Hello Brian,
I think you have not fully understood Quetzal's story about the balloon. It is very important to realize that the balloon is a two-dimensional metaphor for three-dimensional space. We, who live in space, know three spatial dimensions. In simple terms they are: forward/backward, left/right and up/down. The balloon metaphor assumes that we give up one dimension, namely up/down, in order to make it simpler to visualize the idea of an expanding universe. You are to imagine that you live on the surface of the balloon. You know only forward/backward and left/right, i.e. you can only move in the plane of the balloon surface. For you, there's no up and down, you can't even imagine what up and down are like. You yourself are also completely flat. You have no knowledge of the inside of the balloon, nor of the outside. For the purpose of this thought experiment, they do not exist.
Now, suppose the balloon surface is dotted with ink spots and is slowly being inflated, thus stretching its surface. It is absolutely irrelevant that, because of the inflation of the balloon, its surface continuously occupies another position in 3D space. The only effect of the inflation that is of concern here is the stretching of the rubber surface. Remember, the surface of the balloon is the only kind of space you know. The surface is curved in 3D, but you won't notice this, being a 2D creature. So, if you look in one of the directions it is possible for you to look in, namely any direction along the balloon's surface, you will find that every ink spot you can see is receding from you. That's why you start imagining that you are at the center of it all. However, this will be the case wherever you are on the surface of the balloon, and there is no privileged "center of the universe": wherever you are, the ink spots are always receding from you. They are also all receding from each other. And the farther away they are from each other to begin with, the more rubber there is in between them being stretched, and so the faster they will recede from each other.
The only thing left remaining for the analogy to instruct you about the inflation of the real universe is to once again add a dimension to the overall thought experiment. Thus, our universe is like a four (3+1) dimensional balloon which is being inflated. The 2D surface of the balloon becomes 3D space as we know it, and it stretches not just in a (curved) 2D plane, but in 3D space. (Curved? Maybe, but if so, in 4D.) The stretching takes place all over the universe, just like the rubber of the balloon was stretched everywhere between the ink spots.
If we extend the metaphor even further, so as to answer the question of what the universe expands into, the answer would be: into the fourth dimension, wherever that is. But as it is, in modern physics, the fourth dimension is usually reserved for time. And although it is not so strange to say that the universe expands in time, this is not quite satisfying. However, there are theories in physics that talk of seven other dimensions. These are not stretched out, like our normal three dimensions, or timelike like the fourth, but somehow folded inward, or 'shrunken' to infinitesimal sizes. Maybe that's what space expands 'into', making it seem as though it expands into itself. Maybe the expansion is fractal: like a coastline becoming ever more crinkly, and therefore longer, without ever enclosing more area. At any rate, if the universe is all there is, then logic dictates that there cannot be anything
outside of it for it to expand into, that much we can be certain of.
Are you still there?
{edited to correct typo}
[This message has been edited by Parasomnium, 07-25-2003]
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