What does it mean: “The Universe is most probably flat”?
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I understand that it isn’t flat flat. But I thought that because of Big Bang it should look more like a ball and not a sheet of paper
The term “flat” is not the right word but it is the best we have. We can say that a line is straight and a plane is flat but we do not have a similar term for a volume. So we use the term “flat” even though we add a dimension.
When we look out in space at distant stars, galaxies and clusters we do notice that space bends around these massive objects. This creates sort of dimples in spacetime, especially around black holes. But on either ends of these dimples the space seams to be flat. All lines are straight without any curvature to them. This goes on for as far as we can see. There is no noticeable curvature or any shape to the Universe.
The “probably” part is a slight safe guarding. Our measurements are not perfect, although they are extremely accurate. So there is still a possibility that the Universe is actually an extremely large 4D globe and that we just do not see far enough to measure the curvature.
It’s rather easy to conceptualize “flatness” in 2D. You can visually see the difference between a flat piece of paper and a ball. But we can see that because when something 2D is curved, it curves *through* 3D space, and since we exist in 3D space, we can see the curvature.
If, however, we were 2D being living on the surface of those 2D objects, how could we tell if we were living on the paper vs the ball? Remember, that all lines of sight follow along the surface as well; they given no evidence that they are curving through 3D.
The answer is: triangles.
On a flat plane, the angles of triangles always sum to 180, but on a sphere they are greater than 180. So you could construct a triangle, measure its sides and angles and determine whether you are on a flat or curved 2D surface, all using methods available to you as a being constrained to that dimension.
The concept of curvature also applies to 3D, but since we’re 3D beings living in a 3D world, it’s hard to conceive how this might manifest itself. If our 3D world is curved, it would have to be curving through a 4th spatial dimension which we have no access to.
But we have access to triangles.
By picking out distant stellar objects, we can use them to construct imaginary triangles in space, measure their angles, and try to determine if our space is flat or not.
So far, all measurements imply that our universe is flat within a certain margin of error.
A piece of paper is a flat 2D thing. If you were a 2D creature living on the paper, you would be able to move left/right and up/down, but you’d be stuck on the piece of paper.
A ball is a 3D thing. The *surface* of the ball, however, is a 2D surface that has been *curved* through 3D space. If you were a 2D creature living on the surface of the ball, you’d be able to move left/right and up/down, but you’d be stuck on the surface of the ball. If that ball was really really big, it would be really hard for you to tell whether you were on a flat piece of paper or on the surface of a ball.
It’s the same for the universe, but one dimension higher. Our 3D space might be “curved” in 4 dimensions, it might not. Our best measurements suggest that it isn’t curved, but if the “ball” of the universe is really really big, then it would be really really hard for us to measure that curvature, so the possibility is there.
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