The Paradox of an Infinite Universe

Summary

The video explores whether the universe is infinite or finite. It discusses the observable universe, a sphere with a 45 billion light-year radius, containing 200 billion galaxies. The real universe could be finite but much larger, possibly curved into a hypersphere or hyperdonut shape. If infinite, the universe may repeat itself, with exact copies of ourselves existing impossibly far away. While these ideas are intriguing, the video ultimately acknowledges that we may never know the true nature of the universe's boundaries. For us, the observable universe is finite and has an edge in time—a perceptible horizon we can see. Despite its apparent limits, this finite universe offers boundless possibilities for humanity's dreams and aspirations.

Takeaways

• 🌌 The observable universe is a sphere with a radius of 45 billion light-years, containing around 200 billion galaxies.
• ⚫ The real universe is likely bigger than what we can see, but it's still unknown whether it's finite or infinite.
• 🍩 If the universe is finite, it could be a hypersphere or a hyperdonut, where space is curved on itself, and you could eventually return to your starting point if you travel in a straight line.
• ♾️ If the universe is truly infinite, it goes on forever in all directions, with no borders or edges.
• 🔄 In an infinite universe, everything made of a finite number of particles could repeat by chance, leading to the possibility of exact copies of yourself existing infinitely far away.
• 🔭 For us, the observable universe is finite, and we can see its edge in time, but it's still more than enough to fulfill all our dreams and those of our descendants.
• ⏳ We're living in a perfect moment in cosmic time, at the tail end of star formation, with so much still to explore and admire.
• 🌌 The cosmological model used by most scientists predicts an infinite universe, but this scenario is not testable or provable with current knowledge.
• 🧠 The concepts of infinity and infinite possibilities in the universe can be mind-bending and paradoxical.
• 🌈 Brilliant.org offers interactive lessons and hands-on courses to further explore scientific knowledge and understanding of the universe.

Q & A

What is the observable universe?

The observable universe is a sphere centered on us, with a radius of 45 billion light-years. It contains around 200 billion galaxies, each with hundreds of billions of stars, and represents the part of the universe whose light has had time to reach us in the last 14 billion years since the Big Bang.

Why is there an edge to the observable universe?

We see an edge or horizon to the observable universe because information (including light) cannot travel faster than the speed of light. We can only see parts of the universe whose light has had time to reach us in the 14 billion years since the Big Bang. This edge is really more like an edge in time, rather than a physical boundary.

Is the universe finite or infinite?

There are two possibilities: either the universe is really big but finite, or it's truly infinite. We don't know for sure which one is correct based on current evidence and observations.

What is a finite universe like?

A finite universe could be like a hypersphere, where 3D space is curled on itself in a way that means it has no borders or edges. In such a universe, if you travel in a straight line, you would eventually come back to your starting point.

Could the universe be a hyperdonut?

Yes, some scientists have proposed that the universe could have a hyperdonut shape, which is even harder to visualize than a hypersphere. In a hyperdonut universe, the amount of matter and energy would vary in different directions, leading to some strange effects like seeing the same galaxy at different points in time from different perspectives.

What would an infinite universe be like?

An infinite universe would go on forever, with no border anywhere. In every direction, you would find more and more galaxies, stars, planets, and potentially new forms of life and civilizations. The universe could even contain infinite copies of yourself and everything else, distributed unimaginably far apart.

Can we ever know if the universe is infinite?

Unfortunately, if the universe is truly infinite, we will never be able to know or prove it. The reality is that for us, the universe is finite and has an edge, which is the edge in time that we can see with the observable universe.

What is the significance of the observable universe?

Even if the observable universe feels small, it is more than big enough to fulfill all the dreams and aspirations of humanity and our descendants. Everything we can interact with is within this finite observable universe, which is likely all we will ever be able to explore.

What is the purpose of the Brilliant lessons mentioned in the script?

The script mentions that Kurzgesagt has partnered with Brilliant to create a series of interactive lessons that allow viewers to further explore the topics covered in popular Kurzgesagt videos. These lessons are designed to take viewers' scientific knowledge to the next level through hands-on, interactive learning.

What is the significance of the limited edition pin mentioned at the end of the script?

The script mentions a limited edition pin depicting the end of the universe, part of Kurzgesagt's Existential Dread Collection. This pin serves as a reminder that we are living in a perfect moment in cosmic time, at the peaceful tail end of star formation but with still so much to explore and admire in the universe. Purchasing the pin helps support Kurzgesagt's mission to inspire wonder and curiosity about science.

Outlines

00:00

🌌 The Observable Universe and Its Edges

This paragraph discusses the observable universe and its limits. It explains that due to the finite speed of light, we can only see a sphere of the universe centered on us, with a radius of 45 billion light-years. This sphere contains about 200 billion galaxies. The observable universe is an edge in time, as we are looking at the past until there is no past left. However, the real universe is likely much larger than what we can observe.

05:03

🥤 Finite vs. Infinite Universe

This paragraph explores the possibilities of the universe being finite or infinite. A finite universe could be filled with a finite amount of ice cream, but it would have to have an edge, which is problematic. Alternatively, the universe could be finite but without an edge, like the surface of a hypersphere or a hyperdonut. An infinite universe, on the other hand, would go on forever, leading to mind-bending paradoxes and the possibility of infinite copies of ourselves and our observable universe existing, though separated by vast distances. Ultimately, the paragraph concludes that determining whether the universe is truly infinite is not testable or provable with current knowledge.

10:05

🎓 Brilliant.org: Expand Your Knowledge

This paragraph promotes Brilliant.org, an interactive learning platform that offers courses and lessons on various scientific and mathematical topics. It highlights the partnership between Brilliant and Kurzgesagt to create interactive lessons exploring topics from their popular videos. The paragraph encourages viewers to start a free trial and take advantage of Kurzgesagt's lessons on Brilliant.org to further their understanding of scientific topics.

Keywords

💡Observable Universe

The observable universe is the portion of the universe that we can observe from Earth based on the distance light has traveled since the Big Bang. It is a spherical region with a radius of about 45 billion light-years. The video explains that we can only see parts of the universe whose light has had time to reach us in the last 14 billion years. The observable universe contains about 200 billion galaxies, each with hundreds of billions of stars.

💡Hypersphere

A hypersphere is a hypothetical geometry of the universe where 3D space is curved on itself, similar to the surface of an orange. If the universe is a hypersphere, it would have no borders or an 'outside,' but it could be finite and traversable, meaning if you traveled in a straight line, you would eventually return to your starting point. The video explains that a hyperspherical universe could be at least 1,000 times bigger than the observable universe.

💡Hyperdonut

A hyperdonut is another hypothetical geometry of the universe, where space is curved like the frosting of a donut. If the universe is a hyperdonut, traveling in a straight line would eventually lead you back to your starting point. However, the distribution of matter and light would be uneven, leading to strange effects like seeing the same galaxy in two different places and at different points in time. The video suggests that a hyperdonut universe could be just a few times bigger than the observable universe.

💡Infinite Universe

An infinite universe is a cosmological model where space goes on forever without any borders or edges. In an infinite universe, no matter how far you travel, you would continue to encounter new galaxies, stars, and cosmic wonders without ever reaching an end. The video explains that most cosmological models describe an infinite universe, although it is impossible to visualize or confirm whether the universe is truly infinite.

💡Big Bang

The Big Bang is a cosmological theory that describes the origin of the universe as a singularity that expanded and cooled, leading to the formation of the first subatomic particles, atoms, and eventually galaxies and stars. The video mentions that the universe had a beginning around 14 billion years ago with the Big Bang and has been expanding ever since.

💡Cosmic Expansion

Cosmic expansion refers to the observed phenomenon that the universe is continuously expanding, with galaxies moving away from each other at increasing speeds. The video explains that even an infinite universe can become bigger through cosmic expansion, which means the distances between galaxies are growing over time.

💡Cosmological Model

A cosmological model is a theoretical framework that describes the origin, evolution, and possible future of the universe. The video mentions that most scientists use a cosmological model that predicts an infinite universe, although it is primarily used to calculate what happens within the observable universe.

💡Paradox of Infinity

The paradox of infinity refers to counterintuitive concepts that arise when considering an infinite universe. The video highlights several paradoxes, such as how an infinite universe can expand and become bigger or how an infinite space could contain repetitions of finite particles and structures, leading to the possibility of infinite copies of ourselves existing in different parts of the universe.

💡Observable Chunk

The observable chunk refers to the portion of the universe that we can currently observe and interact with from Earth. The video states that even if the universe is infinite, we can only interact with and study the observable universe, which is finite and has an edge in time.

💡Cosmic Time

Cosmic time refers to the time scale of the universe, which spans billions of years since the Big Bang. The video suggests that we are living in a perfect moment in cosmic time, at the peaceful tail end of star formation but with still much to explore in the observable universe.

Highlights

We can only see parts of the universe whose light has had time to reach us in the last 14 billion years.

The observable universe is a sphere with a radius of 45 billion light years, containing around 200 billion galaxies, each with hundreds of billions of stars.

The real universe is for sure bigger than what we can see.

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

Transcripts

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  

occur only once, but an infinite number of times.  So there actually might be an infinite amount of  

copies of yourself. All of them are living within  their own observable universe. All of them looking  

at the sky, never able to ever interact with  each other because all of you are so far apart.

Maybe some of these versions made different  decisions, fell in love with different people,  

took different forks in life. Maybe  one of them has solved physics. Maybe  

another one is living your exact  life but is wearing a funny hat.

But if there are so many, infinite copies of you,  

identical to you, who are  you? Well it doesn’t matter,  

because you are as real as real beings get, if  you exist infinite times or if you exist once.

(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,  

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The next limited edition pin in our Existential  

Dread Collection is here. This time  it contains THE END OF THE UNIVERSE.

Oh no, the lights are going  out in the night sky! What's  

happening? Quick! To the observatory!  We need to find out what’s going on.

When we look into the night sky we  can see all the way back to the Big  

Bang. Let’s turn this telescope  around and look into our future.

It's true! You can see the universe  expanding, galaxies drifting apart and  

stars dying in epic supernova explosions. In the  end nothing will remain. Total darkness.

It turns out that we are actually living in  the perfect moment in time. At the peaceful  

tail end of star formation – but with still  so much out there to admire and explore.

Let’s take a few snapshots. Here, take  them and wear this pin as a reminder  

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Pre-order of this very special limited edition pin  is available for only 72h, so order now before it  

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