how can scientists say the universe is flat, when it seems to go in all directions?
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In curved space, Euclidean geometry doesn’t apply. Two parallel lines don’t remain parallel. If you travel far enough you may come back to where you started. If you take three 90 degree turns to the right, you may not make a rectangle.
In flat space, Euclidean geometry works. Parallel lines never meet. You can travel forever without coming back to where you started. And if you make three 90 degree turns to the right, you will form a rectangle.
Flat space is not two-dimensional, though. That may be the source of your confusion. Flat space is just Euclidean space — except where an object like a star or black hole creates a slight curve. But those are just small bumps in space. Even the most massive objects in space are small compared to the universe.
“Flat” doesn’t mean “two-dimensional,” it means “not curved.” That is to say, the rules of Euclidean geometry apply to the universe: parallel lines remain parallel forever, the angles of a triangle add up to 180º, you can travel in a straight line forever and not loop back around to where you started, etc. A three dimensional space can be flat or curved in the same way that a two-dimensional surface can be flat or curved: a sheet of paper obeys the aforementioned laws, whereas the surface of a sphere does not. On the curved surface of a sphere, triangles add up to more than 180º, parallel lines eventually intersect, and traveling far enough in a straight line will return you to your starting point. These same principles could apply to a 3D space that’s curved instead of flat.
When they say the universe is “flat” they mean in a geometric sense.
There’s 3 possible geometries for universe: Closed Curve, Flat and Open Curve. They all possible solutions of Einstein’s field equations. I know this is probably getting too complicated, lets get back to the main topic.
In a “flat” geometry, 2 straight parallel lines will never diverge or intersect, they will be parallel to infinity.
In an “closed” geometry, 2 straight parallel lines will will eventually converge, imagine it drawing parallel lines on a basketball. Though, to be clear not all possible closed geometries are like a sphere.
Now, an “open” geometry is visualized like a saddle shape, 2 straight parallel lines will eventually diverge and never intersect while slowing getting further apart.
Hope that kinda helps…
They don’t mean “flat” in the sense of the universe being a two-dimensional plane. They mean that spacetime doesn’t ordinarily have its own curvature (though massive objects can force some curvature onto around them, as black holes do).
We grow up learning about Euclidean geometry in school: a straight line is the distance between two points, the angles in any triangle add up to 180, only lines with the same slope can be parallel, that sort of thing. Over short distances, this works out closely enough to be extremely useful, and for centuries it was thought to be the only way you could do geometry. This is the “flat space” scientists are talking about: geometry works more or less the same way in space as it does on a flat piece of paper.
But starting in the 19th Century, methematicians started tinkering with other possibilities. If you draw lines on, say, a horse’s saddle, parallel lines can start curving away from each other depending on their location, and there start being more ways for lines to be parallel. If you draw lines on a ball (and add the constraint that lines must pass through the center of the ball, eventually coming back to meet themselves on the other side), then there are *no* ways for lines to be parallel: any two lines must eventually intersect. These two weird geometries are called hyperbolic and elliptical geometry, respectively. They are *non-Euclidean* geometries, because they don’t fit the assumptions Euclid made when he first described the geometry we’re familiar with.
And the thing is, these geometries also work. They don’t work the same way Euclidean geometry does, of course -the rules are different, as are the properties of shapes- but you can find the rules and do things in them like you can in traditional Euclidean geometry. And that led to the question: sure, Euclidean geometry is close enough at small scales, but is that really how it works everywhere, on the scale of the universe as a whole?
We don’t currently know the answer to that. Again, at small scales, Euclid’s close. But let’s say the universe curves out like a saddle. A straight line is no longer the shortest distance between two points in this case, *if* you can figure out a way to jump off the saddle at one point and land on it at another point. Could we perhaps figure out a way to do that? A similar question holds if the universe curves in like a sphere: could we find a way jump *into* the sphere at one point and burrow through it, emerging at the destination having travelled a shorter distance than we were supposed to? Either way could be used to circumvent the speed of light, but only if the universe’s geometry actually works that way. If it’s flat, these shortcuts won’t work. But we don’t know if it’s flat or not.
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“Flat” basically means “the shortest path is a straight line”.
If you look at the shortest path on the Earth’s surface from London to Tokyo, it’s not a straight line, because to be a straight line it would need to go through the Earth itself, not just remain on the surface.
If you look at the universe and ignore weird stuff like black holes and the theory of relativity, then the shortest path between two points is indeed a straight line. That what’s scientists mean by saying “the universe is flat”.
(If you try to account for gravity as understood since Einstein, then the universe is no longer fully flat and the shortest path is not always exactly “the straight line”. There are some well-known examples with a black hole where there are multiple differents shortest paths from one point to another.)
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