If the Universe is about 13.7 billion years old, and the diameter of the observable universe is 93 billion light years, how can it be that wide if the universe isn’t even old enough to let light travel that far that quickly?
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The balloon/bubble analogy explains why this all occurs, but doesn’t tell you how we know it’s happening. So let’s ignore all the analogies and go straight into some math, because you really can’t get away from it when dealing with astrophysics. When we used our big space telescopes like the Hubble and the James Webb, we can more or less scan in 360 degrees around us in 3 dimensional space, a perfect panorama of the Universe around us. This 360 degree sphere is what we call the “observable universe.”
Now, we can also measure what we observed, but when dealing with such massive distances, time becomes a factor. The farther away something is, the further back in time we are actually seeing it, sort of like the time delay you hear in fireworks. The firework explodes, you see it, and then after a few milliseconds, you hear it. Well, we’re dealing with such massive distances that something happens, and then millions or billions of years occur, and then we finally see it. So when we look back into the furthest reaches of what our space telescopes can see, we end up seeing this extremely dense, low-energy radiation field, and nothing else, almost like we reached the end of our render distance. This is the Cosmic Background Radiation, and it’s theorised to be the state that the universe was in immediately after it formed, before even the first clouds of gas had formed.
So by measuring the distance in light years until we reach CBR and then calculating the volume of a sphere based on that distance gives us the overall “size” of the observable universe, which we just take the diameter of to give us the width. **Please note that the observable universe is almost certainly not the entire universe. It is only the size of the sphere in which light was able to reach us within a certain amount of time. For our purposes, though, anything outside of the observable universe will never be able to influence us, and therefore is irrelevant.** Okay, okay, but what about the age? None of that helps us age the universe. Well, but something else does. Stars. By looking back in time to the furthest stars we can see, and using information we’ve gathered from much closer stars, we can calculate ages of things and move forward. Say that scientists found a star-producing cloud of dust that they calculated to be roughly 12 billion years old. They can do some math to figure out how long it would have taken for such a cloud to form under conditions similar to how we know the universe was (CBR), and then said “if this is the first ‘thing’ in the universe, then the universe is at least this old.” The currently accepted number is 13.7 billion years.
Another, more complicated method involves measuring the expansion rate of the universe itself. It has to do with red-shifting and blue-shifting and measuring distances over time and it’s so much more math heavy that I don’t know how to make it ELI5. However, once they know how fast the universe is expanding, they just work backwards to find the age of the universe. That method also lands around 13-14 billion years.
So the reason we know that the universe is only so old and how we can measure out to a certain distance are two separate things, which is how they can be two different numbers altogether. We know that the universe is expanding because these numbers are different, and we can actually see it and measure it if you know what you’re looking for.
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