in all directions forever, then it makes sense that by pure chance, there would probably be repetition. Although just because something is possible doesn't mean it will actually happen. Maybe the universe goes on forever but only boring things repeat endlessly. Maybe there really is only one. But if the laws of physics are the same everywhere, then, far, far away, gas could have given rise to stars and planets, from which primitive genetic information could emerge from chemistry.

Which could have ended up in cells and animals that evolved in truly improbable ways. And finally, apes that learn to create online videos. It happened at least once, so the probability is not 0. Even if the probability that there is 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 will never meet. Because almost zero still means the probability is incredibly small. The Earth as it exists now is so improbable that you would have to travel incredibly far to find a second identical Earth: about 10 to 10 to 29 (a 1 followed by 100 octillion zeros) times the size of the observable universe.

Until now that means always being away. Still, in a truly infinite universe, every combination of particles could reasonably not simply (sigh). It's time to stop now. While these scenarios are possible on paper, here we have entered into the philosophy of science. Currently, none of these ideas are testable or demonstrable. If the universe is infinite we will never know. The reality is that for us the universe is finite and has an advantage. And we can see the limit, the limit in time. Everything we can interact with is within the observable universe and this will most likely remain the case forever.

Even if this finite universe seems small to you, it is more than enough to fulfill all the dreams that we and our descendants may have. Infinitely enough for all of us. While we can't be sure if the universe is infinite, many fascinating questions have definitive answers in science, mathematics, and technology, and you can learn all about them at Brilliant.org. Brilliant will make you a better thinker and problem solver, with thousands of practical lessons on almost anything you might care about. They recently launched a whole new set of data courses that use real data to tell powerful stories while training your brain to see trends through the chaos of truly massive data sets.

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