Imagine a child blowing up a balloon. Imagine that there are dots painted on the balloon. Notice that all the dots are moving away from each other. The farther any two dots are, the faster they are moving apart.
Now imagine there is an ant living on the balloon. To the ant, the balloon is infinite in two dimensions. The ant, walking on the balloon, could go an infinite distance around the balloon and never reach "the end of the balloon." To an ant, the "universe" would be a two-dimensional, expanding surface, such that the farther the dots are, the faster they move.
If you were to ask the ant, "What is the universe expanding into?," the ant would reply that the question has no meaning. The ant can only move on the surface of the balloon, yet the expansion of the balloon lies in the third dimension, in hyperspace, which is beyond the understanding of the ant. All that the ant understands is that the space between dots is expanding. But it cannot understand "into what is it expanding," since that requires knowledge of the third dimension, or hyperspace, which is beyond the ant's comprehension.
Also, if you ask the ant, "From where did the balloon expand?," the question would have no meaning. The expansion point lies at the center of the balloon, which is off the "universe" of the ant. Thus, the balloon's Big Bang also lies in hyperspace, beyond the understanding of the ant.
To us, however, all these answers are trivial. We live in hyperspace (the third dimension) so we can see that the balloon is finite and is expanding in the third dimension, and that the balloon's Big Bang lies in the center, also in the third dimension.
Likewise, there may be other balloons floating in hyperspace. The ant, which has difficulty understanding its own balloon, would have an even greater problem understanding the fact that there might be other balloons, with other ants on them.
Similarly, we are like the ant, except that our universe appears to be infinite in three dimensions. We can go an infinite distance in any direction, and never reach the "end of the universe."
Likewise, the space between our galaxies is expanding, such that the farther a galaxy is, the faster it is going (this is Hubble's Law). (However, there are also random motions, so galaxies can sometimes collide. For example, our own galaxy may one day be gobbled up by the Andromeda Galaxy.)
But the question, "Into what is the universe expanding?" makes no sense to our three-dimensional brains. The location of the Big Bang is in hyperspace.
(If we try to retrace the early history of the universe, we still cannot locate the Big Bang. If we go back 15 billion or so years, the universe might have been as big as, say, a bowling ball. The entire universe, with all its space and matter, was only that big. But nowhere on the bowling ball was the Big Bang.)
Today, cosmologists are grappling with the question, "What happened before the Big Bang?" Einstein's equations break down at that point, so we need a theory which combines the quantum theory and general relativity (the unified field theory). So far, the only candidate for such a fabled theory is the 10-dimensional superstring theory.
To quantize the universe, let us first consider an electron. We know from chemistry class that the electron can exist simultaneously in infinitely many orbitals surrounding the nucleus. (Because of the Uncertainty Principle, we can never know for sure precisely which state the electron is in, until an observation is made.) These are "parallel electrons." This strange fact about electrons has been verified thousands of times in the laboratory.
Now if we quantize the universe, we must treat it like an electron. Because of Uncertainty, this means that the universe must also exist simultaneously in an infinite number of states. These are parallel universes.
Imagine boiling water (a quantum mechanical phenomenon). Out of nothing, bubbles form and then quickly expand. Similarly, the leading theory among cosmologists today is the multiverse theory, which states that quantum universes are constantly being created out of Nothing. Many of them are probably short-lived; they have a Big Bang, but then rapidly have a Big Crunch and disappear back into Nothing.
(This does not violate the conservation of matter and energy; the matter of the universe has positive energy, but the gravitational field has negative energy, such that the total energy for a closed universe is zero, so it takes zero energy to create a closed universe.)
This means that Big Bangs are probably happening all the time, with entire bubble/universes springing out of the vacuum. However, life probably does not exist in most of these universes. Protons need to be stable for several billion years in order to create DNA (or at least some other auto-catalytic, self-replicating form of stable matter). So many of these other universes in the multiverse are probably lifeless, consisting of, say, a sea of electrons, neutrinos, and photons.
Our universe is probably one of the few in which the expansion is so great that the universe lives for many billions of years, enough for stable matter to form.
This may ultimately explain the Anthropic Principle: the puzzle that the physical constants of our universe seem "fine-tuned" to allow for intelligent life to form. Some have speculated that it was no accident that the physical constants of the universe are precisely those which allow for life to form. If the constants were a bit different, then deuterium and the higher elements would never have formed, and hence DNA could not exist.
However, this multiverse idea argues against that. It says that there are indeed an infinite number of dead universes, and our universe just happens accidentally to be one in which the constants of the universe accidentally came out consistent with life, so we are here to debate the question in the first place.
Can the multiverse theory be tested? Its critics say no, since a real test involves re-creating the Big Bang, which is impossible.
However, a new generation of satellites will soon make precise measurements of the microwave background radiation. Very small perturbations in the smooth "echo of the Big Bang" may possibly prove some version of the "inflationary universe theory," which in turn is nicely explained by the multiverse idea.
Similarly, many physicists (myself included) believe that we will one day solve the superstring theory, in which case we will be able to make precise statements about what happened before the Big Bang.
So until then, the multiverse theory is just that: a theory. However, it is a theory which has generated much excitement and a rash of papers in theoretical physics journals. I, for one, believe that we will one day prove the theory. — M.K.