The other day, I was reading a post by Ethan Siegel on his excellent blog, Starts With a Bang, about whether it makes sense to consider the universe to be a giant brain. (The short answer is no, but read his post for the details.) Something he mentioned in the post caught my attention.

But these individual large groups will accelerate away from one another thanks to dark energy, and so will never have the opportunity to encounter one another or communicate with one another for very long. For example, if we were to send out signals today, from our location, at the speed of light, we’d only be able to reach 3% of the galaxies in our observable Universe today; the rest are already forever beyond our reach.

My first reaction when reading this was, really? 3%. That seems awfully small.

What Siegel is talking about is an effect that is due to the expansion of the universe. Just to be clear, “expansion of the universe” doesn’t mean that galaxies are expanding into space from some central point, but that space itself is expanding everywhere in the universe proportionally. In other words, space is growing, causing distant galaxies to become more distant, and with space growing in the intervening space, the more distant a galaxy is from us, the faster it is moving away from us.

This means that as we get further and further away, the movement of those galaxies relative to us, gets closer and closer to the speed of light. Beyond a certain distance, galaxies are moving away from us faster than the speed of light. (This doesn’t violate relativity because those galaxies, relative to their local frame, aren’t moving anywhere near the speed of light.) That means they are outside of our light cone, outside of our ability to have any causal influence on them, outside of what’s called our Hubble sphere (sometimes called the Hubble volume). Note that we may still see galaxies outside of our Hubble volume if they were once within the Hubble sphere.

How big is the Hubble sphere? We can calculate its radius by dividing the speed of light by the Hubble constant: H 0 . H 0 is the rate by which space is expanding. It is usually measured to be around 70 kilometers per second per mega-parsec, or about 21 kilometers per second per million light years. In other words, for every million light years a galaxy is from us, on average, the space between that galaxy and us will be increasing by 21 km/s (kilometers per second). So, a galaxy 100 million light years away is moving away from us at 2100 km/s (21 X 100), and a galaxy 200 million light years away will be receding at 4200 km/s (21 X 200), plus or minus any motion the galaxies might have relative to their local environment. The speed of light is about 300,000 km/s. If we take 300,000 and divide by 21, we get a bit over 14000. That would be 14000 million, or a Hubble sphere radius of around 14 billion light years.

(If you’re like me, you’ll immediately notice the similarity between the radius of the Hubble sphere and the age of the universe. When I first noticed this a few years ago, it seemed like too much of a coincidence, but I haven’t been able to find any relationship described in the literature. It appears to be a coincidence, although admittedly a freaky suspicious one.)

Okay, so the Hubble sphere is 14 billion light years in radius. According to popular science news articles, the farthest galaxies we can see are about 13.2 billion light years away, and the cosmic microwave background is 13.8 billion light years away, so everything we can see is safely within the Hubble sphere, right?

Wrong. Astronomy news articles almost universally report cosmological distances using light travel time, the amount of time that the light with which we’re seeing an object took to travel from the object to us. For relatively nearby galaxy, say 20-30 million light years away, that’s fine. In those cases, the light travel time is close enough to the co-moving or “proper” distance, the distance between us and the remote galaxy “right now”, that it doesn’t make a real difference. But when we look at objects that are billions of light years away, there starts to be an increasingly significant difference between the proper distance and the light travel time.

Those farthest viewable galaxies that are 13.2 billion light years away in light travel time are over 30 billion light years away in proper distance. The cosmic microwave background, the most distant thing we can see, is 46 billion light years away. So, in “proper” distances, the radius of the observable universe is 46 billion light years.

Crucially, the Hubble sphere radius calculated above is also in proper distance units. (The radius in light travel time would be around 9 billion light years per Ned Wright’s handy Cosmological Calculator.)

We can use the radius of each sphere to calculate their volumes. The volume of the Hubble sphere is about 11.5 trillion cubic light years. The volume of the observable universe is about 408 trillion cubic light years. 11.5 divided by 408 is .00282, or around 3%. Siegel knew exactly what he was talking about. (Not that I had any doubt about it.)

In other words, 97% of the observable universe is already forever out of our reach. (At least unless someone invents a faster than light drive.)

It’s worth noting that, as the universe continues expanding, all galactic clusters will become isolated from each other. In our case, in 100-150 billion years, the local group of galaxies will become isolated from the rest of the universe. (By then, the local group will have collapsed into a single elliptical galaxy. ) We’ll still be able to see the rest of the universe, but it will increasingly, over the span of trillions of years, become more red shifted, and bizarrely, more time dilated, until it is no longer detectable. By that time, there will only be red dwarfs and white dwarfs generating light, so the universe will already be a pretty strange place, at least by our current standards.

If our distant descendants manage to colonize galaxies in other galactic clusters, they will eventually become cut off from one another. If any information of the surrounding universe survives into those distant ages, it may eventually come to be regarded as mythology, something unverifiable by those civilizations living trillions of years from now.