The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [16]
Although observations leave the finite-versus-infinite issue undecided, I’ve found that when pressed, physicists and cosmologists tend to favor the proposition that the universe is infinite. Partly, I think this view is rooted in the historical happenstance that for many decades researchers paid little heed to the finite video-game shape, mostly because it is more mathematically complex to analyze. Perhaps the view also reflects a common misconception that the difference between an infinite and a huge-but-finite universe is a cosmological distinction that’s only of academic interest. After all, if space is so large that you will only ever have access to a small portion of its entirety, should you care whether it extends for a finite or for an infinite distance beyond what you can see?
You should. The issue of whether space is finite or infinite has a profound impact on the very nature of reality. Which takes us to the heart of this chapter. Let’s now consider the possibility of an infinitely big cosmos and explore its implications. With minimal effort, we’ll find ourselves inhabiting one of an infinite collection of parallel worlds.
Infinite Space and the Patchwork Quilt
Let’s start simply, back here on earth, far from the vast reaches of an infinite cosmic expanse. Imagine that your friend Imelda, to satisfy her penchant for variety in personal attire, has acquired five hundred richly embroidered dresses and a thousand pairs of designer shoes. If each day she wears one dress with one pair of shoes, at some point she will exhaust all possible combinations and duplicate an earlier outfit. It’s easy to figure out when. Five hundred dresses and a thousand pairs of shoes yield 500,000 different combinations. Five hundred thousand days is about 1,400 years, so if she lived long enough Imelda would be seen in an outfit she’d already worn. If Imelda, blessed with infinite longevity, continued to cycle through every possible combination, she’d necessarily don each of her outfits an infinite number of times. An infinite number of appearances with a finite number of outfits ensures infinite repetition.
Pursuing the same theme, imagine that Randy, an expert card dealer, has shuffled a gargantuan number of decks, one by one, and neatly stacked each next to the others. Can the order of cards in every shuffled deck be different, or must they repeat? The answer depends on the number of decks. Fifty-two cards can be arranged in different ways (52 possibilities for which card will be the first, times 51 remaining possibilities for which will be the second, times 50 remaining possibilities for the next card, and so on). If the number of decks Randy shuffles exceeds the number of different possible card orderings, then some of the shuffled decks would match. If Randy were to shuffle an infinite number of decks, the orderings of the cards would necessarily repeat an infinite number of times. As with Imelda and her outfits, an infinite number of occurrences with a finite number of possible configurations ensures that outcomes are infinitely repeated.
This basic notion is of the essence for cosmology in an infinite universe. Two key steps show why.
In an infinite universe, most regions lie beyond our ability to see, even using the most powerful telescopes possible. Although light travels enormously quickly, if an object is sufficiently distant, then the light it emits—even light that may have been emitted shortly after the big bang—will simply not have had sufficient time to reach us. Since the universe is about 13.7 billion years old, you might think that anything farther away than 13.7 billion light-years would fall into this category. The reasoning behind this intuition is right on target, but the expansion of space increases