“Light thinks it travels faster than anything but it is wrong. No matter how fast light travels, it finds the darkness has always got there first, and is waiting for it.” –

Terry Pratchett

It’s the end of the week once again, and so let’s have a go at another Ask Ethan! Perhaps inspired by a great giveaway, there have been so many great questions pouring in (and you can submit yours here for four more chances to win), but this week’s comes from our reader and winner Brad (you owe me your email address, Brad), who asks,

When an object is quoted as being 13.8 billion light years away is that referring to the distance of the object now, how far it was when the light left the object, or perhaps just how far the light traveled?

Due to the expansion of the universe it seems that those three distances would be quite different. Thanks!

I wish, Brad, that everyone held to the same definition. The truth is, those three distances *are* all different, but not everyone is consistent about what they mean when they give a distance. Let’s take a simple analogy to put this in context.

Imagine there are two flights of stairs, one next to the other. You stand on one, while your friend stands on the other, below you, holding a ball. Your friend throws the ball to you at a certain speed, the ball takes a certain amount of time to reach you, and if you know those two pieces of information — the ball’s speed and the amount of time it travels — you can figure out how far away your friend is from you. Let’s say, just for an example, the ball moved at 10 meters-per-second, it traveled for one second, and you and your friend were 10 meters apart. (And let’s imagine the ball isn’t affected by the Earth’s gravity, just to keep things straightforward.)

But I could make this problem a little bit different by, instead putting you and your friend on (stationary) flights of stairs, you could be on escalators moving in opposite directions: you moving upwards and your friend moving downwards, each at a speed of (just to pick a number) 2.5 meters-per-second.

Can we imagine that everything was the same as before? It’s not so simple, and here’s why.

If your friend throws the ball at 10 meters-per-second and you start off 10 meters apart, it *won’t* take 1 second for the ball to reach you, and you *won’t* be 10 meters apart when the ball arrives; instead, it will take more like 1.3 seconds for the ball to arrive, and you and your friend will be separated by more like 17 meters.

If your friend throws the ball at 10 meters-per-second and you *end up* 10 meters apart, it *won’t* take 1 second for the ball to reach you, and you *won’t* have been 10 meters apart when the ball was thrown; instead, it will have taken about 0.8 seconds for the ball to arrive, and at the start, you and your friend were only separated by about 6 meters.

And if your friend threw the ball at 10 meters-per-second and the flight of the ball took exactly 1 second, that means you started off about 8 meters apart when the ball was thrown, and you’re now 13 meters apart when the ball arrived. (You can put more significant figures into these numbers, if that’s your prerogative; I rounded.)

The point is, when things are both separated by a distance *and* in motion relative to one another, it’s not so simple to talk about distances, as there are three different meanings to distance:

- The distance that these two objects were apart from one another when the
*emitting*object*sent*the signal that the observer will receive. - The distance that these two objects are apart from one another when the
*observing*object*receives*the signal sent by the emitter. - Or the amount of distance that the
*traveling*signal*actually travels*on its journey from the emitter to the observer.

All three of these distances were the same for the stationary (staircase) example, and all three were different for the moving (escalator) example. Well, guess which one the Universe is like?

While gravitationally bound objects — like planets in a solar system, stars in a galaxy, or galaxies in a cluster — might behave more like the stationary case, the *vast majority* of galaxies in the Universe are expanding away from one another, caught up in the Hubble expansion of the entire Universe! When we look deep into the distant Universe, we’re looking deep into the past, seeing light from a time when objects were closer together, when the Universe was expanding faster, and from long ago. The major difference between space between galaxies expanding and the escalator expanding the distance between you and your friend is that while the escalator moves you both at a *constant* speed relative to one another, the expansion rate of the Universe *changes* over time!

Today, we know our Universe is 13.8 billion years old, give or take a few tens-of-millions of years. What does that mean for a distant object?

Consider the current record-holder for most distant galaxy in the Universe: UDFj-39546284. When we *say* this object is 13.42 billion light-years distant, what are we referring to?

The distance the light from it has traveled. This is — at least to me — a reasonable way to split the difference. In an expanding Universe, remember, the distance between objects was *smaller* in the past, and grows as time goes on. Even as the light travels across the Universe from the emitting object to (eventually) our eyes, the Universe *continues* to expand!

- This galaxy was
*only*1.1 billion light years distant from us when the light reaching us now was emitted. - The light that is reaching us now was emitted when the Universe was only about 380 million years old, or just
**2.7%**of its current age! - The light has been traveling for 13.4 billion years, and has traveled (by definition) 13.4 billion light-years during its journey.
- And this galaxy is now about
**33 billion**light-years from us at this point in time.

So, although you never know *for sure* which of those three numbers a journalist or writer is talking about, those are the possibilities.

People typically use one of the last two methods — either the distance the light has traveled or the distance the object is from us now — when they talk about very distant objects. And a good rule-of-thumb is that if the distance they give (in light years) is *smaller* than the age of the Universe (in years), they’re probably talking about light-travel-time, while if it’s larger, they’re probably talking about how far it is right now!

For closer objects — and for gravitationally bound objects in particular — the differences between the different interpretations are much smaller, but I’d love it if people were more careful about their words. If everyone would specify whether distances referred to *when the light was emitted*, *how far the light traveled*, or *how distant the observed object is now*, there would be a lot less confusion.

And that’s how distances work in our expanding Universe! Brad, get in touch with me, because you won!

Got a question or suggestion for what the next Ask Ethan column should be? Let us know, and maybe you’ll be the next big winner!