# According to WMAP the Universe is flat but....?

....but what do they actually mean with the word "Flat"? The observable universe is clearly a sphere. It stretches in all directions about 46.5 billion light years. But if we move on to a bigger scale, what does a flat universe mean? That is has the shape of a paper without edges? And what would happen, since it is 'flat' if go UP or DOWN (endlessly)?

Personally I don't believe the universe is flat, I believe it's infinite, but with 'space' detached from it, and space itself being limited.

### 13 Answers

- vorenhutzLv 71 month agoFavorite Answer
Flat means no curvature. A piece of paper is flat in 2 dimensions, whereas the surface of a sphere is curved in 2 dimensions. When the universe is said to be flat, it means flat in 3 dimensions. Hard to picture perhaps, but not hard to construct a mathematical model of (relatively speaking).

- daniel gLv 71 month ago
It is flat only because that is how WMAP detects and sees it.

There is CMBR from every point direction known.

Earth is spheroid, 3 dimentional, but maps of it are flat, 2 dimentional.

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- RaymondLv 71 month ago
Flat in this context refers to geometry and to the rules of trigonometry that apply.

For example, in 2D, if you consider the face of a flat sheet of paper, and you draw a triangle on it, the sum of the three angles will be exactly 180 degrees. This will be true whether you draw a small triangle and a large triangle.

There is an equivalent to this rule in higher dimensions. For example, in 3D, we could measure the solid angles at the corners of a tetrahedron (a "pyramid" made of 4 equilateral triangles, for example).

However, being "flat" in that sense is NOT a guarantee of infinity.

For example, take a cylinder. A triangle drawn on the surface of its curved side will still see its angles add up to 180 degrees. In geometry, the surface of a cylinder is a "flat" figure.

A triangle drawn on the surface of a sphere will see its angles add to to more than 180 degrees. How much more? Depends on the surface of the triangle compared to the total surface of the sphere.

Look at a globe. Start from the North Pole and go straight down along the Prime Meridian (longitude 0, going through Greenwich). Stop at the equator. That is the first side of a triangle.

Turn right 90 degrees. You are now going along the equator (going west). Do that until you reach longitude 90 W. That is the second side of the triangle.

Turn right 90 degrees (again) and go north until you reach the North pole. Third side. There, the end of your third side will meet the start of the first side at a angle of 90 degrees (the difference in longitudes).

Three angles of 90 degrees each.

Sum of angles = 270 (not 180) => the Earth's surface is not "flat".

The "spherical excess" is 270 - 180 = 90 degrees, therefore that triangle covers 1/8 of the total surface.

If you are measuring a tiny garden in your backyard, you will not be able to measure the excess and the land will appear "flat" to you. You need a sufficiently large area for it to show up.

The experiment on WMAP was designed to measure this "excess" over the size of the Observable Universe (we know the "whole universe" is bigger than what we can see). The excess kept coming up as zero.

The universe is "flat".

--This COULD mean the universe is infinite in 3-D. Just like the Cartesian plane (the x-y plane) is infinite in in 2-D

--This could mean that the universe is finite but folded around a higher-dimension "multi-verse" in a way that retains its flatness. Just like the flat piece of paper rolled up to form a cylinder, for example. (in 3-D geometry, there are more complicated arrangements that could work)

--This could mean that the Observable Universe is a very small portion of the whole universe. Just like your backyard garden is a very small portion of Earth's surface.

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- 1 month ago
The word "flat" doesn't mean 2 dimensional, like a sheet of paper. Flat means not-curved. The geometry of 3 dimensional space follows Euclid's postulates. (Like the sum of angles of a triangle is 180 degrees.)

If space is flat, it is infinite. It goes on forever in all directions, up, down, left, right, backward, forward.

If space has positive curvature, it is finite but unbounded. It is the 3 dimensional surface of a 4 dimensional hypersphere.

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- az_lenderLv 71 month ago
"Flat" doesn't mean it's not infinite. Indeed, "flat" means it IS infinite … in contrast to something that curves back on itself. That is, if you could go far enough forward, would you bump into the back of your own head? In a "flat" universal geometry, the answer is no. The "flat" universe simply behaves well, as Euclid would postulate. The parallel lines never meet.

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- Ronald 7Lv 71 month ago
You kind of answered your own Question there

Consider the WMAP Image to be like a normal Map

So sign of Earth being a Globe, simply a reference in 2 D

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- DixonLv 71 month ago
They mean its type of geometry is flat. Which is basically saying that three dimensional space works exactly like you would naively imagine, rather than curving into another spatial dimension.

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- nebLv 71 month ago
When they the universe is flat, they mean it is spatially Euclidean, meaning that it is INTRINSICALLY flat. For instance, a flat piece of paper is Euclidean flat since the geometry intrinsic to the piece of paper is Euclidean - internal angles of triangles add to 180 degrees, the area of a circle is πr², etc.

If you were roll that piece of paper up into a cylinder, it’s intrinsic geometry is STILL Euclidean since the intrinsic geometry is still flat. However, it’s EXTRINSIC geometry is not Euclidean which is pretty obvious as seen from the perspective of an embedding space.

General relativity deals with intrinsic geometry. The Riemann curvature tensor is measure of that curvature. If the spatial components of the Riemann tensor are zero, the space has 0 curvature - it is intrinsically ‘flat’ which is just a common way of saying it has zero curvature regardless of the number of dimensions. General relativity is agnostic about extrinsic curvature.

WMAP detected zero curvature with a .4% accuracy although there have been recent studies that challenge that.

If the universe is spatially Euclidean, general relativity says the universe must be infinite IF it has what is called a simply connected topology. This basically means that you can draw a closed loop around any point in the universe, and under continuous deformation of that loop, contract it to a point.

However, IF it is not simply connected, meaning that there are points or regions where you cannot continuously contract a closed loop to a point, then the universe can be intrinsically flat but also still be finite (its extrinsic structure would not be Euclidean). The standard example is a 3-torus (the surface of the torus is 3 dimensional) which is intrinsically Euclidean but can be finite.

Hope this helps ....

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- Tom SLv 71 month ago
This issue is far from being resolved. See link for a fairly recent article regarding the topic.

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Yes I think so. It's a bit like we say the Earth is spherical, but we know there are mountains, etc