If the Universe is flat and expanding at the speed of light, that must mean that we could never leave it, because one would have to travel faster than the speed of light which is not possible. However, what about going straight up or down ? The distance is less and if the Universe is not expanding in depth but only sideways then it would be possible to exit. Could we then find another Universe once we have gone out of this one ?
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When scientists say the universe is "flat," they don't mean that it's shaped like a dinner plate. It's no easier to travel "up" than "forward." In fact, off-planet, those terms don't even have any meaning.
What you're referring to has to do with the shape of the universe:
When physicists describe the universe as being flat or nearly flat, they're talking geometry: how space and time are warped according to general relativity.
Think of it like this: if you draw a triangle on a balloon, is that triangle flat? In one sense yes, because it never rises above the surface of the balloon. Relative to the balloon, it is one-dimensional; you wouldn't be wrong to say that the image of the triangle is "flat." But relative to the rest of the room, it is curved, because it follows the curvature of the balloon's shape.
When most people talk about the universe, they're talking about the triangle. The discussion you're referring to, of the "flatness" of the universe, is discussing the shape of the balloon.
As for flying "out" of the universe and potentially into another, we're like an ant walking on the surface of that balloon: no matter what direction the ant walks, it'll just keep walking around the balloon. The surface of his universe may be curved, but there's no direction he can go that takes him off of that curve. For all he cares, it's essentially a flat surface, because he can only move in two dimensions along it. Similarly, the geometry of our universe may be one thing or another, flat or curved, but either way that doesn't mean we can point a ship in any direction and "leave."
@PeterU - I strongly recommend that you read several introductory books to cosmology and modern physics. Some of the difficulties you're encountering are stemming from the fact that you're looking at popularized science, hear some of the analogies they use to make the public understand difficult scientific ideas, but you're taking those analogies at face value, not realizing they're just metaphors. This is not to accuse you of anything - these are complex matters and it takes time to figure them out. I know it took me many years, and I recognize some of my bewildered musings from the past in the questions you're asking here. I think you're doing fine, just don't get stuck in analogies.
A few clarifications:
When scientists say the universe is "flat", they don't mean it looks like a pancake. They just mean its geometry is euclidean, that's all. The word "flat" is perhaps poorly chosen (it makes sense if you know a lot of geometry, but not everyone does). There are non-euclidean geometries that mathematicians are studying, but our universe does not seem to be built based on them. It is built based on an euclidean metric.
The universe is infinite and it's the same in all directions. There is no privileged up, down, left, right, back, or forth. They're all the same. And it goes on forever and ever.
The analogy with the ant walking on a balloon is just an analogy. It's hard to visualize a 3D space in its entirety. Instead, you could visualize a 2D space (the surface of the balloon) and try to figure out what happens then. But never forget it's just an analogy, nothing more.
The insect cannot fly off the balloon, because then the analogy breaks. The purpose of the analogy is to show what a 2D observer sees in a particular 2D universe, and then try to extend that knowledge back to our 3D universe. But if your insects are flying around willy-nilly, then the toy is broken and it doesn't do what it's supposed to be doing.
Never forget the difference between models (balloons) and reality (the universe).
There is a set number of Stars that formed and our known Universe only extends to a certain distance. Beyond that there can be other Universes in an infinite Space.
This universe we live in is infinite, as far as we can tell. It just goes on forever and ever. What you call "space" is this universe.
Now, there is something called the "observable universe". That's the chunk of universe we can see. That's finite. We cannot see all the way to infinity, because light doesn't go that fast. However, this is just a little chunk in an infinite whole.
the Hubble telescope has picked up the edge of the Universe
No, it has not.
Modern instruments are getting closer to the theoretical limits of the observable universe. In other words, we are getting so good at astronomy, now we can see almost as far away as theoretically possible.
That doesn't mean we're seeing "the edge of the universe". It only means we're seeing as far as the laws of nature allow us to see.
When I say observable Universe I am referring to everything that was formed from the "Big Bang" , so that is finite but the void or Space that it is expanding into is Infinite.
That's not what the term means. "Observable universe" simply means the universe chunk that we can see, that's all.
You imagine that the Big Bang has occurred at a single point and went out from there. That is not the case.
This is an infinite universe and the Big Bang has / is / will occur everywhere, in every single point in that entire infinity. All points of the universe where the Big Bang has occurred have undergone a lot of expansion, and are still doing it now.
You are thinking about the universe in terms of newtonian physics, where space and time are linear and unchangeable. That is not the case. It's impossible to understand modern theories about the universe in that context.
Again, the Big Bang was not a single point that popped. Get rid of that idea. Instead, do this: pick any point in this infinite universe. Now go back in time. If you go back far enough, you will reach a moment when things in that point were super-dense and super-hot. Going forward in time from that moment, things have expanded and cooled down. This is true for every single point in this infinite universe!
It's not a simple expansion out from a single point. The Big Bang has not occurred in a privileged place in the past. Instead, the Big Bang is a property that every point of the universe had, way back in time.
The universe is not only infinite - every single little chunk of it is expanding out from a very dense and very hot past, towards a very sparse and cool future. No chunk is privileged. They are all the same.
the Multi Universe ? If this Universe were infinite then how and where would the other Universes be then ?
Here's an analogy.
I know that this universe is 3D. But imagine for a moment that it's 2D instead. Imagine it's like an infinite sheet of paper, stretching out forever, but only in 2 dimensions.
Now, a hand's width above that infinite sheet of paper place another infinite sheet. And a little higher another one. And so on.
All these sheets of paper are infinite, yet they can coexist just fine. The trick is - they all exist in a 3D space.
Similarly, you could have an infinity of 3D universes all coexisting in a higher dimensional multiverse.
WARNING: This is not a "theory". It is just a hypothesis. We have no proof that the multiverse exists. Some scientists have hypothesized that this is the case because it would help explain certain features of this universe. But so far there is no proof.
This is normal and it's how science works. This is not idle dreaming. Scientists encounter some strange phenomena. They put forth a hypothesis. Other scientists look for proof. If proof is not found, the hypothesis is scrapped. If proof is found, then it becomes a proper theory. The multiverse idea is currently in that stage before proof; we don't know yet how things will turn out. That is all.
Good answer by Nerrolken. I'll also add that our universe is thought to be infinite in size - which is thought to be a consequence of a flat universe. The data from WMAP seems to indicate very strongly that we live in a flat universe, and that, therefore, in an infinite one. It is impossible to leave an infinite universe, no matter how fast you're going.