Problems understanding how universe has no center.

[jman]

I've already googled this question, and its not making sense to me. They keep trying to describe the universe as 4d, but the universe has 3 spatial dimensions that we live in, so how can it not be like a 3d expanding ball?? They use the surface of a 3d balloon as an analogy, but universe is 3D, no 4D. They are making it sound like the universe is 4d.

Also, why can't we visualize 4d objects? If we lived in a 2d universe, we could look at a screen and visualize a 3d universe.

 

[phinds]

I've already googled this question, and its not making sense to me. They keep trying to describe the universe as 4d, but the universe has 3 spatial dimensions that we live in, so how can it not be like a 3d expanding ball?? They use the surface of a 3d balloon as an analogy, but universe is 3D, no 4D. They are making it sound like the universe is 4d.

Also, why can't we visualize 4d objects? If we lived in a 2d universe, we could look at a screen and visualize a 3d universe.

I suggest the link in my signature

 

[Bandersnatch]

Hi jman, welcome to PF!

It is quite impossible to imagine a 3d curved space, as this would require to visualise a four dimensional object.
But, if we scale things back one dimension, we can rather intuitively visualise a 2d space(this is a surface) curved in the third dimension. This is what the balloon analogy is about. The 2d surface(and only the surface!) of the balloon is the analogy of the 3d space we live in. The inhabitants and all the objects on the surface have no concept of the 3rd dimension, no height, can't jump etc. The third dimension of the balloon has got nothing to do with the reality of the 2d surface. It's only there to help us, three-dimensional beigns, see that a space can in general be curved, without edge but finite, and expanding without centre of expansion - for the 2d surface of the balloon has no centre!

Furthermore, while it helps us visualise the curvature and expansion of 2d space, mathematically there is no need to embed the 2d surface in 3d space for it to have curvature. Third dimension may just as well not exist in the 2d universe that looks like the suface of the balloon, just as 4th spatial dimension is not necessary for our 3d universe to be expanding and show curvature.

For more discussion about the subject head to the cosmology section, esp. the FAQs and the "Balloon analogy" sticky thread.

 

[jman]

Hi jman, welcome to PF!

It is quite impossible to imagine a 3d curved space, as this would require to visualise a four dimensional object.
But, if we scale things back one dimension, we can rather intuitively visualise a 2d space(this is a surface) curved in the third dimension. This is what the balloon analogy is about. The 2d surface(and only the surface!) of the balloon is the analogy of the 3d space we live in. The inhabitants and all the objects on the surface have no concept of the 3rd dimension, no height, can't jump etc. The third dimension of the balloon has got nothing to do with the reality of the 2d surface. It's only there to help us, three-dimensional beigns, see that a space can in general be curved, without edge but finite, and expanding without centre of expansion - for the 2d surface of the balloon has no centre!

Furthermore, while it helps us visualise the curvature and expansion of 2d space, mathematically there is no need to embed the 2d surface in 3d space for it to have curvature. Third dimension may just as well not exist in the 2d universe that looks like the suface of the balloon, just as 4th spatial dimension is not necessary for our 3d universe to be expanding and show curvature.

For more discussion about the subject head to the cosmology section, esp. the FAQs and the "Balloon analogy" sticky thread.

To be clear, I do understand the balloon analogy. What I don't understand is why we even have to use an analogy, because space is 3D, and therefore within the real of us being able to recreate and visualize it. My point is that our universe is 3D, so we shouldn't need an analogy to understand how it is expanding. Just like our Earth is 3D, we don't need a balloon analogy to understand what things would be like if it was expanding. This is where my confusion is.

 

[Bandersnatch]

Sure, you can imagine a 3d space expanding in 3d. All you need to get that there is no centre to it is to imagine it being infinite.
But you can't imagine a 3d space being curved in the fourth dimension(I think!). This is what the balloon analogy adresses. It shows how a curved space can produce expansion with no centre also when the universe is finite.

The usual problem with the analogy is that people see the balloon as a 3d construct, and they focus on the centre of this 3d construct, thinking it must represent the centre of the universe.

 

[jman]

OK. So we can't picture it because our 3d space is curved into 4d. So we can't picture the 4d curvature then? But how is it possible that there is even a 4d curvature, given that there are only 3 space dimensions. How can something curve into a dimension that doesn't exist in this 3D universe?

 

[phinds]

OK. So we can't picture it because our 3d space is curved into 4d. So we can't picture the 4d curvature then? But how is it possible that there is even a 4d curvature, given that there are only 3 space dimensions. How can something curve into a dimension that doesn't exist in this 3D universe?

The curvature is not in space, it is in space-time.

 

[jman]

The curvature is not in space, it is in space-time.

Ok. So how does space time curve to 4d in a 3d universe?

 

[Chronos]

It is customary to view time as the 4th dimension. Its awkward and confusing, but, makes sense once you get used to it. To precisely locate a particle in the universe you need xyz coordinates and a time. You might be tempted to ask 'what xyz coordinates?', insinuating there is no absolute reference frame for any such coordinate system. In that case, you are hopelessly dense, just like all the other humans. The usual practice is to use 3 points in space to define one axis [pulsars have been suggested]. Unfortunately, you need another 3 to define a y-axis and another 3 to establish a z axis. Some of the original pulsars used to establish the x-axis can be reused, but, in no case can you get by with fewer than about 7 reference points [pulsars] to unambiguously locate a point in space, along with time. Further confounding the issue is nothing in the universe is truly at rest so all your carefully chosen cardinal points become instantly obsolete.

 

[phinds]

Ok. So how does space time curve to 4d in a 3d universe?

Not saying that Chronos is wrong in any way but seems to me he's overcomplicating the answer to your question which is, I think, "because space-time is a 4D construct".

Google "gravitational lensing" for some discussion. Light follows a space-time geodesic (the equivalent of a straight line) but because space-time is curved, we see the line as curved in space.

 

[jman]

I understand that time is the 4th dimension. I was under the impression that we were just discussing the space dimensions, as I was describing space as 3D. Additionally, post #3 was referring to just the space dimensions, so that's what our convo and my response was based off of.

All this pointless nit picking doesn't answer my OP, which is how a 3 SPACE dimensional universe cannot have a center. And how can a 4 Space dimensional comparason even be made when the universe has 3 space dimensions.

 

[julcab12]

how a 3 SPACE dimensional universe cannot have a center. .

Let's just say you'll never get there. If you insist. Depends on the frame of reference. In your case(universe). Considering a) The observable universe is just the region of space visible from earth. When you look into the night sky. YOU represent the unique point(center) as an average factored by their distances from a reference point(OB universe). Or anyone of us can be center of our OWN observable universe.^^

Anyways. Here's better one found at Cosmology FAQ: https://www.physicsforums.com/showthread.php?t=506991

"Since realistic cosmological models are homogeneous, every point in space has the same properties as every other point, and therefore the models don't have a center".

 

[Ibix]

To be clear, I do understand the balloon analogy. What I don't understand is why we even have to use an analogy, because space is 3D, and therefore within the real of us being able to recreate and visualize it. My point is that our universe is 3D, so we shouldn't need an analogy to understand how it is expanding. Just like our Earth is 3D, we don't need a balloon analogy to understand what things would be like if it was expanding. This is where my confusion is.

The Earth is not a 3d object, of course. It existed in the past and will exist in the future, so is a 4d object. I challenge you to make a model of the Earth expanding and fit it into three dimensions.

Really, you have two options to approximate answering that challenge. One is to take a slice through the equator every second and build a stack of the slices. The end result looks like a cone. The other option is an animation.

For cosmology, the first option becomes the balloon analogy. The second isn't possible because you can't embed a closed 3d object (a spacelike slice through the universe) into another 3d space for the same reason that you can't make a piece of paper into a sphere and a flat piece of paper wthout making two objects.

 

[Bandersnatch]

First of all, I have to include a disclaimer that I barely understand the maths involved.

Having said that, I think including the time dimension in the discussion is not going to help much here. When talking about the shape of the universe we do not usually include the time dimension. What interests us is the spatial section of the 4d space-time.

This 3d section does have properties that could be visualised by making it curved in another spatial dimension, so that it becomes analogous with 2d surface of a sphere being curved in the third dimension to produce the venerable balloon.

But just as with the balloon, this extra dimension does not represent time, or anything "real" for that matter. It's just a tool to help "see" the curvature.

Of course, just as with balloon's 2-manifold, the 3-manifold of our space does not require actual extra dimension to be embedded in. It can have all the properties of curved space by itself. For example, parallel lines will eventually converge and the sum of angles in a triangle adds up to more than 180°.

 

[Chronos]

If you look out into the universe in any direction, the last thing you see is the CMB photons. They are the oldest thing you can see in the observable universe, having been freed from their plasma prison when the universe was about 380,000 years old. Does that make it an 'edge', so to speak, of the universe? It seems logical to assume anything that has a center must have some kind of edge. If you treat the CMB as an edge, you will realize you just happen to be smack dab in the center of the universe. That may seem curious until you realize this is true no matter where you are in the universe. Let's say you hopped aboard a transporter and beamed to the Andromeda galaxy. Aside from the niggling detail the journey will take 3 million years, you will once again find the CMB photons were all emitted when the universe was 380,000 years old and you are again in the center of the universe. It is clear the CMB makes a lousy 'edge'. Trying to locate the center of the universe is the same thing as trying to locate the center of yesterday. The question is meaningless because you are mixing apples with oranges. The universe is bounded by time, not by some arbitrary spatial dimension.