The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [17]
Similarly, the light we’ve been emitting can’t yet have reached those distant regions, so we are beyond their cosmic horizon. And it’s not that cosmic horizons solely delineate what someone can and cannot see. From Einstein’s special relativity, we know that no signal, no disturbance, no information, no anything can travel faster than light—which means that regions of the universe so far apart that light hasn’t had time to travel between them are regions that have never exchanged any influence of any kind, and so have evolved completely independently.
Using a two-dimensional analogy, we can compare the expanse of space, at a given moment of time, to a giant patchwork quilt (with circular patches) in which each patch represents a single cosmic horizon. Someone located in the center of a patch can have interacted with anything that lies in the same patch, but has had no contact with anything lying in a different patch (see Figure 2.1a), because they’re too far away. Points lying near the border between two patches are closer together than their respective centers and so can have interacted, but if we consider, say, patches in every other row and every other column of the cosmic quilt, all points residing in different patches are now so far from one another that no cross-patch interactions of any kind could have taken place (see Figure 2.1b). The same idea applies in three dimensions, where the cosmic horizons—the patches in the cosmic quilt—are spherical, and the same conclusion holds: sufficiently distant patches lie beyond one another’s spheres of influence and so are independent realms.
If space is large but finite, we can divide it into a large but finite number of such independent patches. If space is infinite, then there are an infinite number of independent patches. It’s this latter possibility that’s of particular allure, and the second part of the argument tells why. As we will now see, in any given patch the particles of matter (more precisely, matter and all forms of energy) can be arranged in only a finite number of different configurations. Using the reasoning rehearsed with Imelda and Randy, this means that conditions in the infinity of far-flung patches—in regions of space like the one we inhabit but distributed through a limitless cosmos—necessarily repeat.
Figure 2.1 (a) Because of light’s finite speed, an observer at the center of any patch (called the observer’s cosmic horizon) can have interacted only with things lying in that same patch. (b) Sufficiently distant cosmic horizons are too far apart to have had any interactions, and so have evolved completely independently of one another.
Finite Possibilities
Imagine it’s a hot summer night and there’s an annoying fly buzzing around your bedroom. You’ve tried the swatter, you’ve tried the nasty spray. Nothing’s worked. In desperation, you try reason. “This is a big bedroom,” you tell the fly. “There are so many other places you could be. There’s no reason to keep buzzing around my ear.” “Really?” the fly slyly counters. “How many places are there?”
In a classical universe, the answer is “Infinitely many.” As you tell the fly, he (or, more precisely, his center of mass) could move 3 meters to the left, or 2.5 meters to the right, or 2.236 meters up, or 1.195829 meters down, or … you get the idea. Since the fly’s position can vary continuously, there are infinitely many places it can be. In fact, as you explain all this to the fly, you realize that not only does position present the fly with infinite variety, but