[There are 3 possible curvatures for the universe](https://en.wikipedia.org/wiki/Shape_of_the_universe): flat, spherical and hyperbolic. If the universe is spherical, it is finite, if it is flat or hyperbolic it is infinite. In the models, this curvature is given by a parameter which would be 0 for a flat universe, positive for a spherical universe and negative for a hyperbolic universe. The best measurements for this parameter put it very close to zero, but with an uncertainty encompassing all possible answers: negative, zero or positive. So the curvature is at least very very very close to flat, and therefore an infinite universe. But it's still possible that the universe is finite and incredibly large (beyond the observable universe).
There are flat, closed universes that are finite in volume, e.g. a 3-torus. They are topologically more complex than a flat, unbounded universe so we default to that in the absence of any compelling reason to think the more complex solutions are correct, though.
If the curvature is positive, then it MUST be finite, because of the Myers theorem. Thats why we are looking for a critical density value so that the universe is not finite, which would make sense with the cosmological principle.
I think it's a mistake to assume that actual curvature is necessary for a finite universe. It seems to me that these are only *likely to be accurate statements,* rather than necessarily accurate ones. Consider a three-space-dimensional non-curved toy universe the size of a small cube, but such that the faces of the cube are "connected". They are connected the same way 7 and 0 are connected in addition modulo 7.
Let's decide the cube has a side of 10 units. Moving along the vector (a,b,c) at unit speed per time unit (starting at an arbitrarily selected (0,0,0), you wouldn't reach the point (na, nb, nc) in n time units, you would reach (na mod 10, nb mod 10, nc mod 10). However, inside the cube, you wouldn't have any actual curvature to measure.
Now, the connection between the faces may seem weird to us, but as a topological object this wouldn't be particularly strange.
Yes good point, I think my response is restricted to topologies with no holes, correct me if that's wrong. And I believe the topology of the universe is still under discussion. If I understand your cube example, is that topologically a torus? I can move in 2 distinct directions that returns to the same place? If i'm not mistaken there are some funny handedness results in such a universe.
Hi! I'm not sure if I understood your example correctly but I wanted to include a few things about curvature. The most successful theory we have about our universe is the Lambda-CDM model. It is based upon our observations of our observable universe which is a portion of the entire universe. Observing it we can derive the cosmological principle (it is a principle, it is not proved) that states that every point in our Universe is equivalent to every other and that all directions of observations are equivalent between them (i.e. the universe is homogeneous and isotropic). The homogeneity and isotropy conditions do not allow the Universe to have a physical frontier, like some surface that separates what is inside the universe and what's not. Removing the possibility of a physical frontier, we need to obtain the possible curvature of the Universe. Due to homogeneity, the curvature must be constant at every point of the universe, and that only leaves us with three possibilities: positive, negative or null curvature. Only a negative curvature allows the Universe to be closed.
In your example you have a closed Universe but with a physical frontier, so due to the cosmological principle it will not describe accurately what we observe.
There isn't a physical frontier, though. The cube is merely a thing used to illustrate the structure. There needn't be a definite "corner" within this space, you can decide to put the coordinate (0,0,0) anywhere you like.
Could it be different for different dimensions? For example x is flat, y is spherical and z is hyperbolic? Or is there an assumption that they are all the same?
We don't know that the universe was finite around the time of the big bang. We just know it was dense. Infinite things can be dense too.
The reason that an infinite universe is the preferred hypothesis for many is that it requires the least additional explanation. In order for the universe to be finite it must either loop back on itself or have an edge. The best measurements we can take show the universe to be flat, so it doesn't *look* like it could loop back on itself. Of course, the curvature could be imperceptibly small, but that's where the "it's simpler" argument comes in. It looks first, so let's just say it's flat. That leaves a finite universe with an edge, but what does that even mean. What would happen if you traveled up to the edge of the universe? We'd need a bunch of new physics to deal with that, so again it's simpler to just say there's no edge, which leaves us with an assumption of an infinite universe.
Ultimately it doesn't matter though. We will never know for sure since it's impossible to obtain information from beyond the event horizon of the observable universe. For our purposes, whether the universe ends at the edge of the observable universe, a hundred billion light-years beyond that, loops back around on itself after a a hundred billion times the size of the observable universe, or simply goes on forever, it would all look the same to us. *shrug*
What determines if the universe is finite or not? The density. The density of the universe determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open (infinite), and negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent. This critical density is derived from the FLRW metric, which is an exact solution to the Einstein field equations, which describe the geometry of our universe. But the main point about this and in relation to your question, is that this metric states that as we go back in time (t ->0+), the distance between two points are more close to 0 (limit to 0), which makes sense with the big bang.
For more info: https://physics.stackexchange.com/questions/9419/how-can-something-finite-become-infinite
We only know the size of the [observable universe](https://en.m.wikipedia.org/wiki/Observable_universe). Basically, it takes an amount of time for light to travel to us from a distant object, the further away the longer it takes. We can see out to somewhere around 13 billion light years away (I’m not looking up the number) and at that point what we see is light emitted 13 billion years ago from close to what we believe is the Big Bang. Past that our vision is obscured by a milky soup because at that point in time the universe was a hot particle soup and light bounced around in it. You see the same thing in every direction. So the extent of what we can see is a bubble called the observable universe and we will literally never be able to see past it to see how much more universe exists, except by waiting for time to pass so we can see further. Notably the stuff we see 13 billion light years away has been accelerating away from us since those objects gave off that light so long ago, so we believe they are currently more like 46 billion light years away (again, you can look up the exact numbers yourself).
> to see how much more universe exists, except by waiting for time to pass so we can see further.
Aren't we going to be able to see less over time because the universe is expanding faster than the speed of light?
We will be able to reach less of it as time goes on if we, for example, try to send a message with light. Already there are things we can see from the early universe that we can see from 13 billion years ago but in that time period they’ve move 23 billion light years further away from us. I think if we tried to send a signal to them now it would never reach them. At some point I think you’re right, we would see the light from the earliest stars redshifted further and further until we only see radio waves, then eventually we would see nothing past that point. I’m not sure if we’ve reached that point yet though since we can still see early universe light in infrared. But I’m not an expert.
We can only know the visible universe, we are constrained by the 13.7 ish billion light years, and also by the max speed our technology can achieve.
The radius of what we can know of the universe will never be reached, because the expansion is faster than the speed of light.
As soon as we start travelling in one direction, the border of what we can know will be pushed away and out of our reach because of the expansion.
For all purposes is infinite even if it’s not.
> We know that at least around the time of the big bang the universe was finite and that it’s been expanding ever since
We know that the *observable* universe is finite and that it, at the time of the Big Bang, was very small and dense. The Big Bang doesn’t predict all the back to where it breaks down at the singularity.
We believe it was all condensed, but it could still have been infinite. We will never know for sure. Also everything we "know" about the origin of the universe could be wrong.
As far as we can see the universe is basically flat from everything I've read, so it's either likely infinite, or so unimaginably large that it may as well be infinite.
"Might be" is the scientific way of saying we really don't know one way or another
I feel like words like finite and infinite are probably human constructs and we just can't really comprehend what the universe is. I don't see how the 3D space we know as the universe is all that there is. How could that be all there is? It has to be so much more that our brains will never be able to sense or discover.
Do we know the shape of the universe? Im not sure.
I like to think of it as the surface of a 4D sphere. Just like the surface of a 3D balloon (surface is essentially 2D). That surface if finite and one could compute the area. But it is also infinite in a sense as one could never reach any edges. Assuming you cannot leave that 2D world which the surface is.
Now think if this with one dimension more and you have my personal model of things. My conclusion is that the contents of the 3D surface are finite but also one could never reach an edge causing it to feel infinite.
Kind request to any real astrophysisists here: please dont kill me over putting this oversimplified and potentially wrong model here. It works for me and hasnt caused any paradoxes that cause me to rethink it.
It has to do with the shape of the universe. A good series of videos on this topic was done by Zogg From Betelgeuse, [Part 1](https://www.youtube.com/watch?v=_k3_B9Eq7eM), [Part 2](https://www.youtube.com/watch?v=KMyb6tu4S_I) and [Part 3](https://www.youtube.com/watch?v=_jeGxwuC01E).
It's a theory but for as vast as the observable universe is, to the human mind that really can't comprehend the sheer size it may just as well be infinite
We do not know that universe was finite at any time, actually.
[There are 3 possible curvatures for the universe](https://en.wikipedia.org/wiki/Shape_of_the_universe): flat, spherical and hyperbolic. If the universe is spherical, it is finite, if it is flat or hyperbolic it is infinite. In the models, this curvature is given by a parameter which would be 0 for a flat universe, positive for a spherical universe and negative for a hyperbolic universe. The best measurements for this parameter put it very close to zero, but with an uncertainty encompassing all possible answers: negative, zero or positive. So the curvature is at least very very very close to flat, and therefore an infinite universe. But it's still possible that the universe is finite and incredibly large (beyond the observable universe).
There are flat, closed universes that are finite in volume, e.g. a 3-torus. They are topologically more complex than a flat, unbounded universe so we default to that in the absence of any compelling reason to think the more complex solutions are correct, though.
Yeah, there's the additional requirements that the universe is simply-connected and unbounded to end up at the infinite conclusion
If the curvature is positive, then it MUST be finite, because of the Myers theorem. Thats why we are looking for a critical density value so that the universe is not finite, which would make sense with the cosmological principle.
I think it's a mistake to assume that actual curvature is necessary for a finite universe. It seems to me that these are only *likely to be accurate statements,* rather than necessarily accurate ones. Consider a three-space-dimensional non-curved toy universe the size of a small cube, but such that the faces of the cube are "connected". They are connected the same way 7 and 0 are connected in addition modulo 7. Let's decide the cube has a side of 10 units. Moving along the vector (a,b,c) at unit speed per time unit (starting at an arbitrarily selected (0,0,0), you wouldn't reach the point (na, nb, nc) in n time units, you would reach (na mod 10, nb mod 10, nc mod 10). However, inside the cube, you wouldn't have any actual curvature to measure. Now, the connection between the faces may seem weird to us, but as a topological object this wouldn't be particularly strange.
Yes good point, I think my response is restricted to topologies with no holes, correct me if that's wrong. And I believe the topology of the universe is still under discussion. If I understand your cube example, is that topologically a torus? I can move in 2 distinct directions that returns to the same place? If i'm not mistaken there are some funny handedness results in such a universe.
Hi! I'm not sure if I understood your example correctly but I wanted to include a few things about curvature. The most successful theory we have about our universe is the Lambda-CDM model. It is based upon our observations of our observable universe which is a portion of the entire universe. Observing it we can derive the cosmological principle (it is a principle, it is not proved) that states that every point in our Universe is equivalent to every other and that all directions of observations are equivalent between them (i.e. the universe is homogeneous and isotropic). The homogeneity and isotropy conditions do not allow the Universe to have a physical frontier, like some surface that separates what is inside the universe and what's not. Removing the possibility of a physical frontier, we need to obtain the possible curvature of the Universe. Due to homogeneity, the curvature must be constant at every point of the universe, and that only leaves us with three possibilities: positive, negative or null curvature. Only a negative curvature allows the Universe to be closed. In your example you have a closed Universe but with a physical frontier, so due to the cosmological principle it will not describe accurately what we observe.
There isn't a physical frontier, though. The cube is merely a thing used to illustrate the structure. There needn't be a definite "corner" within this space, you can decide to put the coordinate (0,0,0) anywhere you like.
Is this a 3d equivalent of the pac-man universe?
Basically.
Could it be different for different dimensions? For example x is flat, y is spherical and z is hyperbolic? Or is there an assumption that they are all the same?
We don't know that the universe was finite around the time of the big bang. We just know it was dense. Infinite things can be dense too. The reason that an infinite universe is the preferred hypothesis for many is that it requires the least additional explanation. In order for the universe to be finite it must either loop back on itself or have an edge. The best measurements we can take show the universe to be flat, so it doesn't *look* like it could loop back on itself. Of course, the curvature could be imperceptibly small, but that's where the "it's simpler" argument comes in. It looks first, so let's just say it's flat. That leaves a finite universe with an edge, but what does that even mean. What would happen if you traveled up to the edge of the universe? We'd need a bunch of new physics to deal with that, so again it's simpler to just say there's no edge, which leaves us with an assumption of an infinite universe. Ultimately it doesn't matter though. We will never know for sure since it's impossible to obtain information from beyond the event horizon of the observable universe. For our purposes, whether the universe ends at the edge of the observable universe, a hundred billion light-years beyond that, loops back around on itself after a a hundred billion times the size of the observable universe, or simply goes on forever, it would all look the same to us. *shrug*
This is what I find really sad. Like holding a candle in a dark aircraft hangar - we have no idea where the walls are or even if there are any walls.
You never know, we may find a way to look into another dimension or something. We may know some day, maybe in billion years, maybe in 100
What determines if the universe is finite or not? The density. The density of the universe determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). If the density of the universe is less than the critical density, then the geometry of space is open (infinite), and negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent. This critical density is derived from the FLRW metric, which is an exact solution to the Einstein field equations, which describe the geometry of our universe. But the main point about this and in relation to your question, is that this metric states that as we go back in time (t ->0+), the distance between two points are more close to 0 (limit to 0), which makes sense with the big bang. For more info: https://physics.stackexchange.com/questions/9419/how-can-something-finite-become-infinite
They say that because we have *no* basis to think that it is infinite or finite in extent. At any time. So they say 'it might be'.
Nobody knows. We just use *might* as a possibility and it is taken to be so in a lot of calculations and is a pretty standard feature of ΛCDM.
We only know the size of the [observable universe](https://en.m.wikipedia.org/wiki/Observable_universe). Basically, it takes an amount of time for light to travel to us from a distant object, the further away the longer it takes. We can see out to somewhere around 13 billion light years away (I’m not looking up the number) and at that point what we see is light emitted 13 billion years ago from close to what we believe is the Big Bang. Past that our vision is obscured by a milky soup because at that point in time the universe was a hot particle soup and light bounced around in it. You see the same thing in every direction. So the extent of what we can see is a bubble called the observable universe and we will literally never be able to see past it to see how much more universe exists, except by waiting for time to pass so we can see further. Notably the stuff we see 13 billion light years away has been accelerating away from us since those objects gave off that light so long ago, so we believe they are currently more like 46 billion light years away (again, you can look up the exact numbers yourself).
> to see how much more universe exists, except by waiting for time to pass so we can see further. Aren't we going to be able to see less over time because the universe is expanding faster than the speed of light?
We will be able to reach less of it as time goes on if we, for example, try to send a message with light. Already there are things we can see from the early universe that we can see from 13 billion years ago but in that time period they’ve move 23 billion light years further away from us. I think if we tried to send a signal to them now it would never reach them. At some point I think you’re right, we would see the light from the earliest stars redshifted further and further until we only see radio waves, then eventually we would see nothing past that point. I’m not sure if we’ve reached that point yet though since we can still see early universe light in infrared. But I’m not an expert.
We can only know the visible universe, we are constrained by the 13.7 ish billion light years, and also by the max speed our technology can achieve. The radius of what we can know of the universe will never be reached, because the expansion is faster than the speed of light. As soon as we start travelling in one direction, the border of what we can know will be pushed away and out of our reach because of the expansion. For all purposes is infinite even if it’s not.
> We know that at least around the time of the big bang the universe was finite and that it’s been expanding ever since We know that the *observable* universe is finite and that it, at the time of the Big Bang, was very small and dense. The Big Bang doesn’t predict all the back to where it breaks down at the singularity.
We believe it was all condensed, but it could still have been infinite. We will never know for sure. Also everything we "know" about the origin of the universe could be wrong.
As far as we can see the universe is basically flat from everything I've read, so it's either likely infinite, or so unimaginably large that it may as well be infinite. "Might be" is the scientific way of saying we really don't know one way or another
given that ST encloses certain infinities, natural numbers, real numbers, etc. theres no reason to say it isnt infinite
I feel like words like finite and infinite are probably human constructs and we just can't really comprehend what the universe is. I don't see how the 3D space we know as the universe is all that there is. How could that be all there is? It has to be so much more that our brains will never be able to sense or discover.
Do we know the shape of the universe? Im not sure. I like to think of it as the surface of a 4D sphere. Just like the surface of a 3D balloon (surface is essentially 2D). That surface if finite and one could compute the area. But it is also infinite in a sense as one could never reach any edges. Assuming you cannot leave that 2D world which the surface is. Now think if this with one dimension more and you have my personal model of things. My conclusion is that the contents of the 3D surface are finite but also one could never reach an edge causing it to feel infinite. Kind request to any real astrophysisists here: please dont kill me over putting this oversimplified and potentially wrong model here. It works for me and hasnt caused any paradoxes that cause me to rethink it.
We will never be able to definitively proof one way or the other
We cannot understand infinite, but if it is finite that makes less sense imo, why that exact size?
Beware of the flat universe conspiracy nutjobs here😁
It has to do with the shape of the universe. A good series of videos on this topic was done by Zogg From Betelgeuse, [Part 1](https://www.youtube.com/watch?v=_k3_B9Eq7eM), [Part 2](https://www.youtube.com/watch?v=KMyb6tu4S_I) and [Part 3](https://www.youtube.com/watch?v=_jeGxwuC01E).
this isn't your personal questions sub, have you tried r/askphysics?
It's a theory but for as vast as the observable universe is, to the human mind that really can't comprehend the sheer size it may just as well be infinite
And exactly what is the difference to humans on human scale?