There must be a center of the universe....?

[Loren]

Oops. Sorry. Must have misinterpreted that one. It's just that this is a very heated ' discussion', and I got a bit excited. haha

:-)

 

[russ_watters]

I'm not sure if this is already taken care of, but:

But there are other good analogies. For example... (3) Suppose we live in the 'volume' and not the 'surface' of a sphere. If the universe sprang from a singularity at t=0; then our local universe could be a small sphere within the volume of a much larger sphere, which is all expanding outward from the singularity. The same effects of looking in any direction appears that all other galaxies are moving away from ours.

The problem is that that expansion has a very different geometry from the one we observe. The galaxies on one side would have different velocities from the galaxies on the other, which would point us toward the center.

 

[zylon]

Instead of considering the universe, let's just consider the question of shapes and geometry.

In two dimensions: a disc (the area within a circle) has a centre that is part of the disc, but the centre of a circle is not part of the circle. If you were compelled to live on a circle, there would be no centre that you could visit.

In three dimensions, you have the same situation with a solid sphere (the centre is part of the sphere) and a spherical surface (its centre is not part of itself).

In higher dimensions, you have similarly the concept of a hypersurface.

To begin with, you could expand your knowledge of shapes and geometry. Then use this knowledge to understand what people are saying about the universe.

Then the center of the universe is "under" every point in space (since the big bang), the same way that the center of the Earth is "under" every country on earth.
The fourth dimension of space visualized here may not be physically real, but it should clear up the "center of the universe" confusion. Do you agree?
Of course, this would cause us to ask what is outside the aforementioned hypersphere, which would get into the subject of things existing before they are created.

 

[Seeking]

In a 4d space-time, why is the center not the limit as time approaches 0? In this view the center does not exist in the present (not on the surface of the balloon).

 

[Bandersnatch]

the other point that people try to make is that with the balloon analogy it has volume, and the volume has a centre. comparing this to volume in the universe completely missing the abstraction the balloon analogy makes to simplify things - specifically using 2D as a substitute for 3D because people struggle with visualising and understanding 4D representations. in that sense, if the universe was an unbounded 3-sphere then we have a 'hypervolume' inside of it which also very much has a centre in that 'fictional' 4-space - note, that this 4-space is not a minkowski style space-time but a 'fictional' euclidean 4-space, in the same sense that the 3-space the balloon is embedded is not a 2,1 space-time, but euclidean 3-space - or alternatively an extension of the sphere's local coordinate system that replaces intrinsic curvature with extrinsic curvature by embedding the system in a space with higher dimensionality.

The point here is that you don't actually need that hypervolume to have a fully defined geometry of space.
That is, if we're talking in terms of the 2D analogy, you don't have to postulate the existence of the 3rd dimension to describe the geometry of the 2D surface as spherical, toroidal, etc., and without the 3rd dimension there can be no meaningful notion of a centre in the 3rd dimension, or of a volume.

An easy to relate example of how this can be true is the way some video games are made - in particular Asteroids, or similar ones in which a player's avatar can move off a computer screen and reappear from the opposite edge. This is an example of a toroidal geometry of space, and yet the screen remains flat. It is easy to calculate the hypothetical dimensions of the actual 3D torus that would exhibit the same geometry, and talk about its centre(s) of curvature, but those would remain 'virtual', or as you say 'fictional' dimensions, and would not indicate that there exists some actual 3rd dimension to the space displayed on the computer screen.

Similarly, the 3D geometry of our universe may turn out to be that of a hypersphere (but it is not supported by observations so far!), but it doesn't necessitate the existence of a higher, fourth spatial dimension for it to be embedded in. One can talk about radius of the curvature of the universe, but it's a virtual notion, not pointing to an actual centre of a 4D hypersphere.

That's why readers introduced to the balloon analogy are always asked to focus on the 'flatland' of the surface and disregard completely the 3rd dimension. It's not necessary for the analogy to work, and can make the reader leave with an erroneous notion that from the expansion of the universe follows that there must be a fourth spatial dimension.As a side note, and I keep hammering this in but nobody ever seems to care, 'unbounded' has a precise mathematical meaning, and in the context of finiteness of spaces means the same as infinite. So surface of every sphere is always bounded (but has no boundary). There isn't such a thing as an unbounded sphere.

In a 4d space-time, why is the center not the limit as time approaches 0? In this view the center does not exist in the present (not on the surface of the balloon).

Then the center of the universe is "under" every point in space (since the big bang), the same way that the center of the Earth is "under" every country on earth.
The fourth dimension of space visualized here may not be physically real, but it should clear up the "center of the universe" confusion. Do you agree?
Of course, this would cause us to ask what is outside the aforementioned hypersphere, which would get into the subject of things existing before they are created.

These posts propose essentially the same idea - to place the centre of the universe in the fourth spatial dimension.

If we do that, we are postulating that the fourth spatial dimension actually exists, which is unnecessary to describe the geometry and expansion of the universe. Could there exist a fourth dimension in which the universe is embedded? Sure. But when presented with two models, you always need to choose the one with the least assumptions, unless those assumptions are necessary to explain observations. The fourth dimension is unnecessary.

Additionally, and perhaps more importantly, this looking for the centre of the universe in the centre of a hypersphere assumes a priori that hypersphere is the shape of the universe, for which there is no indication. The universe looks flat, and keeps looking flat despite ever improving measurements.
That is, coming back to the balloon analogy, it would be more appropriate to use an infinite rubber sheet as a model that would better represent the shape of the universe as it is known today, but then the analogy would not work so well for its intended purpose, which is not to present the geometry, but how expansion makes everything look like receding away from everything else - no matter the vantage point.

So, again, the analogy always specifically asks to focus on the 2D surface only, and not try to forcefully extract from it any conclusions that it was not meant to convey. Trying to give the centre of the balloon any meaning is one such conclusion.

 

[phinds]

As a side note, and I keep hammering this in but nobody ever seems to care, 'unbounded' has a precise mathematical meaning, and in the context of finiteness of spaces means the same as infinite.

Actually, we got together last year and decided to keep saying it incorrectly just to annoy you (Blame @Drakkith . It was his idea )

 

[Drakkith]

Actually, we got together last year and decided to keep saying it incorrectly just to annoy you (Blame @Drakkith . It was his idea )

I blame everyone but myself.

 

[phinds]

I blame everyone but myself.

Yes, but you always do that so it doesn't count.

 

[Thierry Clicot]

Expansion and recession makes each observable object in the universe seem to be moving away from us, the observer. The resulting conclusion that we are at the center of the universe is therefore unfounded when it is based solely on this visual appearance.

Well, Andromeda (and A LOT of other objects) is blue-shifted and supposedly moving TOWARDS us, so your statement is unfounded at the start.
Also, your statement's conclusion is a non-sequitur--if everything was moving away from us, one could *logically* draw the inference that we ARE at the center of the "universe".

But all of this begs the question of the fact that THERE IS NO OUTSIDE...hence we cannot think of the "Universe" in any anthropomorphic sense. We have ZERO points of reference to envision a space/time construct that just "appears" and is not linked to a locality, and expands/creates more of itself, into space that DIDN'T EXIST beforehand...

Since "infinity" is an abstract that cannot be grasped or understood by 3-4-space beings like ourselves (it's akin to saying "and than a miracle happens..."), I don't think we have enough reference to even debate what that entails, or really means...

 

[Thierry Clicot]

About the singularity stuff. If the universe began as a singularity, the singularity was,at that instant, the entire universe. After that, the entire universe expanded. Every part. There was no part that did not, and hence there is no centre.

And your statement is again, a "thought experiment" -- probably stated as correctly as we 4-space humans can do, but nevertheless like saying "magic occurred". The problem lies in not being able to grasp the REAL reality of how our Universe works (I can't even say "came to be", since infinity implies it was ALWAYS-and that, to a human, is "magic")...

 

[Bandersnatch]

Well, Andromeda (and A LOT of other objects) is blue-shifted and supposedly moving TOWARDS us, so your statement is unfounded at the start.
Also, your statement's conclusion is a non-sequitur--if everything was moving away from us, one could *logically* draw the inference that we ARE at the center of the "universe".

It should be obvious from the context that thetexan meant large-scale universe. Clusters of galaxies and beyond. All blue-shifted galaxies are close enough for their peculiar motions to exceed the recession caused by the expanding space.
And yes, one can draw that conclusion. But one must also follow up with the conclusion that every other observer in the universe can see himself at the centre of the expansion. This is what all those analogies, like the expanding balloon, are meant to convey - metric expansion of space means that everywhere you're standing, the universe will always look like it's expanding away from you.

Also, I think you're being too hard on human ability to work with infinities, or higher dimensions. Sure, these might be hard, or even impossible to imagine in one's mind's eye, but we can nevertheless work with those with some considerable mathematical precision. The whole of calculus is founded on the concept of infinities, any secondary school graduate should have no problems with counting infinite series through the use of limits, and linear algebra is quite happy to manipulate n-dimensional vectors and spaces.
Just because it's mind-blowing doesn't make it magic. With that attitude we'd still be staring at fire and lighting with awe, and telling ourselves that we just can't cope, man, we just can't cope!

 

[Jim Hasty]

I'm not sure if this is already taken care of, but:

The problem is that that expansion has a very different geometry from the one we observe. The galaxies on one side would have different velocities from the galaxies on the other, which would point us toward the center.

But what if the expansion of space was accelerating with distance from the singularity, i.e. the epicenter of the universe, like we see today? Then if you looked in the direction of the expansion those galaxies would be accelerating away from you; and looking in the direction of the center those galaxies would appear to be accelerating away but it is actually you moving away from them. Would there be a way to discern the true direction of a center? I am not convinced that this gives the same picture as the balloon surface scenario; but I hope I am conveying my idea.

 

[phinds]

But what if the expansion of space was accelerating with distance from the singularity, i.e. the epicenter of the universe, like we see today? Then if you looked in the direction of the expansion those galaxies would be accelerating away from you; and looking in the direction of the center those galaxies would appear to be accelerating away but it is actually you moving away from them. Would there be a way to discern the true direction of a center? I am not convinced that this gives the same picture as the balloon surface scenario; but I hope I am conveying my idea.

Your concept is clear, and clearly wrong. You are not thinking through the geometry of your proposed situation. Think about how you would see a different speed for objects not directly on a line with this magical center you want to invoke than you would for ones on that line. That implies a preferred frame of reference and that's a no-no.

 

[Thierry Clicot]

Also, I think you're being too hard on human ability to work with infinities, or higher dimensions.

I am just stating the obvious--Yes, humans "work" with infinities as Limits or as constructs that make an equation valid, but these concepts of Infinity are strictly theoretical, or "constructed" by acclamation, to make the mathematics work. We are no more sure of Infinity on a physical level, than we are of life-after-death...

In practice, we have no idea of what PHYSICAL Infinity is -- and we cannot use it, or prove it either exists, or doesn't.

 

[Bandersnatch]

Your concept is clear, and clearly wrong. You are not thinking through the geometry of your proposed situation. Think about how you would see a different speed for objects not directly on a line with this magical center you want to invoke than you would for ones on that line. That implies a preferred frame of reference and that's a no-no.

I'm not sure if that's entirely correct, phinds. As long as we're not talking about some explosion with particular, uneven distribution of matter, but about metric expansion, then expansion 'from' the point specified as the centre should look just like metric expansion from any other point in the universe. The point being not that the distribution of recession velocities would look different, letting you to discard that hypothesis, but that you can't distinguish that point from any other point, making it meaningless.
To find the centre of the expansion one would need to postulate boundaries to the universe, i.e. edges, from which one could calculate the equidistant point that could be called a centre.

 

[DaveC426913]

The idea of there being no centre and no outside is fairly easily grasped (IMO) if one contemplates the wraparound universe. Any point on the surface of a sphere looks the same as any other point. And there are no points that are not on the surface. If you head in any direction on the surface of a sphere, you will arrive back at your starting point.

Is it expected that our universe does indeed wrap around?
i.e. if we were able to fly around in the universe just a short while after its creation (or a short time before the Big Crunch), would we eventually return to our starting point (speed of light limitation notwithstanding)?
Or are there models of the universe where there is no centre, no outside, and yet it does not wrap around?

 

[Bandersnatch]

Or are there models of the universe where there is no centre, no outside, and yet it does not wrap around?

All the infinite models (i.e. with flat or saddle-like geometry).

 

[Jim Hasty]

Your concept is clear, and clearly wrong. You are not thinking through the geometry of your proposed situation. Think about how you would see a different speed for objects not directly on a line with this magical center you want to invoke than you would for ones on that line. That implies a preferred frame of reference and that's a no-no.

Why is it a 'preferred frame of reference' ? A frame in line with a center of mass is no more preferred than any other frame I choose to use. I am free to choose any frame of reference and the laws of physics are equally valid in all frames. I respectfully disagree that the universe having a center makes THAT FRAME a preferred frame. HOWEVER, I am working towards your original question (about the geometry) just not there yet.

 

[Chronos]

Einstein never, AFAIK, ever used the term 'fabric of space', only the term 'fabric of space-time' to emphasize the inseparable link between space and time in GR. You cannot have one without the other. It also reinforces a deeper point - that gravity plays a vital role in the universe. If you could shut off gravity in an isolated region of the universe, the concepts of distance and time within that region would be rendered meaningless.

 

[OCR]

If you head in any direction on the surface of a sphere, you will arrive back at your starting point.

Then, how could you know this, if...?

Any point on the surface of a sphere looks the same as any other point.

And there are no points that are not on the surface.

Even in a wraparound universe, doesn't the spacetime mathematical model still apply... "time" has changed (passed), does your starting point actually still exist?

In any given spacetime, an event is a unique position at a unique time.

Am I way off base on this?

 

[russ_watters]

But what if the expansion of space was accelerating with distance from the singularity, i.e. the epicenter of the universe, like we see today? Then if you looked in the direction of the expansion those galaxies would be accelerating away from you; and looking in the direction of the center those galaxies would appear to be accelerating away but it is actually you moving away from them. Would there be a way to discern the true direction of a center? I am not convinced that this gives the same picture as the balloon surface scenario; but I hope I am conveying my idea.

That's exactly the scenario I was just describing. Yes, you could tell which direction the center was. If the center was to your left, the galaxies to your right would be moving away from you faster than the galaxies to your left (and with speed differences that depend on distance from the center). That's not what is observed.

 

[DaveC426913]

If you head in any direction on the surface of a sphere, you will arrive back at your starting point.

Then, how could you know this, if...?

Any point on the surface of a sphere looks the same as any other point.

I should have been more precise to say 'observing from any point on the surface looks the same as observing from any other point on the surface'
i.e no matter where you are, you will head out in any direction and arrive back at your starting point.
So, no point is special, denoting any kind of centre.

Even in a wraparound universe, doesn't the spacetime mathematical model still apply... "time" has changed (passed), does your starting point actually still exist?

In any given spacetime, an event is a unique position at a unique time.

Yes, I have not suggested otherwise.
But if every point in the universe can lay claim to the same form of 'uniqueness' then none of them are preferred i.e. no centre.

Notice that this actually has nothing to do with the type of curvature. It applies equally to the flat and saddle shapes universe Bandy mentions.

 

[Jim Hasty]

That's exactly the scenario I was just describing. Yes, you could tell which direction the center was. If the center was to your left, the galaxies to your right would be moving away from you faster than the galaxies to your left (and with speed differences that depend on distance from the center). That's not what is observed.

Yes, I see that now. I did a little geometry and math and the fit with observations is much better using the 'surface of a balloon' analogy. In the google research I found some discrepancies with the cosmology principle [2011-2012] but a recent article [2014] validates symmetrical expansion. Thanks for everyone's patience.

 

[Jim Hasty]

Your concept is clear, and clearly wrong. You are not thinking through the geometry of your proposed situation. Think about how you would see a different speed for objects not directly on a line with this magical center you want to invoke than you would for ones on that line. That implies a preferred frame of reference and that's a no-no.

Update on my recent reply. I see what you mean now by 'preferred frame' in the context of the cosmological principle. There are several googled articles [2011-2012] which mention 'preferred frames' in the context of 'asymmetrical expansion'. So yes, I agree with you in that context.

 

[DrStupid]

But what if the expansion of space was accelerating with distance from the singularity, i.e. the epicenter of the universe, like we see today? Then if you looked in the direction of the expansion those galaxies would be accelerating away from you; and looking in the direction of the center those galaxies would appear to be accelerating away but it is actually you moving away from them. Would there be a way to discern the true direction of a center?

As long as the expansion follows Hubble's law, there is no way to find the "true direction of a center". The universe looks identical in all directions from any position.

 

[Infintelycuriou]

Arthur Edington's 1933 balloon analogy of big bang is the most confusing one. We should remember that nothing exists outside the balloon surface. The balloon surface is increasing because it is expanding but you cannot decrease the surface area, go back in time and then reach to a singularity. That provision is there in principle but do not do it, because, then the analogy breaks. The surface area of the balloon is not known, but it has to be infinite because curvature has found to be nill. The balloon expands but not the objects that make the balloon, means expand everything but not the galaxies, observations show no expansion of galaxies. So, balloon and even Big Bang lives in a highly protected physical scenario.

Several people in this forum tried to create a center of the universe, those are not scientific nonsense. "It is less well known that Lemaître found a more general class of solutions that describe a spherically symmetric expanding universe. These solutions, now known as Lemaître-Tolman-Bondi (LTB) models, describe possible forms for a universe that could have a centre. Since the FLWR models are actually a special limiting case of the LTB models, we have no sure way of knowing that the LTB models are not correct. The FLWR models may just be good approximations that work well within the limits of the observable universe but not beyond." Therefore, many of the proposals and comments for finding the center of the universe is not nonsense. These were the early days of Big Bang theory development.

Science is not blind it accepts all views, if you are aware about scientific literatures, wild ideas do come, very scientifically. Several proposals which I found have been discarded as "nonsense", are not that nonsense at all, scientists thought and those thought led to enormous protections.

 

[rootone]

Several proposals which I found have been discarded as "nonsense", are not that nonsense at all.

The aim of science is to discover good explanations for things which are observed, explanations which make predictions that are testable.
A proposal which does not explain something or is not testable is not in the domain of science,
so yes it would likely be discarded as being invalid scientifically, it would not even deserve the status of being 'wrong'.
What kind of proposal did you have in mind though?

 

[DaveC426913]

What kind of proposal did you have in mind though?

 

[OCR]

Thanks for responding, Dave...

 

[DaveC426913]

Thanks for responding, Dave...

Tongue only half-in-cheek. Rootone is in danger of giving carte blanche to the posting of a personal theory of a new member who may not be aware of PF's policy on personal theories.

 

[rootone]

T... Rootone is in danger of giving carte blanche to the posting of a personal theory of a new member who may not be aware of PF's policy on personal theories.

No!, it may have seemed that way I can see your point.
I was not inviting personal theories, just asking what Infinitelycurio meant by proposals being rejected,
and trying to convey that it shouldn't be surprising if untestable ideas are not given much credibility as science.

 

[AgentSmith]

Instead of considering the universe, let's just consider the question of shapes and geometry.

In two dimensions: a disc (the area within a circle) has a centre that is part of the disc, but the centre of a circle is not part of the circle. If you were compelled to live on a circle, there would be no centre that you could visit.

In three dimensions, you have the same situation with a solid sphere (the centre is part of the sphere) and a spherical surface (its centre is not part of itself).

In higher dimensions, you have similarly the concept of a hypersurface.

To begin with, you could expand your knowledge of shapes and geometry. Then use this knowledge to understand what people are saying about the universe.

Are you saying the universe is the surface of a 4-D sphere?

 

[PeroK]

Are you saying the universe is the surface of a 4-D sphere?

No. Why would you think that?

 

[DaveC426913]

No. Why would you think that?

It's a logical deduction when projecting 2D geometry to 3D geometry.

Are you saying the universe is the surface of a 4-D sphere?

It turns out that the geometry of curvature works perfectly well without having to invoke a 4th dimension. This has been demonstrated mathematically.

 

[phinds]

Update on my recent reply. I see what you mean now by 'preferred frame' in the context of the cosmological principle. There are several googled articles [2011-2012] which mention 'preferred frames' in the context of 'asymmetrical expansion'. So yes, I agree with you in that context.

You are not being clear here as to whether or not you still argue that the universe has a center. Are you now convinced that it does not?