# Centre of the universe?

1. Jan 1, 2008

### yuiop

We are generally told these days that the universe is infinite and therefore has no definable centre. Is that correct? I see the subject the subject of an edge of space has already been discussed but I would like to put a new angle on the subject.

Let's say for the sake of argument, that the vacuum of space is infinite. Let's also say that the number of baryons in the universe is much greater than estimated 10^80 in the visible universe, but nonetheless finite. If the mass of the universe is finite, then there is a definable centre of mass for the universe, even if there is not a definable centre of vacuum space.

If it is claimed that the mass of the universe is infinite, then that is an extraordinary claim if we use the true meaning of infinite, and don't just mean the largest number we can possibly imagine. If that is the claim, what is the evidence that rules out a finite mass for the universe?

2. Jan 1, 2008

### DaveC426913

No, the universe is not infinite. If you are being told this, seek a more informed source for your information.

By current estimates the universe is about 156 billion light years wide.

Last edited: Jan 1, 2008
3. Jan 2, 2008

### marcus

but Dave! that estimate of 156 was a LOWER BOUND calculated by Neil Cornish and David Spergel back around 2004-2005. I remember when it came out.
There was never a hint from them that the the universe was finite! Only that it could be either finite or infinite and if it was finite it was AT LEAST that big.

The standard model cosmology called LCDM comes in two main versions----spatial infinite (Omega = 1)
and spatial finite (probably something like Omega = 1.01, nearly flat but with slight positive curvature).
which one is an undecided question. for the time being most cosmologists ordinarily use the spatial infinite Omega=1 case for calculating, absent evidence that rules it out. It's simpler.

Last edited: Jan 2, 2008
4. Jan 2, 2008

### marcus

Not quite. In conventional cosmology it has no definable center. Right!
But that would be so in either case.

You should not be being told that the universe is infinite because cosmologists DON'T KNOW if it is finite or infinite.

They assume that matter is more or less evenly distributed, so if space if infinite of course matter is infinite too.
===========================

That would be highly idiosyncratic cosmology. I have never heard of anyone assuming that. Space and matter are assumed coextensive.

The "if-then" statement here is false. This is not a logical implication.
Normal cosmology is LCDM which comes in two versions both fitting the data about equally. The finite version (e.g. Omega = around 1.01) has finite volume space and finite amount of matter and NO CENTER OF MASS.

The space is S3 which is the first thing you should learn about when you first approach cosmology---the 3D analog of the 2D surface of a sphere. It is finite volume with no boundary. In that picture matter is distributed more or less evenly throughout.

It is not true that if the mass of the universe is finite then there is a definable centre of mass.

There is no evidence that rules out a finite volume space, of the S3 type.
In fact the latest measurements of Omega---the decisive number as regards this finite/infinite issue----have an errorbar for Omega which is on the UPside!
That means the observations slightly FAVOR a finite volume space (with of course finite matter approx. evenly distributed.)

Last edited: Jan 2, 2008
5. Jan 2, 2008

### PseudoIntellect

156 billion light years wide? If the radius is around 78 billion light years, and the estimated age of the universe is around 15 billion years, would that not mean that enormous amounts of matter traveled faster than the speed of light from a theoretical point of singularity in the past? Or am I missing something...

6. Jan 2, 2008

### marcus

Nobody said the universe was 156 billion LY wide. That was Dave's misconception.

there is no one unique point in space where the expansion originated

also recession speeds are typically superluminal

Last edited: Jan 2, 2008
7. Jan 2, 2008

### nicksauce

Is it (somewhat) analogous to say that a Sphere with a uniform mass density (sigma) will have a finite mass, $$4\pi R^2\sigma$$, but no centre of mass?

8. Jan 2, 2008

### Garth

No - for a start a sphere of constant density $\rho$ will have a total mass of
$$M = \frac{4}{3} \pi r^3 \rho$$

Secondly, it will have a centre of mass, the centre of the sphere.

Thirdly, in standard cosmology if the 3D spatial universe is finite yet unbounded then, with one of its dimensions suppressed, it is analogous to the 2D surface of a 3-sphere.

Garth

9. Jan 2, 2008

### nicksauce

Sorry, I meant a uniform surface mass density. (Hence why I used $$4\pi\ R^2$$)

10. Jan 2, 2008

### lewis198

If Hubble discovered red shift from all points from Earth, doesn't that mean that a universal center is somewhere near Earth?

11. Jan 2, 2008

### Garth

No - in standard cosmology the universe is assumed to be isotropic, which means it looks the same on the largest scales in every direction from all points on Earth.

It is also assumed to be homogeneous on the largest scales, which means every observer anywhere in the universe will observe a Hubble red shift in all directions, isotropically.

Garth

12. Jan 2, 2008

### muccasen

In summary then:
If you exist on the surface of a ball how can you have a centre somewhere on that surface? This applies to a Universe finite in extent. The only sense in which you can conjure a centre would be to refer to the BB origin i.e. roll back time. As the experts here have said already the ball surface image is used to represent our 3d normal space (one spatial dimension suppressed to enable more easy perception).
In the case of flat infinite space I cannot imagine how a centre can be conjured.

All of this is of course different to the visible universe as apposed to the whole universe. Going back to the ball surface that represents the whole finite universe, if you were situated at the north pole say, then your visible universe might be represented by the artic circle. Your visible universe would then have a centre. It would be the North Pole.

Note that YOU are your own unique centre for your own visible universe. Well only by a smigin I admit!!

13. Jan 2, 2008

### Garth

Yes. in your North Pole illustration you are right to say that "you are your own unique centre for your own visible universe", but of course this is not the centre of any other ET being's universe.
Even referring to the BB will not give you a centre because the BB happened everywhere, at t=0 'everywhere' was compressed into the BB!

Garth

14. Jan 2, 2008

### marcus

Hi Nick, I think you have it exactly right and really no need for me to reply except to agree. But at risk of over-explaining in case this is new to any other readers, I'll add some talk:

what limits the analogy is that we typically see a 2D sphere living in 3D space
so the 2D spherical surface is not all there is.

indeed, as you say, the 2D sphere contains no center of mass
a 2D being living somewhere in it would not have a direction he could point and say "the center of mass is over there!"

but we outsiders who are 3D beings can see that in our higher-dimensional space there IS a center of mass. It just is not in the original 2D space.
================

I think your analogy is exactly right, with the proviso that the 3D sphere S3 is all the space there is.
If we are living in a universe that is spatially S, we do not know about any higher dimension in which a center of mass might exist. There is no direction in our world where we could point and say "the center of mass is over there." So as far as we are concerned, or have knowledge, such a point does not exist.

=================
I see while I was typing there were a lot more comments.

I agree with posts #12 and #13----with Muccasen's summing up and with Garth's reply to that.

Last edited: Jan 2, 2008
15. Jan 2, 2008

### muccasen

Yes I agree Garth but I am often guilty of thinking in 4d space i.e. the embedding space which to me is simpler, lol confusing or what? Anyway "Everywhere" is good and of course we have the perfect illustration : The CMBR which you can consider to be a near graphic of the original Quantum Fluctuation " Spread Everywhere"!!

16. Jan 2, 2008

### muccasen

17. Jan 2, 2008

### yuiop

I have seen the balloon analogy which represents an unbounded surface to a 2 dimensional creature. That creature would assume a flat surface and no matter how far it kept going in one direction, it would never find an edge. However, if the balloon surface was tiled and it marked those tiles it would eventually work out that it was going round in circles and that the number of tiles (galaxies) was finite.

In a typical description of the evolution of the universe, it is explained that the expansion of the universe is accelerating "now", but in an earlier epoch the expansion was slowing down when gravity dominated the cosmological constant. The problem I have is that if the universe is infinite with an infinite amount of mass, then that slow down would have been impossible because every massive body would equally attracted in all directions by an equal amount of mass in all directions. There would be no preferred direction for any body to move in.

I agree this is idiosyncratic view, but I just have difficulty imagining an infinite amount of mass. The closest thing I can imagine to the concept of an infinite universe is one expanding at the speed of light making it impossible for any observer to travel fast enough to get to the “edge” of that universe. However, if the expansion of the universe is due to the expansion of space itself, then the apparent superluminal recession of the most distant galaxies is not an insurmountable problem because any traveller would be moving relative to the local space and the traveller would eventually appear to have superluminal velocity relative to a stay at home observer.

The 2D surface of the balloon wraps around on itself in a 3D universe that is not visible to the 2D inhabitants of the balloon surface. The analogy implies our universe is a 3D space that wraps around on itself in a 4D space that is not visible to us. I believe some researchers have tried to find evidence of this wrapping around effect by looking for symmetries in the pattern of distant galaxies in different directions at the edge of the visible universe and never found that evidence.

Another difficulty I am having is how the universe started everywhere at the same time. Assuming that an initially finite universe cannot turn into an infinite universe later on, then if the universe is infinite now, it must have been infinite at the start.

How would the start of initially infinite universe be synchronised so that it starts everywhere at the same time? Any synchronisation could not be coordinated by signals constrained to the speed of light. The best explanation I have seen is that the universe was kick started by the collision of two “branes” The 2D analogy would be two parallel sheets colliding, making the collision and start of the universe happen simultaneously everywhere on the surface of those sheets. The 3D version would two infinite 3D branes floating around in God knows what, before colliding and starting our universe. Now all we have to do is figure out how the infinite 3D branes were created.

18. Jan 2, 2008

### WFWINTERS

Lewis198,

To help give a visual of how every point has equal footing on saying it's the center, based on redshift, picture this. Using the example stated previously of 3D space being analogous to the 2D surface of a sphere, let's further imagine that this sphere is a balloon. If you were to plot many equally spaced points on the surface of that spherical balloon, you would find that as you inflated the balloon and uniformly increased it's surface area, any one of those points would see all of the other points moving away from it. An observer at any point on the surface of an inflating sphere can confidently say that every other point it sees is retreating from their location, giving that observer the illusion that they are at a special central location.

This is an interesting effect because it implies that any point in the universe would give an observer the impression that they are at the origin of the universe's expansion, and in a way, all of those observers would be correct.

Using this example further, to give a visual of Garth's statement that "the BB happened everywhere"...

Imagine that this balloon will maintain a spherical shape as it deflates. Imagine that instead of becoming a floppy loose deflated balloon (as we are familiar with seeing deflated balloons fresh out of a package) this balloon is instead perfectly elastic and deflates from a sphere the size of a basketball to a baseball to a golf ball to a pea all the way to a singularity. If you let the air out of this balloon, it would maintain a spherical shape as it deflated to a single point. That isn't to say that there is a point in the center of the Balloon that is the center of our universe, because the 3D universe in this analogy exists only on the 2D surface of this Balloon. The point in the center of the balloon, the point that the balloon deflates to, is t=0. When the surface deflates to its t=0 state, all points in the universe that exists on the surface of this balloon can correctly say that they are the location of the BB and all other points are heading away from them when inflation occurs.

I hope this helps give a visual.

19. Jan 2, 2008

### muccasen

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I think I am correct to say that in modelling these Branes it is assumed slight imperfections means some areas contact and others do not. I might be out of date there though. Remember these branes are multidimensional and the flat surface image is obtained by dumping a number of dimensions.

20. Jan 2, 2008

### yuiop

Muccasen, thanks for replying to my controversial post in such a pleasant manner.

I have to pop out for a while, but would like to continue this discussion later.

21. Jan 2, 2008

### marcus

kev, this is good post, with points that are interesting to reply to

I see Muccasen already responded, and also that you said you had to go and would be away for a while. But I will reply to one or two things immediately.

I am glad you are familiar with that "nearly flat" slight positive curvature alternative to the infinite case. Recently cosmology papers are using phrases like flat or nearly flat. The majority still think spatial infinite (with mass infinite of course) but they increasingly allow this S3 finite volume case as a possibility.

I see you have a conceptual problem with the INFINITE case:

This is a keen, insightful objection, but it fails because of General Relativity. So far GR is dominant as the theoretical basis of Cosmology because it predicts successfully to high accuracy the way no other theory of gravity does. Cosmology is based on a highly simplified model called the Friedmann equation which is derived from the Einstein GR field equation. It is one particular solution of GR. In the Friedmann model distances are either all increasing or all decreasing. With the parameters of our particular universe, as measured to date, we expect continued increase (no eventual collapse).

In the Friedmann model there IS NO PREFERRED DIRECTION to the expansion, and no preferred direction to any acceleration or deceleration of expansion. Expansion does NOT CONSIST OF GALAXIES MOVING THRU SPACE.
Expansion is just a percentage increase in the distance between stationary points.

GR teaches us to expect distance to change unless it is a distance locked in by atomic or other forces----like the crystal bonds of a metal rod, or the orbit dynamics of a planetary system. Within certain bound structures, forces keep distances from changing, but otherwise one should expect them to be expanding or contracting. The Friedmann equation is beautifully simple and you can see immediately how it governs the rate of expansion/contraction. It works either in the finite volume or infinite volume case and (as I said) doesn't need any force vector in any preferred direction. There's just this timedependent scalefactor a(t) and an ordinary differential equation that tells about the time derivative a'(t) and how it is determined. It is probably easier to understand in that form than in the form of words.

Currently the percentage rate of expansion or more exactly the fractional rate (which you could write a'(t)/a(t) if you want) is one percent every 140 million years. You can see why it has to be. The left hand side of the Friedmann equation is actually the square of that very quantity----(a'(t)/a(t))2.
Actually there are two Friedmann equations, both are simple and you should look at both. But for some reason everybody always talks about THE equation as if there were just one. the other one is about the second derivative of the scalefactor: a''(t).

when you look at these two Friedmann equations the first thing you see is that they work for both the infinite volume case and the positive curved S3 case. that is made explicit with a parameter k which can be either +1, 0, or -1

You are right that expansion, as far as observations can tell us by fitting the data, was DECELERATING until some 4 or 5 billion years ago! That was when matter was denser and its effect prevailed over the cosmological constant. And then with expansion matter thinned out and the cosmological constant effect of acceleration began to prevail.
But all this stuff works equally well in the Friedmann model whether you pick the infinite case or the finite case!. This doesn't need any preferred direction. And the expansion is not outwards from any particular point. Basically it is just GR effects involving the dynamics by which distances change (GR's dynamic geometry).

Well, in that case just picture space as S3! A large balloon is almost flat. This fits the data even slightly better than the infinite space model-----it is just that the infinite flat version is mathematically simpler and the difference in fit is not statistically significant at this point.

That is right. I mentioned some of that research----papers by Neil Cornish and David Spergel----in an earlier post in this thread. They did not rule out the finite picture. They just proved that if it was finite it had to be BIG.

But that is what the curvature data already suggested anyway.

IIRC a 2007 Ned Wright paper presented a good fit for Omega as 1.011, and in a landmark 2006 paper by Spergel et al the errorbar all on the upside of 1------something like [1.010, 1.041] at 68 percent confidence. Ned Wright's 1.011 falls in that range.
And that 1.011 would indicate an S3 circumference of some 800 billion LY, which was way more than the lowerbound that Cornish and Spergel came up with in 2004 (and later refined in 2006). So that much agrees.

====================

What I have still not given you is INTUITION for why an infinite flat volume that starts off expanding should ever slow down! The real reason is that GR is the most accurate theory of gravity at large scale that we have and if you buy GR then you buy Friedmann derived from it and you buy that in the interesting cases expansion slows down unless there is a cosmological constant. But this is unsatisfying. One still wants some intuition for why in the hell it happens.

The puzzle is in the infinite flat case. There is no preferred direction, the net effect of everything should be zero---why should expansion be slowed down? I hope someone else has some intuition about this. When I think about it I come up short on the intuition end.

One thing to remember is that GR is a field theory and information only travels at a finite speed. So in some big region the local patch of geometry doesnt KNOW about the matter way out there. the effective distribution of matter in its past light cone could be very different from the instantaneous (approximately even) distribution. But I'm not sure enough about this. the problem of how you get intuition for the slowing down is interesting----maybe there is some obvious answer that i'm missing. We might hear from SpaceTiger or Garth about this.

Last edited: Jan 2, 2008
22. Jan 2, 2008

### muccasen

Marcus:"lots more to say but I too have to go out"

We look forward to yr return!!

23. Jan 3, 2008

### lewis198

If the universe is homogeneous on the largest scales, then shouldn't other observer's red shifts produce at least an equal amount of blue shifts to red shifts for us? That assumption surely has not been verified. Why did Hubble and so many other scientists reject a nearby center when observations say otherwise?

24. Jan 3, 2008

### lewis198

Thanks for the balloon explanation, but hear is the problem that I have with that model:

If space is expanding, then aren't lengths themselves expanding? What is the expansion relative too then? What I see happening are masses moving away from each other, nothing more. I think historically this has been interpreted as space expansion to fit the large scale homogeneity model.

25. Jan 3, 2008

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