system
Given the following post, respond as if you're commenting on Reddit:
human
Imagine that eventually humanity sets out to colonize the universe at near light speed. How much of the universe could they reach before it is too far to catch due to the expansion of space?

Assuming that the time it takes for humanity to develop near light speed travel and set out to colonize is negligible on the cosmic scale, how much could we actually reach?  Would it be comparable to the observable universe or much smaller?
gpt
It's smaller than the observable universe. To observe something, light must have been able to leave there and reach us within the age of the universe. For light to reach us, there are two competing effects. One is that the light is moving towards us at the speed of light (of course). The other is that the universe is continuing to expand. If the expansion of the universe means that the distance between us and the light is increasing faster than the speed of light, then the light won't ever reach us. Nothing moves faster than light, so if light can't reach us, nothing can reach us.

But the expansion of the universe also means the *source* of the light is moving away at an ever increasing rate. That means that things that *used to be* close enough that we could exchange light are now so far away that we will never see the light they emit now. And vice versa - anything emitted from Earth that moves at or below the speed of light will never reach those distant galaxies.

So we can see galaxies that we can never reach. In the distant past, they were close enough that their light could reach us, even if it's only just arriving now. So we see them as they were in the very early universe.

In terms of what you *can* reach - there's no limit to the *distance* you can go. But because the universe is expanding, there's a limit to how much *stuff* you can reach. All of the galaxies you can visit are within a present-day distance of about 16 billion light years. They will move away as the universe continues to expand, but if you moved at (or near) the speed of light, you should be able to "catch up" with anything within this present-day radius. For comparison, the "observable universe" has a radius of about 46 billion light years, in the sense that the most distance galaxies we can observe are *presently* 46 billion light years away, because the universe has been expanding since the light was emitted.