# Why is the observable universe flat?

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Okay, so I couldn't understand why the universe is flat after the big bang theory. Because obviously it should be shaped like a ball.

So I did good old fashion googling and found that the answer is: "Technically we only know  the observable universe is flat."

But why is the observable universe flat?

I mean, we can see for 46.6 billion lightyears in either direction of the XY coordinates.

Why can't we look "up" figuratively, and see for another 46.6 billion lightyears?

If we only know the observable universe is flat, wouldn't it be pretty easy to look up and figure out really quickly that it expands just as far up and down as it goes sideways?

Please don't say that flat is relative. I understand the universe is not 100% flat, that it's 3D, but over 46.6 billion lightyears I'd expect slightly more "roundness" to it. It's relatively flat in comparison of width to height. Why?

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It doesn't mean flat like a pancake. It means flat as in "not curved" or described by Euclidean geometry.

If we reduce it to two dimensions, if the universe were like the surface of a sphere, then it would be curved. The angles of a (large enough) triangle would not add up to 180º, there could be zero or multiple parallel lines that go through a single point, and so on. If this 2D universe were like a sheet of paper (or the surface of a torus) then it would be geometrically flat and Euclidean. Now just imaging a 4D hyper-torus...

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Posted (edited)
3 minutes ago, Strange said:

It doesn't mean flat like a pancake. It means flat as in "not curved" or described by Euclidean geometry.

If we reduce it to two dimensions, if the universe were like the surface of a sphere, then it would be curved. The angles of a (large enough) triangle would not add up to 180º, there could be zero or multiple parallel lines that go through a single point, and so on. If this 2D universe were like a sheet of paper (or the surface of a torus) then it would be geometrically flat and Euclidean. Now just imaging a 4D hyper-torus...

Okay.

In this sense, why is the observable universe shaped like a rectangle rather than a sphere?

Edited by Raider5678

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2 minutes ago, Raider5678 said:

Okay.

In this sense, why is the observable universe shaped like a rectangle rather than a sphere?

Nooooo....!!!

My fault, I guess. I didn't use a piece of paper as the analogy because it is square -- if it is a 2D analogy to the observable universe, then it would be circular. It is the flatness (contrasted with say a spherical or hyperbolic surface) that is important. The piece of paper remains geometrically flat even if you roll it into a cylinder. Or even a torus.

Note that, when we think of the surface of a sphere as a curved surface, we are seeing the 2D surface in a 3D space. In the case of the (3D) universe) if it were curved it would not require an extra dimension. The curvature is what is known as "intrinsic". (Which is almost impossible to get your head round - excuse the pun.)

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Posted (edited)

So if you were to stand anywhere on earth, from the equator to the south pole, etc. And shine an infinitely powerful laser that would get through the atmosphere without any disruption, and go infinitely, ignoring gravitational curvature, would all the lasers keep expanding into the observable universe?

As in all three dimensions, XYZ?

Because I feel like thinking of the universe as a surface doesn't really work.

The big bang caused the universe to expand from a single point, why would there be a "surface"?

OR

Does the curvature of 4D space only make the universe look flat? In which case could you explain.

Because I clearly have no idea what I'm talking about.

OR

Are you saying that the big bang happened.

All the matter in the big bang expanded FROM that single point, but it went away from the original spot. Meaning there's no matter at the big bang.

As it kept expanding farther and farther away, there was a sphere of matter expanding away from it. However, the two sides of the sphere are separated by a massive expanse of emptiness, because of the big bang.

And we can't see if the observable universe is curved because we can't detect the curvature simply because of how large it is.

Is this right?

Edited by Raider5678

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29 minutes ago, Raider5678 said:

So if you were to stand anywhere on earth, from the equator to the south pole, etc. And shine an infinitely powerful laser that would get through the atmosphere without any disruption, and go infinitely, ignoring gravitational curvature, would all the lasers keep expanding into the observable universe?

As in all three dimensions, XYZ?

Because I feel like thinking of the universe as a surface doesn't really work.

Pick any plane. Its geometry will be flat rather than curved.

edit: this is an example of looking at 2D rather than 3D because we don't have examples of 3D objects in curved space, making that hard to picture — we don't have a fourth spatial dimension available to use in our imagination. (see also: the rubber sheet analogy)

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When you were googling you should have found out that the universe is locally flat.

This is a mathematical requirement of continuity which means there are no tears or gaps in it,

As in a wiggly line that you can draw without taking your pen from the paper.

It is this property that allows us to move from on point to the next.

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4 minutes ago, swansont said:

Pick any plane. Its geometry will be flat rather than curved.

But what will happen to the lasers?

How far will they go before they reach the end of the observable universe?

Will they all travel an equal distance?

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2 minutes ago, Raider5678 said:

But what will happen to the lasers?

How far will they go before they reach the end of the observable universe?

Will they all travel an equal distance?

That's an issue of expansion — what the radius of the observable universe will be in the future. But it should be the same in all directions.

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What is the locally flat part then?

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Here are some more thorough explanations of what is meant by flatness

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Posted (edited)
16 minutes ago, Raider5678 said:

What is the locally flat part then?

Take Strange's example of a sphere.

Pick any point on that sphere.

Draw in a disk of tangents to the sphere at that point.

(you do understand that there are an infinite number of tangents running radially round the disk don't you ?)

If we now consider a sphere point an infinitesimal distance away from our base point the difference between the sphere point and the disk point is infinitesimal or the difference is effectively non existent.

That disk can be extended to infinity in all directions, defining one of Swansont' planes.
As you move further and further away from the sphere along the plane, the difference between the sphere and the plane becomes larger and larger.

That is what is meant by locally flat.

In terms of the Earth, surveyors usually use what is known as 'flat Earth theory' for a disk of radius less than 10 kilometers.

This means that they can use plane trigonometry and straight lines to measure things to better than one second of arc and one tenth of one millimetre of distance.

Edited by studiot

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Just now, studiot said:

Take Strange's example of a sphere.

Pick any point on that sphere.

Draw in a disk of tangents to the sphere at that point.

(you do understand that there are an infinite number of tangents running radially round the disk don't you ?)

If we now consider a sphere point an infinitesimal distance away from our base point the difference between the sphere point and the disk point is infinitesimal or the difference is effectively non existent.

That disk can be extended to infinity in all directions, defining one of Swansont' planes.
As you move further and further away from the sphere along the plane, the difference between the sphere and the plane becomes larger and larger.

That is what is meant by locally flat.

In terms of the Earth, surveyors usually use what is known as 'flat Earth theory' for a disk of radius less than 10 kilometers.

This emans that they can use plane trigonometry and straight lines to measure things to better than one second of arc and one tenth of one millimetre of distance.

Alright.

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We use a 2D analogy because we cannot picture curvature in 3D space, let alone 4D space-time.

Imagine a beach ball. If you look at any point on its surface, you see curvature, because you are looking at it from a third dimension.
If, on the other hand, you were an ant on the surface of the beach ball, you might not see the curvature as you only see the 'locally' flat area you are standing on, and an Ant Einstein would need to come along and notice that the metric has a slight curvature, and you live in fact on a spherical surface.

Now imagine that beach ball has been expanding, so that all points on it are becoming increasingly separated. We attempt to measure the curvature of the beach ball, and find that even after 14 bill yrs, it is almost perfectly flat. And this is puzzling until an Ant Guth comes along with an idea, that shortly after T=0, a universal false energy level caused an exponential inflation which violently expanded the universe by many orders of magnitude. This had the effect of 'smoothing' it out, and neatly solved many other observational problems.

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Posted (edited)

Yeah, I really can't understand any of this.

Basically, the universe is not flat it's curved, and we just can't see it, measure it, test it, or prove it.

Additionally, that's not what I was wondering.

You guy's have proven that two parallel lines will not stay parallel. At least according to the second link swansnot gave me.

Why are there not galaxies and stars in every direction, instead of simply sideways?

Edited by Raider5678

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11 minutes ago, Raider5678 said:

Yeah, I really can't understand any of this.

Basically, the universe is not flat it's curved, and we just can't see it, measure it, test it, or prove it.

Additionally, that's not what I was wondering.

You guy's have proven that two parallel lines will not stay parallel. At least according to the second link swansnot gave me.

1

Maybe your confusion stems from the concept that the big bang was an explosion.

16 minutes ago, Raider5678 said:

Why are there not galaxies and stars in every direction, instead of simply sideways?

What makes you think sideways is a direction? Or that stars and galaxies don't exist in every sideway direction?

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That's funny, I could have sworn there ARE galaxies in every direction.

Can you imagine curvature in every direction ?
It can be done mathematically, but you cannot 'picture' it in your head.
So we reduce the problem to two dimensions for tractability.
That does not mean galaxies lie in a plane !!!

The observable universe is, by all measurements, very nearly flat, so the larger universe is even more so.
So it would take more than 100 bill yrs ( grater than the extent of the observable universe ) for the two light beams to converge.

I suspect you problem lies with your understanding ( or lack of ) of geometry.
Nothing that a little studying won't fix.
Try a book called Flatland ( I believe Gutenberg has it available as a free download ) for an example of how 2D reduction can give insights into 3D geometry.

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31 minutes ago, Raider5678 said:

Yeah, I really can't understand any of this.

Basically, the universe is not flat it's curved, and we just can't see it, measure it, test it, or prove it.

No, the links I gave say it's flat and show how this was demonstrated.

"If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today. But they're not. To best of its ability, ESA's Planck space telescope, can't detect any distortion at all. The universe is flat."

31 minutes ago, Raider5678 said:

Additionally, that's not what I was wondering.

You guy's have proven that two parallel lines will not stay parallel. At least according to the second link swansnot gave me.

Nope, that's not what it says.

What it does say is "We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense."

31 minutes ago, Raider5678 said:

Why are there not galaxies and stars in every direction, instead of simply sideways?

There are.

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13 minutes ago, dimreepr said:

Maybe your confusion stems from the concept that the big bang was an explosion.

What makes you think sideways is a direction? Or that stars and galaxies don't exist in every sideway direction?

Perhaps.

I think of 3D space as directions in XYZ. I'm fairly certain this is correct because nobody disagrees.

The big bang was a rapid expansion of something we don't know. I assumed that matter would expand evenly in every direction of XYZ.

So up, down, left, right, forward, and backward. Yet those are all respective.

My thoughts are that the universe is a lot like the bottom one. Not that it'd 2D, but that it's flat in the sense of 3D. It has height, but the height is smaller than the width.

If the universe expanded from a single point, I thought the universe should look like the top one, where matter is spread evenly from the central point in all directions. Hence, big bang = spherical distribution of matter.

The solar system, for the most part, lies on a plane. Other then asteroids orbiting the sun at odd inclinations, all of the planets inclinations are less than 4 degrees. Which I consider flat(ish).

While it's 3d, most of the matter is spread in a flat(ish) manner.

The milky way is the same, at 100,000 light-years wide, and 1,000 lightyears thick.

Somewhere along the way, I got the notion that the universe is the same way.

I was mistaken.

1 minute ago, swansont said:

Nope, that's not what it says.

What it does say is "We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense."

1

I thought it meant: "We SAY that the universe is flat, and this means that parallel lines will always remain parallel."

But just because we SAY it doesn't mean it's true.

I thought the whole point of this link was that the universe is not flat?

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Angular momentum is a local phenomenon.

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56 minutes ago, Raider5678 said:

I thought it meant: "We SAY that the universe is flat, and this means that parallel lines will always remain parallel."

But just because we SAY it doesn't mean it's true.

I thought the whole point of this link was that the universe is not flat?

No, it's "We say the universe is flat, because that's what the evidence shows. Here's what that bit of jargon means"

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Maybe you didn't notice...

The three pictures you posted of positive, negative, and no curvature ( flat ) are all 2D surfaces, as they only have two co-ordinates.
They are reduced dimensionality analogues of 3D space, because you cannot show these curvatures in 3d.

Or would you like to try and draw a positively curved 3D volume ?

Stop confusing the model ( 2D representation ) with the reality ( 3D volume )

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22 minutes ago, MigL said:

Maybe you didn't notice...

The three pictures you posted of positive, negative, and no curvature ( flat ) are all 2D surfaces, as they only have two co-ordinates.
They are reduced dimensionality analogues of 3D space, because you cannot show these curvatures in 3d.

Or would you like to try and draw a positively curved 3D volume ?

Stop confusing the model ( 2D representation ) with the reality ( 3D volume )

All surfaces are 2D,  by definition.

They can be embedded in any number of dimensions of 2 or greater.

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What I've understood so far from Raider's comments, is that he's under the impression that 'flat', in reference to the universe, implies that it is planar.
That we only see galaxies along the plane, and since the plane has limited thickness, we see none in the third direction.

I, and others, have been trying,  unsuccessfully it seems, to convince him that is not the case, and that 'flat', in 3D, is NOT planar or a surface.

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On 1/2/2018 at 12:36 PM, Raider5678 said:

On 1/2/2018 at 6:35 PM, MigL said:

I, and others, have been trying,  unsuccessfully it seems, to convince him that is not the case, and that 'flat', in 3D, is NOT planar or a surface.

1

I was mistaken.