If the universe is finite in size, what is at the end of it?

[Kutt]

If you travel "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx" number of light years in any direction, eventually you will reach some sort of "end" since the universe is finite in size.

What exactly is at this "end?"

Hypothetically, what would happen if you flew a spaceship into this "end?"

 

[Jimmy Snyder]

If you traveled in an airplane in any direction you would never reach any sort of "end" even though the Earth is finite in size.

 

[Whovian]

since the universe is finite in size.

Just wanted to point out that, in addition to Jimmy's statement (though, for this example, we're not thinking of the Earth as a two-dimensional surface embedded into three-dimensional space, it's just the two-dimensional everything,) that this quote isn't necessarily true.

 

[nanosiborg]

If you travel "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx" number of light years in any direction, eventually you will reach some sort of "end" since the universe is finite in size.

What exactly is at this "end?"

Hypothetically, what would happen if you flew a spaceship into this "end?"

It's unknown if the universe is finite or infinite in extent; what it's made of; what, if anything, existed before; if there are other universes; etc. etc. We're free to construct models of our universe according to various speculative parameters. This is one sense in which the OP question is meaningless.

If you traveled in an airplane in any direction you would never reach any sort of "end" even though the Earth is finite in size.

Yes, if you're traveling on the outside of a bounded object, then you would never reach any sort of 'end' even though the object is finite in size.

But if you're inside a bounded, finite in size, object, then presumably you could get to the boundary or outside edge if you traveled long enough. Unless the object is expanding faster than you can possibly travel, or there's some sort of 'curvature' re the spatial structure of the interior which prohibits reaching the boundary even if the object isn't expanding.

 

[Number Nine]

Yes, if you're traveling on the outside of a bounded object, then you would never reach any sort of 'end' even though the object is finite in size.

But if you're inside a bounded, finite in size, object, then presumably you could get to the boundary or outside edge if you traveled long enough. Unless the object is expanding faster than you can possibly travel, or there's some sort of 'curvature' re the spatial structure of the interior which prohibits reaching the boundary even if the object isn't expanding.

There is no reason to believe that a finite Universe has a boundary (much less has to have one), unless the Universe has a flat topology. A sphere is finite and unbounded in any number of dimensions.

 

[WannabeNewton]

There is no reason to believe that a finite Universe has a boundary (much less has to have one), unless the Universe has a flat topology. A sphere is finite and unbounded in any number of dimensions.

Well there seem to be some gaps in your statements here. First of all I have no idea what you mean by a "flat" topology. Topological structures do not deal with curvature; that is dealt with by riemannian structures. Secondly, any manifold (which excludes manifolds with boundary) has an empty topological and manifold boundary. Finally, the term finiteness is being used very loosely here. What do you mean by the n - sphere is finite? It is definitely not a finite set so I suspect you mean it is compact; it is unbounded in the sense mentioned in the second remark but it is certainly bounded in the metric sense as a subset of R^n.

 

[nanosiborg]

There is no reason to believe that a finite Universe has a boundary (much less has to have one), unless the Universe has a flat topology.

If you agree that we're free to construct models of our universe according to various speculative parameters, then is there some particularly compelling reason to believe that our universe isn't finite and bounded?

A sphere is finite and unbounded in any number of dimensions.

Or, the word sphere can refer to an object that's finite and bounded. Do you see any problem with using sphere in the latter sense (keeping in mind that the OP question is expressed in ordinary language)?

 

[Jimmy Snyder]

Yes, if you're traveling on the outside of a bounded object, then you would never reach any sort of 'end' even though the object is finite in size.

I'm glad that you were able to visualize this.

But if you're inside a bounded, finite in size, object, then presumably you could get to the boundary or outside edge if you traveled long enough. Unless the object is expanding faster than you can possibly travel, or there's some sort of 'curvature' re the spatial structure of the interior which prohibits reaching the boundary even if the object isn't expanding.

To be sure, in the case of the airplane, there is an object, the 3 dimensional earth, outside of which you are. However, there is also a two dimensional object, a spherical surface, curved in the third dimension, inside of which you are. You have in mind the 3 dimensional earth, I have in mind the 2 dimensional surface. Come with me into my world if you are willing. It is really two dimensional in that, locally, you can only move back and forth or side to side, but cannot move up and down. Yet it is also three dimensional in that it is curved in that third dimension into a spherical shape. Now simply add one to all of these dimensions.

It may be that the universe is a thin three dimensional curved sphere. If it is, then it is finite just as the 2 dimensional sphere of my airplane is finite. And being a three dimensional sphere with its curvature in the fourth dimension, just as the airplane's sphere was a two dimensional sphere curved in the third dimension, it has no boundary.

We already know that the universe is not completely flat. We have measured a small amount of curvature at the surface of the sun. What we don't know is whether the entire shebang is so curved as to close in on itself like a sphere does. Although you may be impressed with the logic of your arguments, there is no amount of logic that will answer this question. It can only be answered with experiment. Look out into the sky, if you can make out the back of your head, then it's curved.

 

[nanosiborg]

Jimmy Snyder, thanks for the elaboration.

You have in mind the 3 dimensional earth, I have in mind the 2 dimensional surface.

Ok. I'm presenting a speculative visualization of our universe as being the interior of a 3D bounded volume (and therefore of finite extent) embedded in, and possibly expanding into, a preexisting medium. Are you saying that enough is known about our universe to rule this out?

We already know that the universe is not completely flat. We have measured a small amount of curvature at the surface of the sun.

How does measuring "a small amount of curvature at the surface of the sun" rule out the possibility that our universe is flat, ie., 3D Euclidean?

In connection with this, is it possible that describing gravity in terms of curvature is a simplification, maybe even an oversimplification, of 3D wave mechanics in an underlying reality that's actually 3D Euclidean?

What we don't know is whether the entire shebang is so curved as to close in on itself like a sphere does. Although you may be impressed with the logic of your arguments, there is no amount of logic that will answer this question.

Agree. I'm just trying to get a better idea of how speculation on this (for the purpose of dealing with the OP question) might be restricted. Yours and others' comments have been helpful.

 

[Jimmy Snyder]

Ok. I'm presenting a speculative visualization of our universe as being the interior of a 3D bounded volume (and therefore of finite extent) embedded in, and possibly expanding into, a preexisting medium. Are you saying that enough is known about our universe to rule this out?

Up until now I hadn't said anything at all on this subject. Now I break my silence. The universe is not the interior of anything. There is no medium, preexisting or otherwise, in which the universe is embedded. This is not because of what is know about our universe, it is because of the definition of the word universe. The universe includes everything. Everything.

 

[nanosiborg]

Up until now I hadn't said anything at all on this subject. Now I break my silence. The universe is not the interior of anything. There is no medium, preexisting or otherwise, in which the universe is embedded. This is not because of what is know about our universe, it is because of the definition of the word universe. The universe includes everything. Everything.

You only need to allow the possibility of a larger, encompassing structure in order to differentiate the terms universe (everything) and our universe (not necessarily everything). Maybe everything is a multiverse? Whatever you want to call it, I don't think the possibility of our universe as being embedded in a preexisting medium can be ruled out.

 

[WannabeNewton]

I don't think the possibility of our universe as being embedded in a preexisting medium can be ruled out.

You have to define what you mean by universe. If we are talking about a solution to the Einstein field equations and the space - time it is endowed upon (M,g) that describe a model universe then in the context of GR this is not an embedding in some ambient space.

 

[Jimmy Snyder]

not necessarily everything.

Everything.

 

[nanosiborg]

You have to define what you mean by universe. If we are talking about a solution to the Einstein field equations and the space - time it is endowed upon (M,g) that describe a model universe then in the context of GR this is not an embedding in some ambient space.

Ok. Does that necessarily prohibit an approach in which our universe is embedded in some ambient space, or in which our universe is part of a multiverse?

 

[nanosiborg]

Everything.

The way I'm using the term, our universe doesn't necessarily refer to everything.

 

[Jimmy Snyder]

The way I'm using the term, our universe doesn't necessarily refer to everything.

The OP asked about the universe.

 

[Pjpic]

opposition in terms

There must be other, more nuanced and technical, meanings to 'finite' and/or to 'unbounded' because to us 99.9 percenters finite actually means bounded.

 

[russ_watters]

That will be disconcerting news to racecar drivers...

 

[WannabeNewton]

Finite in this context does not mean bounded, it means compact. Bounded only makes sense in metric spaces and in general relativity we do not have a natural metric to impose on arbitrary space-time solutions. It is true that a subset of $\mathbb{R}^{n}$ is compact iff it is bounded and closed but space-time manifolds are not naturally embedded in a higher dimensional euclidean space. We must make use of topological notions when looking at global characteristics hence the term "finite" (which I agree with you is a horribly ambiguous and non-technical term) refers to compactness. I should note that for arbitrary topological spaces, compactness does not always bear resemblance to the intuitive notion of finiteness; what it does allow us to do is to turn local properties of a topological space into a global property so in this way it codifies a sense of the space being "finite" in a loose sense.