How can we measure the size of the universe?

The universe is about 14 billion years old, but the most distant galaxies are much further than 14 billion light years. How can that be? In this week's "Ask a Physicist," we'll find out.

In my last "Ask a Physicist" column, I asked you to give me questions about cosmic inflation, and to the many of you who did, I thank you, and don't worry, I'll get to it.

Image by Bruce Rolff/Shutterstock

Apparently the internet has other ideas. In an informal poll on my facebook fanpage it became clear that I had a more pressing question to address this week: How do we measure the universe? This was prompted by a question sent in by Kim Bowman, who asks:

As we are looking deeper into space, we are looking deeper into the past. The most distant quasars are as far away as 30 billion light years, but the universe is only 13.8 billion years old. There seems to be some sort of contradiction there.

Talking about distances in an expanding universe is a bitch. The problem is that the ground (or at least space-time) is quite literally shifting underneath your feet as you're trying to make the measurement.

Don't Worry. Nothing's going faster than light.

Way back in my very first "Ask a Physicist" column, I talked about the expanding universe, and touched on a couple of very common misconceptions. The most important of these (at least for today's purposes) is that for the most part, galaxies are more or less sitting still while the fabric of space is expanding underneath them.

While you'll sometimes hear "Galaxy X is flying away from us at half the speed of light", what it really means is that "the distance between us and Galaxy X is increasing at half the speed of light." At the same time, as light travels through the universe, the wavelengths get stretched. This means that the cosmological redshift is really a measure of how much the universe has expanded since the light left the source. This is a subtle distinction, perhaps annoyingly so, but important. Incidentally, I talk a lot more about what it means for the universe to expand in my previous column and especially in my totally awesome book

If the galaxies were really flying away from us then everybody writing in worrying about the universe expanding "faster than light" — and believe me, I hear that a lot — would really have a cause for complaint. On the other hand, for "faster than light" to have any real meaning, you need to be able to beat a photon in a fair race, and the expanding universe simply doesn't allow you to do that.

You can think of this kind of like those walkways at the airport. Nearly all of you get on those things you start running, and feel like you're the grand champion of the universe because you're going so fast. You might even foolishly think that you can outrun anyone. But what happens when a drug-sniffing dog joins you on the walkway? Lo and behold, he moves even faster because he gets the boost from the walkway, too.

The same is true with the universe. If I shot the world's most powerful laser pointer at some distant galaxy, it doesn't matter that the galaxy appears to be receding from us at faster than light, as long as the galaxy is within a certain distance (which I'll talk about in a bit), ultimately the laser pointer will make a little dot on the wall in the faraway galaxy such as to delight and amaze extraterrestrial kittens. (Ultradork bonus: Except the kitties would have to be wearing infrared goggles). Even though light always travels locally at the speed of light, it seems to be carried away even faster by the airport walkway of the universe.

How can we measure the size of the universe?

Image by Bill Fehr/Shutterstock

Which distance do you mean?

The major headache from living in an expanding universe comes from the fact that you can't just say that it's a five billion light years to a particular galaxy. You have to say exactly what you mean.

You could mean, for example, "How far away would it be if I could freeze time right now and drive out to the galaxy and look at my odometer?" This distance is called the "proper distance," and it's taking all of my impulse control not to boldface vocabulary words right now.

The proper distance is not the same as "How far would I actually have to drive to get there if I started right now?" Since the universe is expanding underneath us, you'd have to drive a fair amount extra. Normally, when you read articles here and elsewhere, writers simply give you the proper distance, but it turns out that doing it that way creates a lot of confusion. Incidentally, that new "oldest" galaxy that everybody's talking about? 32 billion light years away.

But you could also mean the transparently similar, "How far away is the galaxy RIGHT NOW?" where "right now" is this particular moment rather than a billion years from now. Some time in the future, when the universe is twice the size it is now, the proper distance between us and galaxy X will have doubled, but the so-called "comoving distance" will be the same.

There are still others which are even more abstract (but which you can ignore and still tell your friends that you understood the entire column), like the "angular diameter distance," which is simply a function of the fact that things look smaller as they get further away, and the "luminosity distance," which is just a function of the fact that things look dimmer as they get further away. Luminosity distance is particularly important because it's the number that astronomers use when measuring the distances to Supernova explosions as a test of the accelerating universe. Even if we're looking at the exact same galaxy, each of these distances will be a very different number.

The upshot is that you can take all of the parameters of your universe: how much Dark Matter, Dark Energy, there is, how much the universe has expanded since the light left the distant source (the redshift), voila! We can calculate all of these different distances. All things being equal, for instance, universes with large fractions of dark energy are bigger and older than universes with large fractions of dark matter.

How can we measure the size of the universe?

Image by Benjamin Haas/Shutterstock

So how big is the universe?

By now you should be getting a pretty good idea how the most distant galaxies can be further away than 13.8 billion light years. For the first part of the trip, the light that is just now reaching us was traveling through a much more compact universe than we have now. As time went on and space expanded, the distance between the photon and where it started increased at "faster than light." Again, this doesn't mean that light was traveling faster than light. Anyone watching the beam go by would measure it at 3x108 m/s, the ordinary cosmic speed limit.

Even so, there's a maximum distance that light could have traveled since time began. This is known as the horizon, and based on our best cosmological measurements, it's about 48 billion light years. The light that we see from the Cosmic Microwave Background Radiation is reaching us from a point very near to the horizon.

What lies beyond the horizon? Nobody knows. The assumption, of course, is that the universe out there looks pretty much like it does here, at least from a statistical point of view, but we can't be sure. Probably robots in cowboy hats.

Of course, if we were very patient, we'd get to see what's beyond the horizon. Tomorrow's horizon is slightly further away than today's. But here's where super-weirdness sets in. Our universe is accelerating, and as a result of that, there will eventually reach a time when no matter how long you wait, you won't be able to see any further. This means that in about a hundred billion years or so (provided we're patient enough), we'll be able to see all we'll ever get to see.

In case you're curious, the ultimate horizon for us seems to be about 63 billion (comoving) light years away. And beyond that, we can't ever know.

Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (follow us on twitter, facebook, twitter or our blog.) He is an Associate Professor of Physics at Drexel University. Feel free to send email to askaphysicist@io9.com with any questions about the universe.