With the balloon analogy it’s not about the center of the volume, we ignore the volume and assume that the surface is a 2d universe. That’s what’s impossible to find the center of. I don’t really like that analogy though personally so I’m not going to discuss that one further.
Just think about it this way: the observable universe can only be so big (because when the expansion between two distant enough objects is faster than the speed of light/causality, they no longer have a means of interacting). We don’t observe any sort of obvious boundary to the universe within our visible portion that we might be able to assume a center based on. So it’s not that we know that there isn’t a center (afaik, someone correct me if I’m wrong), it’s that it’s likely impossible know that there is, let alone find it from our position in the universe. So, we might as well assume that it’s all relative.
Imagine you woke up on a raft in the middle of the ocean on an alien planet. It’s foggy, you can’t see stars, you can’t see any landmarks at all. There are other things floating in the water too though. There might be a geometric center to that ocean, but you can’t see it, and you have no other hint at where it is. For all you know, the entire planet is ocean and there’s is no center to find. This is sort of the situation we Earthling are in now, except that at least the the rafter can drift and perhaps eventually find and map out a coast. Because our space-time is expanding, our observable universe will never be bigger than it is now.
With the balloon analogy it’s not about the center of the volume, we ignore the volume and assume that the surface is a 2d universe. That’s what’s impossible to find the center of. I don’t really like that analogy though personally so I’m not going to discuss that one further.
Just think about it this way: the observable universe can only be so big (because when the expansion between two distant enough objects is faster than the speed of light/causality, they no longer have a means of interacting). We don’t observe any sort of obvious boundary to the universe within our visible portion that we might be able to assume a center based on. So it’s not that we know that there isn’t a center (afaik, someone correct me if I’m wrong), it’s that it’s likely impossible know that there is, let alone find it from our position in the universe. So, we might as well assume that it’s all relative.
Imagine you woke up on a raft in the middle of the ocean on an alien planet. It’s foggy, you can’t see stars, you can’t see any landmarks at all. There are other things floating in the water too though. There might be a geometric center to that ocean, but you can’t see it, and you have no other hint at where it is. For all you know, the entire planet is ocean and there’s is no center to find. This is sort of the situation we Earthling are in now, except that at least the the rafter can drift and perhaps eventually find and map out a coast. Because our space-time is expanding, our observable universe will never be bigger than it is now.