The radius of the observable universe is often stated to be 46 billion light years. From a certain point of view, this is true, but I think it’s a bit of a misleading statement. Occasionally you also see people say that the observable universe is 13.8 billion light years in radius, which is also true, from a certain point of view.
How can both be true? It has to do with two things: the finite speed of light, and the ongoing expansion of the universe.
Gazing upon the past
The speed of light is about 300,000 kilometers per second. Whatever we see, we’re seeing in the past. When you’re looking at an object across the room, what you’re seeing is on the order of nanoseconds in the past, but in the past nonetheless. When looking at the sun, it’s about 8 minutes in the past, and when looking at the next closest star, it’s over 4 years in the past.
Of course, Proxima Centauri probably hasn’t changed much in the 4.24 years since its light started traveling to us, or even the Andromeda Galaxy since the light from it started traveling around 2.5 million years ago. But when you start looking at objects billions of light years away, the evolution of those objects and the universe starts to become an important factor.
When we look out into the distant universe, we’re not seeing things as they are right now, but as they were in the distant past. For cosmology, this is a good thing, because it allows astronomers to study the evolution of the universe, but it also means that we have limited insight into what the state of matter is billions of light years away right now. Stars go through their lifecycles, galaxies form, merge, collide, and go through other transformations.
Now, many relativity purists will say that the concept of “right now” applied to cosmologically distant objects is meaningless. Strictly speaking, they’re right. Of course, technically the concept of what you are doing “right now” as I type this post is also meaningless.
The concept of “right now” is useful to us because we’re close enough to interact, and we have a common objective measure of time to synchronize what we mean by “right now”, namely the time the Earth takes to rotate which we divide into numbered time slots, as well as the time the moon takes to orbit the Earth and for the Earth to orbit the Sun. Of course the time the Earth takes to orbit the Sun is meaningless when observing regions and events that took place before there was a Sun and Earth.
Do we have any objective measure of time that is useful over cosmic distances? Actually, we do. The universe is constantly expanding, having started in an infinitessimally small and dense state. As time passes, the average density of matter in space (averaged across hundreds of millions of light years) is decreasing. Given the observed consistency of the early universe as seen in the cosmic microwave background, we can use the average density across cosmic distances as an objective measure of time since the Big Bang.
So, if you are a relativity purist, when I say “right now”, just substitute, “at the time when that distant region is at the same average density of matter that our region currently has.”
Our growing universe
As I mentioned above, the universe is expanding. Actually, the better way to say that, is that space itself is growing. Over billions of years, this becomes an important factor in considering distances.
Consider that the matter that generated the cosmic microwave background radiation that we’re currently seeing, when it generated that radiation, was only about 42 million light years away from the matter that eventually became us. (To be clear, the cosmic microwave background was generated everywhere in the observable universe at the time, but the cosmic microwave radiation we actually detect today started traveling around 13.8 billion years ago.)
However, the matter that generated that cosmic microwave radiation is currently 46 billion light years away. Why? Because of the expansion of the universe. That’s why many people will say that the radius of the observable universe is 46 billion light years. But the light traveled for 13.8 billion years, across a distance of 13.8 billion light years while space was expanding around it, so that’s why others will say that the radius of the observable universe is 13.8 billion light years.
The furthest galaxies we can currently see are from light that has been traveling over 13 billion years. When that light started traveling, those galaxies were only a couple of billion light years away from the matter that now makes up our galaxy. Today, the matter that makes up those distant galaxies is over 30 billion light years away, and those distant galaxies have almost certainly radically evolved from what we’re now seeing.
So, how far into the universe can we see?
The furthest thing we can currently see is the cosmic microwave background radiation generated from matter that is now 46 billion light years away, but we have limited insight into what that matters look like now. We see galaxies that are composed of matter that is now over 30 billion light years away, but which have evolved in ways we can’t predict, except to say that on cosmic scales, they probably aren’t that different from those in our region.
There may be further complications in the future. Astronomers may eventually be able to examine primordial gravitational waves from the time of cosmic inflation to reach conclusions about regions of the universe far more distant than the cosmic microwave background radiation. If so, some people may conclude that the radius of the observable universe is much larger than any of the current numbers.
When we look out into the universe, we are looking into both space and time. Given that, the size of the observable universe could be said to simply be around 13.8 billion years (not 13.8 billion light years, just 13.8 billion years).
You may disagree (if so, I’d love to read why in the comments), but regardless of what we consider the size of the observable universe to be, the important thing to keep in mind are the limitations of what we can actually observe in the observable universe.