[oatman (OP)]

Sort of linked onto the last question,

This is one of those things I have never been able to get my head around!

If the universe is all there is, and nothing beyond it, what are we expanding into?

I've heard it described like inflating a balloon, or something like that, but that doesnt make it any clearer for me, expansion to me means occupying slightly more space than before, but if there is no more...!

[Bill S]

This is obviously one for the experts, but I find it difficult to keep my nose out of anything that involves infinity.  []

First, I should say I find it very difficult to understand how our Universe can be infinite, as it apparently had a beginning.  If it is infinite, and expanding, I suppose we would have to argue that ∞ x 2 = ∞, and so on.  I feel sure this would fit in with Cantor's mathematical infinities, but, like you, I have problems with it when it comes to physical infinity.

"expansion to me means occupying slightly more space than before"

Presumably, expansion could also mean creating more space.  Again, there would probably be no reason why this could not be done with mathematical infinities, but it is difficult to apply it to physical infinity.  

I bet this doesn't help, but I gave up being helpful when I retired.   []

[QuantumClue]

Sort of linked onto the last question,

This is one of those things I have never been able to get my head around!

If the universe is all there is, and nothing beyond it, what are we expanding into? (1)

I've heard it described like inflating a balloon, or something like that, but that doesnt make it any clearer for me, expansion to me means occupying slightly more space than before, but if there is no more...! (2)

(1) - There are two answers. One possible one comes directly from relativity: It expands into nothing. Since nothing exists outside our universe, there is nothing for our universe to expand into. Otherwise, the other comes from string theory. In certain parts of string theory, our universe is a brane which floats in a multidimensional pool. Our universe could be expanding in this pool.

(2) - You are right. More space appears - more space than now, and this is how infinity is defined. You will always find one more than now. Spacetime is completely self-contained. Any space and time appearing, appears from within the structure of spacetime itself, possibly from a singularity.

[QuantumClue]

Mind you it could be argued also that for the universe to be infinite, it needs to expand for an infinite amount of time.

[Bill S]

Mind you it could be argued also that for the universe to be infinite, it needs to expand for an infinite amount of time.

This seems to raise its head in one guise or another in lots of places, and never be resolved fully.  IMO, it could never become infinite because it could never be said to have expanded for a infinite amount of time, so the Universe could be infinite only if it had always been infinite.

[Soul Surfer]

This mathematical expression infinite is a nuisance that causes all sorts of problems it should not be used in physical situations like this.  I far prefer the term indefinite.  It is highly probable that our universe is finite but far bigger than the parts of the universe that we can ever see.   It is also highly probable that our universe started at a specific time and will eventually fade out after an indefinite time very much longer than the time that we can measure since its start.  From a logical point of view it is also reasonably probable that our universe is only one of an indefinite number of non interacting universes that make up the multiverse on an indefinite scale totally beyond comprehension but even that may not be mathematically infinite but we will never be able to prove it physically one way or the other.   The best that we could ever do is to prove that this is a reasonable situation based on what we know of the fine details of the properties of the parts of our universe that we can see.  This is very different from the purely mathematical process of summing a series to infinity or integrating a mathematical function over the range from minus infinity to plus infinity

[Bill S]

This mathematical expression infinite is a nuisance that causes all sorts of problems it should not be used in physical situations like this.

I absolutely agree! but then, you knew I would, didn't you?

[graham.d]

Sort of linked onto the last question,

This is one of those things I have never been able to get my head around!

If the universe is all there is, and nothing beyond it, what are we expanding into? (1)

I've heard it described like inflating a balloon, or something like that, but that doesnt make it any clearer for me, expansion to me means occupying slightly more space than before, but if there is no more...! (2)

(1) - There are two answers. One possible one comes directly from relativity: It expands into nothing. Since nothing exists outside our universe, there is nothing for our universe to expand into. Otherwise, the other comes from string theory. In certain parts of string theory, our universe is a brane which floats in a multidimensional pool. Our universe could be expanding in this pool.

(2) - You are right. More space appears - more space than now, and this is how infinity is defined. You will always find one more than now. Spacetime is completely self-contained. Any space and time appearing, appears from within the structure of spacetime itself, possibly from a singularity.

It's hard to think of a better concise answer than this. It leaves a whole lot of philosophical (and physics) questions but, ultimately, nobody really knows the answers. Just to clarify, when QC say space expands into "nothing" this is not "Space" or "Spacetime" which, for this idea, comprises a mesh of quantum foam. The "nothing" is "no space" and "no time" and it is not terribly easy to imagine.

[Pikaia]

This Cosmology FAQ answers your question:

http://www.astro.ucla.edu/~wright/cosmology_faq.html#XIN

This illustrates how to look at the infinite universe:

http://www.astro.ucla.edu/~wright/infpoint.html