Mathematically speaking, we’d expect that there will be a limit to the size of the universe before things start getting weird. If the universe is truly infinite then there will be copies of things that just spawn randomly because there is so many ways for matter to arrange itself. That is to say that in the infinite universe there would be copies of you.
We honestly don’t know. We will forever be stuck in our little bubble we call “Observable Universe” so we will never be able to fully prove the infinity of the universe.
As of now, we have no real evidence that suggest the universe is finite so, many scientist believe that the universe is infinite. But make no mistake, the lack of evidence for one doesn’t imply the opposite. The universe equally can be finite or infinite.
Let’s explore the infinity. What does it means for the universe to be infinite? Like above, we don’t know but we can imagine. Maybe it’s truly infinite, you can travel in any direction and you will always see the same old things, stars, galaxies, nebulae, maybe even life, forever and ever, no matter how far you go. You might even find another you that live the exact same life as you are, in fact, there might very well be infinite copies of you out there…
Maybe it’s only infinite in space, the further you go, the less and less stuff you will find. At some point, you might reach a point where there’s nothing but space left. Does this count as infinite? That would depends on if you consider “space” and “nothingness” something. Personally, if you can still travel pass the border where matter ceases to exist into “nothingness” then that nothingness must be something.
Basically, we don’t know. Contemplating the question might never arrive at any answer but asking and thinking is fun and that’s what human do and will continue to do so, even if it drives us crazy.
Oops, let me stop now before this turn into an essay, we still have finite universe to talk about but since you only ask about infinite, we will stop there.
Edit: Minor typos and grammatical mistakes.
Take sand like we have on earth, beaches, deserts and everything. If we were to put all the sand in one big pile one could still count all the grains. It might take thousand people a thousand years but at one point all the grains would have been counted. The catch is that we have a limit defined. All the sand on earth is the limit so there is a limited amount of sand.
This is not the case with the universe. One cannot create a pile with all the stars as you will never stop adding stars to the pile as there will always be more stars that can be added. It doesn’t matter if you take a million years wit a million people.
The universe or the observable universe? Two different things.
It’s not known if the universe is infinite or not. The observable universe had a beginning, so that’s not temporally infinite in both directions, and there’s a fixed limit to its size, as measurable by the speed of light. But the universe itself? Unknown. Experts mostly suggest it’s possibly infinite, though, either because it simply expands forever in every direction, or because it’s curved and has no edge.
The former because the universe is expanding in all directions, at all times. No matter which direction you go, nor for how long, you won’t reach a limit and you’ll move further away from where you started. Rather than a globe, think of it like an infinite set of points, each of which is expanding away from every other point. There’s no middle or edge, unlike the observable universe.
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