This is a new idea I've been considering for a while, so pardon me if it's bit ill-formed.
Before we ask if the universe is infinite, we've to understand the the concept of infinity better. The commonly understood idea is that something is infinite if it has no boundary or no limit. But what we'd accept as a boundary or limit is completely determined by us. We are the ones who are setting these rules.
For example, a line is infinite while a line segment is finite. The boundary condition in this case are the end points.
A plane is infinite while a geometric figure is finite. The boundaries here are determined by line segments.
However, consider a circle. It has no start or end points. Anytime we do measurements upon it we artificially define the boundary. Similarly, the surface of the sphere has no beginning or the end because there are no line segments to determine the boundaries. Both of these things can - in a sense - be considered infinite.
Imagine you are a single dimensional being capable of moving only along a line. Any boundary you define would be as an endpoint. Imagine you are living on the surface of a circle. Then, you can spend an eternity trying to find an endpoint on it, but still not find one. The same goes for a 2-d being on the surface of a sphere. If it is small enough not notice the curvature, it can spend a lot of time trying to find the edge and not find one. Actually, the second one isn't that hard to imagine. Just look back at a time when people thought that the earth was flat and that it had an edge that you'd fall over.
Currently, we are sort of hard-wired to think in 3-d terms. When we talk about whether the universe if finite or not, what is going on in our minds is that if we go far enough, we'll either find some sort of membrane that we just can't cross, which defined the limit of this universe or we won't find any such membrane, in which case we can call it infinite. But as we know from our practical experience with circles and spheres, it wouldn't really be infinite. So the question of whether the universe is infinite or not would boil down to understanding what boundary conditions are applicable. And since we are not built to think in those terms, trying to imagine it gives me a headache.
On a side note, here's a cool site giving you some idea about the scale of the universe.
http://htwins.net/scale2/
Before we ask if the universe is infinite, we've to understand the the concept of infinity better. The commonly understood idea is that something is infinite if it has no boundary or no limit. But what we'd accept as a boundary or limit is completely determined by us. We are the ones who are setting these rules.
For example, a line is infinite while a line segment is finite. The boundary condition in this case are the end points.
A plane is infinite while a geometric figure is finite. The boundaries here are determined by line segments.
However, consider a circle. It has no start or end points. Anytime we do measurements upon it we artificially define the boundary. Similarly, the surface of the sphere has no beginning or the end because there are no line segments to determine the boundaries. Both of these things can - in a sense - be considered infinite.
Imagine you are a single dimensional being capable of moving only along a line. Any boundary you define would be as an endpoint. Imagine you are living on the surface of a circle. Then, you can spend an eternity trying to find an endpoint on it, but still not find one. The same goes for a 2-d being on the surface of a sphere. If it is small enough not notice the curvature, it can spend a lot of time trying to find the edge and not find one. Actually, the second one isn't that hard to imagine. Just look back at a time when people thought that the earth was flat and that it had an edge that you'd fall over.
Currently, we are sort of hard-wired to think in 3-d terms. When we talk about whether the universe if finite or not, what is going on in our minds is that if we go far enough, we'll either find some sort of membrane that we just can't cross, which defined the limit of this universe or we won't find any such membrane, in which case we can call it infinite. But as we know from our practical experience with circles and spheres, it wouldn't really be infinite. So the question of whether the universe is infinite or not would boil down to understanding what boundary conditions are applicable. And since we are not built to think in those terms, trying to imagine it gives me a headache.
On a side note, here's a cool site giving you some idea about the scale of the universe.
http://htwins.net/scale2/
