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

#### nanosiborg

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

Its boundary, which lies at infinity.
Bounded yet infinite is a mathematical concept. Physical objects which have boundaries are, either observationally or by definition, not infinite.

Finite in size $\neq$ has an edge.

Look at our earth: it's finite in size but it doesn't have an edge.
What would you call the outer crust? What about an expanding wave shell ... in any medium?

I think OP is referring to the 3D projection of the multidimensional universe (or as we normally see it). Although multidimensional universe might not have an edge, our 3D representative one might have one.

e.g. circle, which is a projection of a sphere in 2D.
I think the OP is asking a very straightforward, and unanswerable, question about the possible nature of our universe. Eg. our universe might be a bounded finite entitiy (eg., the interior of a 3D wave shell in some medium of unknown strutcture). If, per the OP, the universe is "finite in size", then, by definition, the universe under consideration isn't infinite, and has a boundary, or edge. (The boundary or edge being, presumably, the same 'stuff' that mediates the interior. Which remains unknown.)

Projection of the universe on what?? The universe is all that there is
"All that there is" can refer to some metaphysical speculation or it can refer to all that's amenable to detection. Either case can be projected onto a speculative preexisting background.

A cop. If you ever got there, you definitely must have been speeding.

BTW, despite what everyone here has said, I'm convinced it's somewhere in the state of Nevada.

#### WannabeNewton

"All that there is" can refer to some metaphysical speculation or it can refer to all that's amenable to detection. Either case can be projected onto a speculative preexisting background.
No there is a precise mathematical distinction micromass is making. Space - time is a 4 - manifold that is not embedding in some ambient space.

#### nanosiborg

No there is a precise mathematical distinction micromass is making. Space - time is a 4 - manifold that is not embedding in some ambient space.
Amazing that you can tell that from what he wrote:
Projection of the universe on what?? The universe is all that there is

#### Jimmy Snyder

Amazing that you can tell that from what he wrote:
It's more amazing than that. I was able to tell the same thing.

#### Dremmer

There's a wall at the edge of the universe.

#### Whovian

There's a wall at the edge of the universe.
Hoping that was a joke.

#### ahaanomegas

Of course that wasn't. That was a joke.

#### 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.

#### 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.