Jared409 said:
I'd just like to preface by saying that I'm not in any way an expert on high-level physics, but I would like to think that after reading a few books and taking a healthy interest in things like cosmology that I have a decent understanding of some concepts, so if you could please bear with me.
My question is that if we live in an infinite multiverse and that if inter-universe travel is possible, then wouldn't we have already had an infinite number of beings pass into our universe? If the probability of a plausible action occurring approaches one given an infinite set of universes, then wouldn't that imply that if inter-universe travel was possible, there would be an infinite number of beings that were not only capable of such travel, but also an infinite number that had decided to choose our particular universe to travel to at this very instant?
They would, however, also have an infinite number of universes to choose from, so the result is indeterminate. Basically, what you'd be asking for is the ratio of the number of universes which support life over the typical number of universes they visit. For example, if only 1% of universes support life, and life within those universes tends to visit only one or two other universes on average, then we're unlikely to have visitors.
That said, there are very good reasons to believe that this isn't even remotely possible. But to see this, first we have to nail down what sort of universe we're talking about. Consider three basic multiverse types:
1. Different initial conditions. This is basically a corollary to the fact that our universe almost certainly extends beyond our horizon. The problem, then, is that traveling beyond our horizon requires faster-than-light travel. This is highly unlikely to be possible.
2. Different quantum wavefunction. In quantum mechanics, there are many branches of the wavefunction that all coexist, and we are generally constrained to see one branch at a time. The other branches are almost certainly there, but we cannot interact with them. This is largely down to the quantum phase of the particles that make us up. Traveling to another quantum multiverse would require fine-tuning the quantum phase of every individual particle of our bodies. I just don't think that's even remotely possible. In fact, I'd be willing to bet that there's a good quantum-mechanical argument that proves it is fundamentally impossible (though I don't know that argument offhand).
3. Different low-energy physics. It seems to be the case that the fundamental laws of physics allow for many possible realizations of low-energy physics. These amount to different vacuum states. And this is the least possible of all: different vacuum states have different energies. When vacuum states of different energies come into contact, the lower energy state spreads and destroys the higher-energy state. So if it were possible to visit a region with a lower-energy vacuum state than our own, the unfortunate explorer would pretty much instantly explode into a flash of high-energy particles. If, on the other hand, an explorer were to travel to a region with higher vacuum energy state, then our lower-energy state would rapidly expand and destroy that universe. The explorer would likely be vaporized by the radiation resulting from the universe's destruction.