I have a question for El_SI unless you happen to know the answer. How is it the universe is finite and what happens when you hit the edge. Isn’t thinking that the universe has an outer limit as silly as thinking that the world is flat.
El_Si interjected:
I have a question for El_SI unless you happen to know the answer. How is it the universe is finite and what happens when you hit the edge. Isn’t thinking that the universe has an outer limit as silly as thinking that the world is flat.
Hiya Moony! Haven’t been here for a while. It’s good to be back.
oldguy has asked me to answer this for you, so here goes…
This is a good question and the answer relies on the mathematics of “topology” and “differential geometry” as well as general relativity.
First of all, you’re really asking a couple of questions: (1) Can the universe be finite without having an “edge” (in topological terms, can a surface, (a “manifold” to be really technical), be finite but without “boundary”); and (2) Is the universe finite or infinite, with or without boundary. I think that most of what you really want to know is really in (1).
To answer (1), yes, it is possible to have a universe (or mathematical domain) that is finite but without boundary. The simplest way to think about this is to think of the surface – and only the surface – of a sphere or ball. That is, consider a round 2-dimensional spherical surface that has no depth. To someone (or something) living in that 2D universe there would be no boundary, no edge, but it would still be finite; go far enough in any direction and you’ll get back to where you started.
Now you may be thinking that we don’t live in a 2 dimensional universe and if you look at the surface of a sphere in our 3D world it really does have depth and that could be considered an edge (or actually a pair of them, the inside and the outside). That is entirely correct… an M-dimensional manifold in a N-dimensional space, where N is greater than M, is said to be “embedded” in that higher dimensional space and cannot be finite without some sort of boundary in the higher dimension(s). But an N dimensional manifold in an N dimensional space can exist and be finite without boundary.
It’s very difficult to visualize a surface without intuitively embedding it in a higher dimensional “container”. This is one of the reasons that people have trouble visualizing concepts like the beginning or end of time; they naturally assume a larger box, complete with a clock or timer, in which the “beginning” of time can start and the “universe” can unfold. However, current theory neither needs nor includes such a container. The beginning of time is not a boundary or edge… it’s more like the north pole relative to the surface of the earth; that’s as far north as you can get… but it’s not an edge.
General relativity actually describes our universe as a 4 dimensional Riemannian manifold (so called spacetime) and some of the proposed unified theories use even more dimensions but… in none of them (the mainstream ones anyway) is our universe embedded in a higher dimensional space. So, according to current theory, it is possible for our universe to be finite and unbounded.
But it doesn’t have to be. So thinking that the universe has a limit of some sort, in the form of an edge or boundary, isn’t silly if it’s done in a way that is consistent with gravity (and the rest of physics)… unlike the flat earth picture.
It’s possible to “cut” manifolds so there are parts that are essentially missing. Some of the mathematical models describing singularities of different sorts effectively have points or lines cut out of the manifold where the singularities are, though it’s not at all clear whether these mathematical models describe real physical phenomena. Nevertheless it is possible that our universe has internal edges that might correspond to black holes, particles or “strings” of some sort.
Now all of this addresses the question of a finite or infinite universe in terms of how “big” it is spacially (and/or temporally). Depending on how you want to define “universe” there are other ways it could be infinite such as including all the infinitely possible outcomes of all the events that occur (ie many-worlds like models). But most people don’t picture the universe that way so I’m not going to address those here.
So, finally, to answer question (2) yes, the universe is currently believed to be finite and without boundary, though there have been models with internal boundaries proposed. These spacetime surfaces tend to fold back around on themselves, like the surface of a sphere curves around to meet itself, in such a way that you can connect any two points on the surface without bumping into an edge. The models that best seem to match what we actually see out there (a) don’t have an “outer” edge (or boundary) and probably don’t have “internal” edges either, (b) show huge growth over time, and (c) even if they’re not infinite and/or won’t grow forever and become infinite, are so very, very large that they are effectively so.
Hope I’ve clarified more than I’ve confused 
Now back to your regularly scheduled old dude…
- Moony