what does ‘the universe is flat’ mean? How can it be flat when there are stars, planets, galaxies etc. everywhere we look?
In: 0
[deleted]
It means the universe doesn’t curve, so parallel lines remain parallel.
It’s a flat, three dimensional infinity.
The alternative is that it does have a fourth-dimensional curvature, and parallel lines either intersect or veer away from one another. If that is the case, it may form a finite hypersphere rather than being infinite.
The observable universe is a different matter entirely, that’s a three dimensional sphere simply due to the finite speed of light.
[deleted]
According to the Theory of Relativity, it’s possible for spacetime to have an intrinsic curve. One way to think of it is even if you travel in what appears to be a completely straight line to you, for an outside observer it would appear that you were travelling a curved path.
A sort of analogy would be how we generally view the Earth. Ignore the oceans and topography for a second, and imagine walking directly forwards across the entire Earth. From your perspective you’re walking in a straight line , but in reality you’re walking a big circle around the planet. The Earth has a curvature, even if it’s slight enough that at our human scale on the surface, we don’t notice it. But you still follow it when you travel across the planet.
The universe could potentially be kind of like that, with an intrinsic curve to spacetime that we don’t notice locally. According to careful studies of various cosmological data (most notably the Cosmic Microwave Background), we can put some limits on the amount of curvature to spacetime, and at least as far as our instruments can see, the universe seems to be flat or at least very close to flat. We can’t really see any noticeable curvature. That doesn’t mean for sure that’s it’s flat, but if our spacetime is intrinsically curved, the curve is extremely gradual.
“Flat” means that on the largest scale there’s no meaningful curvature of space-time, which means the angles of a giant triangle add up to 180 degrees and parallel lines always stay parallel.
You probably know about the Pythagorean theorem which says that if you measure out a triangle you get s^2 = x^2 + y^2. This only works on a flat surface, so if I draw a triangle on a sphere it doesn’t work out that way.
The 3D version of this is s^2 = x^2 + y^2 +z^2. When they say the universe is “flat” they mean this equation holds true.
Think of the surface of a sphere, and walking on it. No matter what direction you choose, upon walking far enough you will always return to your starting position, if you continue on in a straight line. This is known as *spherical geometry*, and we say that a surface with this geometry has a *positive* curvature.
There is also *negative* curvature, this is known as *hyperbolic geometry*. It is somewhat harder to explain, but it is often depicted as a sort of ‘saddle-shape’
And finally, there is *zero* curvature, or *euclidean* geometry. Euclidean geometry acts how you’d expect things to act; parallel lines do not diverge (like in hyperbolic geometry) or converge and eventually cross (like in spherical geometry), the interior angles of triangles add up to 180 degrees (which is not so in spherical and hyperbolic geometries), etc.
Now it’s important to distinguish two types of curvature, *local curvature* (which varies place to place) and *global curvature* (which is the same everywhere)
So far as we can tell, our global curvature is zero, or very close to zero.
So the universe ‘being flat’ is not so much a statement about its shape and more a statement of its curvature, or lack thereof
Flat in this case does not meant flat as in 2 dimensional, it means space is not “curved.” In other words’ it obeys Euclidean geometry, which is the geometry we’re all familiar with where parallel lines never meet and the sum of the angles in a triangle is always 180 degrees. In curved geometry, parallel lines *will* meet and the sum of the angles in a triangle will not necessarily be 180 degrees.
I think of it like a thick pane of glass. All the architecture is within. Closed off by a force greater than themselves.
Latest Answers