9.2 What if the universe were finite?

This week began by asking how far we could see out into the universe. Let’s imagine for a moment that the universe is indeed closed and finite, just like the surface of the Earth. By looking deep enough, could we – metaphorically speaking – see the backs of our own heads?

If the universe is finite but larger than the observable universe, then this wouldn’t be possible, even in principle. Light from the back of our heads could not get back to our eyes within the age of the universe; the CMBR would get in the way.

On the other hand, some researchers have speculated that the universe might actually be smaller than the observable universe. In this case, the Hubble deep fields might reveal the same patterns of galaxies – including our own Milky Way – recurring at increasing distances. This would mean that we were seeing the same regions more than once between us and the background radiation, albeit at different stages in their evolution. But so far, there is no evidence of such patterns. Video 3 brings together and illustrates some of this week’s concepts.

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Transcript: Video 3 The size of the universe

RUSSELL STANNARD

When one thinks about the great distances between the stars, between one galaxy and another, between one cluster of galaxies and another, it prompts the question: how big is the universe? Here we have to make a distinction between the universe and the observable universe.

We see stars by the light that they send us. It takes time for light to get here. Light is fast. It travels at 300,000 kilometres per second. But the distances involved are immense. It takes four years for light to reach us from even the nearest star. As for crossing from one side of the galaxy, like our Milky Way galaxy, to the other, that takes 100,000 years.

The universe came into existence around 14 billion years ago in the Big Bang. That means we can see only those galaxies for which the light from them could reach us in less than 14 billion years. That’s us, OK? And these are the surrounding galaxies. So let’s suppose it takes 14 billion years to get from here to where we are.

Now that defines the observable universe. We can see everything inside this radius. And beyond the observable universe lies the rest of the universe – presumably. How far does that go on for? Forever. The universe is infinitely big. At least, that’s what we assume.

Why? Why do we assume that? Because we can’t imagine what it would be like to come to the edge of the universe. If, in our mind’s eye, we underwent a long distance journey and we did come to an edge, what would lie beyond the edge? Nothing. A stretch of emptiness. Empty space. But wouldn’t that empty space be part of the universe? It just has nothing in it. So, we wouldn’t have come to the end.

There was one very ingenious attempt to get around this problem. Suppose the picture we have here is not the right one. Space isn’t flat, and it doesn’t go on forever. It’s more like this. OK. That’s us. And we go on a long distance journey, going off into space. And what happens? We carry on, and on, and on, and on, and-- we get back to where we started. You don’t go on forever. The size of the universe? Well, it’s a nice measurable distance. No trouble with infinities.

OK. With a two-dimensional surface like this, it’s easy enough to see how it’s curved. It curves in the third dimension. But with three-dimensional space, how can that be curved in on itself? We don’t see any additional spatial dimensions that take up the curvature, and it’s not something we can form a mental picture of.

Yet Einstein’s theory of relativity does allow for three-dimensional space to be curved. It’s curved by the objects in it. It’s a bit like this. OK. There’s a two-dimensional surface, OK? And if I get a hold of a heavy object, I put it in that space. See what happens? It curves the space. And the heavier the object, the greater the curvature.

Einstein’s theory tells us that heavy objects in three-dimensional space, such as this for example, it curves the space around it. And if the sheer amount of stuff in the universe as a whole is great enough, it will cause an overall curvature sufficient to close the universe in on itself.

Now, what would that mean? A closed up universe. Well, suppose this is a spacecraft, OK? And here we have the Earth. Spacecraft starts off at the North Pole. It goes vertically upwards, up and up and up. Always sticking to the same direction on, and on, and on, and on, and on, and on, and on, and on, and on, and on, and on. And it ends up where it started, only at the South Pole.

No edge to the universe. No nasty infinite distances. What could be neater? The trouble is, it doesn’t work. When you do the sums and you tot up everything in the universe, there just isn’t enough stuff. Not enough to curve space back on itself. So, that’s the end of the finite, closed universe idea. Which is a pity, because that was a very good example of the kind of lateral thinking that’s sometimes called for when dealing with very deep questions.

No, we appear to be stuck. Stuck with a universe that’s infinite in size. But is that a satisfactory answer? What does it mean to say the universe is infinite? Might that simply be a cop-out, a way of disguising the fact that we simply do not know how to answer the question: how big is the universe?

End transcript: Video 3 The size of the universe

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Video 3 The size of the universe

In the end, we can be confident that the universe is expanding, but perhaps we can never be certain whether it is infinite. It may well be one of those things we cannot know.