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How the Universe Expands

Although I consider myself knowledgeable about science, it wasn't until after college that I learned the right way to think about how the universe expands. I'd heard about the big bang, of course, and naturally I imagined everything first being concentrated into a single point in empty space, and then—bang!—flying outward in every direction. Unfortunately, that picture is completely misleading: among other things, it suggests that the universe has a center and that there was (and is) lots of empty space sitting around doing nothing.

To come up with a better picture, it will help to imagine that the universe is two-dimensional (as in Flatland) rather than three-dimensional; and not just an infinite two-dimensional plane, but rather the surface of a sphere, or balloon. The way the universe expands is the same way the balloon expands when it's inflated. All the inhabitants agree that the universe is expanding, but the expansion is uniform; no point in the universe can be distinguished as its center.

To us as three-dimensional observers, of course, there is a center, it's just not part of the two-dimensional universe. Does it follow that our three-dimensional universe is actually embedded in four spatial dimensions, and has a center we can't reach? Nope! It's possible to have surfaces with curvature, and to study them, without requiring that the surfaces be embedded in any particular space. The method is not obvious—in fact, when first discovered (by Riemann), it was a major conceptual breakthrough—but I don't want to try to explain it here. Sorry. I learned it when I took a differential geometry class in college, but in the natural order of things you don't get to it until near the end.

Since everyone's used to time being the fourth dimension, I should point out that the putative embedding would use a fourth spatial dimension, not the fourth temporal one we already have. Technically, then, we should be wondering whether the (3+1)-dimensional universe needs to be embedded in a (4+1)-dimensional space, but the answer's the same.

Speaking of curvature, that's another benefit of the balloon picture, that it illustrates how space can be curved. Unfortunately, it illustrates positive curvature, instead of the zero or negative curvature that the real universe seems to have, but it's still a worthwhile thing to imagine—surfaces of constant zero or negative curvature aren't nearly as photogenic.

Finally, I'd like to present a way of disentangling the concept of an expanding universe, which is fairly well understood, from the question of why the universe exists, which as far as I'm concerned is not understood at all. (See my essay on religion for more thoughts on the latter.) As I see it, the reason there's a tangle in the first place is that when we imagine a series of events, we naturally want to imagine the events all at once, in the correct order, and that means starting at the beginning. There are alternatives, however. We can start at the present day, and imagine the events running forward into the future and backward into the past; or, if we want to avoid having events run backward, we can pick some moment far in the past, far enough that we don't care about previous events, and just imagine events running forward from there.

I like to imagine the universe as a videotape. We naturally want to watch it from the beginning, but when we try, we find the beginning is full of static, and we can't even really tell how far back it goes. That shouldn't prevent us from watching the rest of the tape.


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@ October (2000)