Flat Stanley | by Brian Koberlein



17 August 2014

One of many issues we frequently say concerning the universe is that it’s “flat.” After all this often raises the query about what that really means. How can area be flat? Certain, a floor comparable to a desk will be flat, however area?

A simple square.
Brian Koberlein
A easy sq..

It seems that the 2 are considerably associated. For those who have a look at the floor of a desk, it’s fairly straightforward to see that it’s flat, at the least in a primary sense. However what when you have been a flat creature dwelling on the desk’s floor? How would you establish that it’s flat? One factor you may do is to mark a place to begin, then go ahead for a set distance, flip 90 levels, go the identical distance, flip one other 90 levels, similar distance once more, a ultimate 90 levels, after which the identical distance. What you’d discover is that you just’ve traced out a sq. to reach at your start line.

A triangle on the Earth can have 3 right angles.
Andrew Steele
A triangle on the Earth can have 3 proper angles.

Suppose you probably did the identical factor on the Earth (treating it like a sphere for a second). You might stroll alongside the equator for 1 / 4 of the Earth’s circumference, flip 90 levels and stroll north till you attain the north pole, then flip 90 levels and stroll straight to return to the equator. Once more, you come back to your start line, however on this case it solely took two turns, not three. That’s as a result of the floor of the Earth just isn’t flat.

Extra usually, we will do an identical factor with triangles. Any three factors on a flat floor will be related to kind a triangle, and the angles of a flat triangle will all the time add to 180 levels. If a floor is curved, such because the floor of the Earth, then the angles will add to greater than (positively curved) or lower than (negatively curved) 180 levels. What makes this handy is that it isn’t restricted to surfaces. Any three factors in area will be related to kind a triangle, and if area is “flat” then the angles will add to 180 levels. In precept we may use three laser-bearing spacecraft to find out the native flatness of area.

We could use lasers to determine flat space.
We may use lasers to find out flat area.

Given all that, how do we all know the universe as a complete is flat? A method is to take a look at the distribution of galaxies within the universe. One precept of cosmology is that on massive sufficient scales the universe is homogeneous and isotropic. In different phrases, galaxies are distributed pretty evenly, and the universe seems just about the identical in all instructions. That isn’t true on the dimensions of galaxy clusters, however on a cosmic scale throughout billions of sunshine years it appears to be true. If the universe wasn’t flat, then the sunshine from distant galaxies can be distorted just like gravitational lensing, however on a cosmic scale. We don’t see such an impact, so it appears the universe is flat. A extra exact check of cosmic flatness makes use of the cosmic microwave background (CMB). From fluctuations within the CMB we will decide each the Hubble fixed of the universe and the mass density. From these we will calculate the flatness of the universe. What we discover is that to the bounds of statement, the universe seems to be flat.

Though we all know with excessive certainty that the universe is flat (or very, very near flat), we nonetheless aren’t positive why it’s flat. It’s typically known as the flatness downside, and it stays an unsolved thriller in cosmology.

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