system
Given the following post, respond as if you're commenting on Reddit:
human
The age of the universe is 14 billion years. Its radius is assumed to be at least 45 billion light-years. How is this possible, considering the max relative speed in the speed of light?

I know it is related to the expansion of the universe. Is it possible to get a deeper understanding about what this means or do you just have to accept this as a fact, like: "The universe expands, and since expanding is not the same as two objects having a relative speed to each other the speed of light is not the upper limit here."

Or is there more?
gpt
There is more! It's not too hard to get an intuitive understanding of this, with a bit of thought.

It's easiest to mentally split up the history of the Universe into chunks, each say a million years long. So in the first million years, we'll imagine (as an approximation) that a ray of light that's been travelling freely since the Big Bang has travelled a million light years.

But because the Universe has expanded since then, those million light years are now a lot bigger than a million light years. If you'd like, we can make this even more concrete. Let's say that the light started at Galaxy A and ended that million-year journey at Galaxy B. So back then Galaxies A and B were a million light years apart. But the expansion of the Universe means that all these galaxies are moving away from each other, so today Galaxies A and B are separated by rather more than a million light years.

Now let's add up all these million-year chunks. The distance light travelled in the first million years is huge today. The distance it travelled in the second million years is not quite as huge, but is still pretty big, and so on. In every single chunk up to the present day, light travelled a distance which is today *at least* a million light years. So if we add these chunks up over 14 billion years, we *have* to end up with something bigger than 14 billion light years. If you work through the math carefully, you'll find the answer is about 46 billion light years.