WHAT'S UP: The universe is finite and unbounded

Jul 15, 2011

And what does it mean to say the universe is expanding equally in all directions? Naively, we might imagine a spherical universe that is getting bigger and bigger, with all the stars and galaxies flowing away from a center like the luminous colored specks of a large fireworks burst.

However, in order to reconcile our view of the universe with this simple-minded perspective, Earth would have to lie precisely at the center of the universe. If Earth were not at the center, our view of the universe would be asymmetric: We would see “the edge of the universe” closer in one direction than in others, and we would see the universe expanding unequally.

The odds that the solar system lies at the center of the known universe are astronomically long: Of all the stars in all the galaxies of the entire universe, the sun and Earth would need to be at the very center.

Modern cosmological theories of the universe, however, don’t need the solar system to occupy such a special place because these theories claim the universe doesn’t have edges or a center.

Which makes one wonder how the universe can be finite in size but without a center or bounding edges.

It seems that cosmologists — who are mostly mathematicians — can imagine just about anything. But a finite-yet-unbounded universe is not as fanciful as it seems at first blush. To see why, however, it is best to think through an analogy.

Suppose you are an ant that lives in a two-dimensional universe — you know only of north and south, east and west; but not up and down. Your world has length and width, but not depth.

If the 2-D ant version of you lived on a flat plane — like a large, round sheet of paper — your universe would be finite, like our own, but it would have an edge. And if you were not exactly at the center of the round, flat universe, the edge would be closer in one direction than in others.

But suppose the 2-D ant version of you lived on the surface of a very, very large ball. Your universe would be finite (in that it could fit in a larger ball), but it wouldn’t have an edge that you could run into. And your universe would look the same in all directions (remember, you can’t look up or down, into or off the surface of the ball) no matter where you were.

Suppose further that the ball was expanding. For the 2-D ant version of you, that would mean that every point in your curved, 2-D universe would be expanding away from every other point equally in all directions.

The analogy recreates every observable aspect of our own universe — in two dimensions, not three.

To imagine the reality of our own universe, you only need to think about how our 3-D space is curved around on itself somehow in a fourth spatial dimension to form a finite but unbounded 3-D space.

— By Doug Furton, a member of the physics faculty at GVSU. Send questions and suggestions to dgf@inbox.com.

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