Amy was asking me some questions on "alternate dimensions" and "parallel universes". Here's my answer, which is entirely non-scientific although it is based on a few things I know (or think I know) about physics. I'm suspecting for example that the string theory stuff is a little shaky as I never really studied the math in there.
Alternate dimension doesn’t mean much in itself: alternate to what, and how? A dimension is a direction in space-time. We experience the four known ones every day: width, height, length and time. But there are many physical theories such as string theories that postulate additional dimensions. Why we don’t experience them has different explanations. One is that some of those dimensions may be closed on themselves (think circle vs. open line) with a very small radius. Such an additional dimension would be hard but not impossible to detect. We may actually know in the next few years as there are experiments being built right now to test that hypothesis (negative results wouldn’t entirely rule out the possibility but would put a limit to the radius of space along those dimensions). By the way, there is an interesting theory from the 20th century that was able to unify gravitation and electromagnetism through an additional closed dimension. It suffered from a number of problems and was more or less proven wrong but it was an interesting idea that all forces would somehow come from the geometry of a larger space-time.
Now a parallel universe is a completely different idea. It’s the idea that what we perceive as our universe is only a fraction of physical reality, and that other similar or entirely different universes may exist somewhere else. You then have the idea of a metaverse that contains all of those, which should be what we really call Universe if we used words appropriately.
As to where those universes might be, there are several possibilities, not necessarily exclusive of one another. First, according to string theories, we live on a kind of multi-dimensional “brane” which is like a slice of a bigger space-time (read with more dimensions) to which the particles we’re made of cling. There would be more open dimensions in this view that we don’t see because the particles we’re made of are inherently bound to a particular brane: they only exist as part of it, they are a property of that particular brane if you want. In that view, there are other branes with other universes that may be as big as ours. Sometimes, actually, these branes can get close to one another or even collide, which gives us a possibility of confirming their existence by observing the effects of cross-brane interaction (for example, matter from one brane might gravitationally affect matter on another, and the closer branes are, the bigger the effect, which is interesting as branes are not flat and distance between them is not fixed).
Another idea that is also realized in string theory is that there is a multi-dimensional landscape of universes, and that one universe can experience a local instability that turns into a completely new baby universe that expands on its own, with physical laws that are a variation of the ones in the parent universe. It’s an interesting concept because it gives rise to the idea that a large number of universes might evolve from a larger cosmos. Here the word “evolution” is not used lightly: it would really be the case that there would be a form of survival of the fittest where the most common universes would survive and give birth to more and more stable baby universes. In both versions of parallel universes, the smaller universes are still connected within a larger Universe
But there is yet another possibility which I think is quite interesting, although completely untestable.
The idea would be that parallel universes don’t have to be connected to one another at all: why should there be one single connected universe, all in one piece? You could actually postulate that any universe that is self-consistent would just exist by virtue of being possible. For example, the group Z2, which is a mathematical structure described by: 1 x 1 = 1, 1 x -1 = -1, -1 x 1 = -1 and -1 x -1 = 1 just exists, and it exists outside of any universe we may be in. It’s just universal, it doesn’t need a creator god or to be observed to exist. It just is. How about our universe just is one of those mathematical structures, only much more complex, that just exists by virtue of being consistent? Am I confusing the map for the territory? Am I? I mean, if we discover one day that the world’s natural laws can be reduced to a relatively simple mathematical structure (and we have lots of indication that it could from looking at elementary particles), how much of a stretch would it be to say that the universe actually *is* that mathematical structure? I mean, if it’s indistinguishable from it, isn’t it just the same?
We could then talk about how consciousness fits into all this but that’s a whole ‘nother discussion.