Where is the COM of the Observable Universe?

[m74z00219]

Well, two questions actually.

1. Where is the center of the oUniverse? Is it simply where the observer's eyes are? Or is there a more complicated definition?

2. Where is the center of mass of the oUniverse? Is it within our solar system? Is it thousands of light-years off? Does this have any bearing on question one?

Thanks. I find question two especially interesting. Never thought about it until today!

Thanks,
m74

PS: oUniverse being the sphere with radius equal to 47 billion c-y

[hhEb09'1]

PS: oUniverse being the sphere with radius equal to 47 billion c-y

Where is the center of the sphere?

[m74z00219]

Where is the center of the sphere?

haha, yes, that's what I want to know!

[sohh_fly]

I don't think there is a center of the universe. unless you want complication.
I'm pretty confident that the SS isn't the center of mass,maybe because the 1st question doesn't have an answer.
I think

[AndreasJ]

I'm guessing oUniverse = observable universe, so the centre would be Earth.

The centre of mass of the observable universe would very approximately be at Earth, too, since at sufficiently large scales the observable universe is homogenous. Very approximately as in +/- 100s of millions of lightyears.

[hhEb09'1]

Then, where does the "47 billion c-y" come from?

[AndreasJ]

Then, where does the "47 billion c-y" come from?

I don't know. If "c-y" means light years, perhaps an estimate of the present distance of the most distant visible objects? (Expansion will have been carrying them further away since they emitted the light we see 10+ Ga ago.) I seem to recall seeing a similar figure for that somehwere.

[m74z00219]

Then, where does the "47 billion c-y" come from?

That's the currently agreed upon radius of the observable universe.
http://en.wikipedia.org/wiki/Observable_universe

@AndreasJ
c-y is indeed a shorthand for light-years. i picked it up a few years back.

Right, that distance is the distance to the particle horizon. It's the farthest distance a particle (in this case, a massless particle) could have traveled to reach our eyes.

The Atlas of the Universe explains far better than I could.
http://www.atlasoftheuniverse.com/redshift.html

Thanks for the answer AndreasJ. It seems to stand to reason that this COM will move around quite a bit as the universe expands. As galaxies move beyond the observable universe and we're left with just the milky way (or andromeda/MW hybrid), I imagine the COM of the oUniverse will be different.

[hhEb09'1]

That's the currently agreed upon radius of the observable universe.
http://en.wikipedia.org/wiki/Observable_universe

From that article: "the observable universe is a solid sphere (a ball) centered on the observer"

Next question, I guess, is, who is your observer?

[AndreasJ]

c-y is indeed a shorthand for light-years. i picked it up a few years back.

A commoner abbreviation for light-year is "ly" - as an added bonus it's faster to type.

[AndreasJ]

That's the currently agreed upon radius of the observable universe.
http://en.wikipedia.org/wiki/Observable_universe

On some reflection, it appears profoundly weird to define the extent of the observable universe by the comoving-frame present location of the most distant visible objects. The limits of observability cut through time as well as space, and simply do not include the present of those objects. Light-travel distances may, as they put it, "have no direct physical significance", but if the comoving present distance has any observational significance it's that we can't see objects at that distance!

[a1call]

From the wiki link:

It is also possible that the universe is smaller than the observable universe. In this case, what we take to be very distant galaxies may actually be duplicate images of nearby galaxies, formed by light that has circumnavigated the universe.

Where is the center of the surface of a sphere?

[DrRocket]

Well, two questions actually.

1. Where is the center of the oUniverse? Is it simply where the observer's eyes are? Or is there a more complicated definition?

2. Where is the center of mass of the oUniverse? Is it within our solar system? Is it thousands of light-years off? Does this have any bearing on question one?

Thanks. I find question two especially interesting. Never thought about it until today!

Thanks,
m74

PS: oUniverse being the sphere with radius equal to 47 billion c-y

Think about it a bit harder. Generally by the center of something you mean the center of mass under the assumption of uniform density. In the case of the universe, it is generally thought that the mass distribution is, on the largest scales, homogeneous and isotropic. So the center really is the center of mass -- if either exist.

The universe is, at least in general relativity, a 4-dimensional space-time manifold. If you make a large-scale approximation assuming isotropy and homogeneity then the spatial part can be considered to be some sort of 3-dimensional space-like slice, a 3-manifold of unknown but constant curvature.

It is not at all clear what is mean by the center of mass of such an object. Consider a simple one-dimensional example, a ring or circle embedded as usual in ordinary 2-space. Where is the center of mass ? At the usual center of the circle. It is not a point on the circle at all. The concept of a center of mass for the circle is logically tied to the space in which it is embedded. The same analysis holds for a sphere (not a ball but the surface of a ball) in any dimension.

Now consider the manifold that represents space. As far as we know it is an intrinsic manifold, not embedded in anything. It might be just a copy of ordinary 3-space, with mass uniformly distributed. That has no center of mass. It might be some compact manifold of positive curvature. Since it is not embedded in anything it may not have a center of mass. It might be some hyperbolic non-compact manifold, with no center of mass. It might even be something else.

If you consider only the observable universe, then you have a different problem. The observable universe is just that part from which, in principle, photons could have reached us since the moment of the big bang. That is apparently a 3-ball, and the observable universe seems to be flat or nearly so. But the particular 3-ball depends on the specific observer, and it is centered on that observer. So if the observable universe is approximately flat, homogeneous and istotropic the center of mass is the observer, and that holds for any observer.

[01101001]

On some reflection, it appears profoundly weird to define the extent of the observable universe by the comoving-frame present location of the most distant visible objects.

I don't think it's weird. It's necessary to give context to the 47 (46.5) billion lightyear figure.

I wish everyone would get in the habit of making sure the distance measure is understood when a distance value is provided. If you don't give the distance measure, you might just as well skip providing the units, too. It matters for communication that much.

Here that distance measure of comoving distance provides an immediate mapping to other distance measures, with different values attache, such as (from Wikipedia: Distance measures (cosmology)):

• Angular diameter distance. Angular Diameter Distance is a good indication (especially in a flat universe) of how near an astronomical object was to us when it emitted the light that we now see.
• Luminosity distance.
• Comoving distance. The distance between two points measured along a path defined at the present cosmological time.
• Cosmological proper distance. The distance between two points measured along a path defined at a constant cosmological time. The cosmological proper distance should not be confused with the more general proper length or proper distance.
• Light travel time or lookback time. This is how long ago light left an object of given redshift.
• Light travel distance (LTD). The light travel time times the speed of light. For values above 2 billion light years, this value does not equal the comoving distance or the angular diameter distance anymore, because of the expansion of the universe. Also see misconceptions about the size of the visible universe.
• Naive Hubble's law, taking z = H0d/c, with H0 today's Hubble constant, z the redshift of the object, c the speed of light, and d the "distance."

Perhaps you feel one or more of them is less weird. They're just different ways of thinking about the same thing. Maybe they are all equally weird, depending on point of view.

[astromark]

Hmm... lets try a different way of looking at this. Because it would seem that to see and understand this. Is to comprehend the enormity of the universe. Because of humanities ability to conceptualise things that we can not actually see as real and proper explanations of reality. All of this is fine but, does not help answer your question :Where is the centre of the universe ?
If you mean the observable universe then sorry but that's not the same question is it ?
As we have understood and have tested as true the concept of a expanding universe finding the start point would seem to be unavailable to us. It went that way.... and a very long time ago... We can not answer your question as we can not define any of the parimitars. We can say that our observable universe has us right in the middle. The same might be said for any point anywhere across this universe. The fact is the universe seems to have had a starting moment. That moment was at the very outset of space and time. We have become comfortable with 'The Big Bang' as the explanation of that event. Where was it. Right here, and over there and behind that fellow over there also.
Can you find that acceptable ?

[AndreasJ]

I don't think it's weird. It's necessary to give context to the 47 (46.5) billion lightyear figure.

If we're using that figure, certainly, we have to specify it's the comoving distance, but this ought be perfectly orthogonal to whether using that distance in the first place is weird or not.

Perhaps you feel one or more of them is less weird. They're just different ways of thinking about the same thing. Maybe they are all equally weird, depending on point of view.

They're each a bit weird, because the universe at cosmological scales doesn't obey our everyday notions of time and space.

Comoving distance, however, seems to me partcularly weird in the context of the size of the observable universe - it's a distance between the present locations of things, but the observable universe is not a slice orthogonal to comoving time, but a light-cone centered on the observer. The gas that gave off the CMB is inside the observable universe as that gas, but outside as the galaxies it may have formed in the (comoving) present, yet the comoving distance is the distance to the later.

The light travel time distance might do greater violence to our intuitions of distance, but at least it's a distance to the right event.

[speedfreek]

Comoving distance, however, seems to me partcularly weird in the context of the size of the observable universe - it's a distance between the present locations of things, but the observable universe is not a slice orthogonal to comoving time, but a light-cone centered on the observer. The gas that gave off the CMB is inside the observable universe as that gas, but outside as the galaxies it may have formed in the (comoving) present, yet the comoving distance is the distance to the later.

The light travel time distance might do greater violence to our intuitions of distance, but at least it's a distance to the right event.

As long as we remember that, for events with a light-travel time of more than around 9 billion years or so, as light-travel time and comoving distance increase, the angular diameter distance decreases, then it all makes sense!

[neilzero]

True the surface of a sphere can have only an arbitrary center, but why should we think the universe is like the surface of a sphere instead of the interior of a sphere which can be mapped in xyz co-ordinates and does have a distinctive center?
The surface of a cube has 6 distinctive centers, but we don't think the universe is a cube surface. Neil

[astromark]

If its on the surface of a sphere or some point inside the mass... It does not answer the question. If we can not define the size or shape of the universe because at the edge of the observable universe its moving away from us faster than its image can be transmitted then we can not and never will know where the actual edge might be. , or if there is one. Without knowledge of an edge we can not define a centre. accepting that is important. As the question does not have an answer we can ever find.

[m74z00219]

If its on the surface of a sphere or some point inside the mass... It does not answer the question. If we can not define the size or shape of the universe because at the edge of the observable universe its moving away from us faster than its image can be transmitted then we can not and never will know where the actual edge might be. , or if there is one. Without knowledge of an edge we can not define a centre. accepting that is important. As the question does not have an answer we can ever find.

Hi astromark, (I always enjoy your postings by the way) I indeed was always referring to the observable universe.

By Dr. Rocket's sensible reasoning, it seems there is not COM for the observable universe. While we (at the center) can feel the gravitational influence of particles 46 billion ly away, those same particles are also affected by a sphere of influence with radius 46 billion ly. This can be considered ad nauseam. This seems to make sense to me.

I'm still a little shaky on the center of the observable universe thing, though. Well, this brings up another question. Is the surface of the observable universe perfectly "spherical"? I suppose that's not quite the right word; even the observable universe is 4-D. I suppose the heart of the question is: no matter where and when I am, the center of the observable universe is defined as "in my eyeballs"??

[Cougar]

I'd say we are at the center of the observable universe, rather by definition, and with the homogeneous-isotropic thing going on, we are also at the center of mass of the observable universe. However, an alien at any other point in the universe could say the same thing (about its observable universe).

[Jens]

I'd say we are at the center of the observable universe, rather by definition, and with the homogeneous-isotropic thing going on, we are also at the center of mass of the observable universe. However, an alien at any other point in the universe could say the same thing (about its observable universe).

Unless it was a one-eyed alien with a tree-like body planted on a non-rotating planet. In which case it would be at the very edge of the observable universe.

[chornedsnorkack]

I'd say we are at the center of the observable universe, rather by definition, and with the homogeneous-isotropic thing going on, we are also at the center of mass of the observable universe. However, an alien at any other point in the universe could say the same thing (about its observable universe).

No, I donīt think so.

Remember, the universe is not precisely homogeneous. There are observable inhomogeneities, such as presence of galaxy clusters, and nonuniform temperature of relict radiation.

Is it possible to actually define relict radiation rest frame? I mean, if the Milky Way or Sun is moving, obviously one hemisphere is blueshifted and another redshifted. But if there are hotter and colder patches (more than just one hot and one cold patch), then what is the relevant average of the radiations, to define exact rest?

Does the density of matter at relict radiation vary together with its temperature, or are those independent variables? For example, what is, physically, a "hot spot" of relict radiation? Is it a quantity of gas which was moving towards Milky Way (and therefore blueshifted)? Or is it a void in the gas, which was hotter but less dense than the rest and therefore became transparent to radiation at a slightly higher temperature?

If we kept watching a hot spot of the relict radiation, how long would it last? A few tens of thousands of years, or longer?

[AndreasJ]

As long as we remember that, for events with a light-travel time of more than around 9 billion years or so, as light-travel time and comoving distance increase, the angular diameter distance decreases, then it all makes sense!

I'm not at all clear how the counterintuitive behaviour of angular diameter distance is supposed to make sense of defining the observable universe in terms of the unobservable (viz., the present location of the farthest objects)?

[hhEb09'1]

By Dr. Rocket's sensible reasoning, it seems there is not COM for the observable universe. While we (at the center) can feel the gravitational influence of particles 46 billion ly away, those same particles are also affected by a sphere of influence with radius 46 billion ly. This can be considered ad nauseam. This seems to make sense to me.

Having matter outside of the area under consideration doesn't affect whether or not it has a Center Of Mass, though. My computer has a COM, and it is nowhere near the entire universe.

I suppose the heart of the question is: no matter where and when I am, the center of the observable universe is defined as "in my eyeballs"??

As long as you insist on that word "observable", yeah you're probably stuck.

[speedfreek]

I'm not at all clear how the counterintuitive behaviour of angular diameter distance is supposed to make sense of defining the observable universe in terms of the unobservable (viz., the present location of the farthest objects)?

It all comes down to the definitions used in cosmology. The unobservable universe is the parts of the universe from which we have never received light, or information. The parts of the universe from which we have received information, however out of date that information is, are part of our observable universe. That is how it has been defined, due to the cosmological principle that we can apply what we observe over here to what has gone on since, over there.

It is when you consider the implications of the angular-diameter distance redshift relationship that you realise that you have to include comoving distance in our definition of the observable universe for the whole thing to make any sense. One does not make sense without the other. Remove both and all you are left with is light-travel time, which is not a distance through space and doesn't lead to much insight on its own.

How can we have very dim looking, high z, long light travel time galaxies that look to be closer to us than much brighter looking, lower z, shorter light travel time galaxies? That is the angular diameter distance relationship at work. How can light take longer to travel from a closer distance than it did from a further distance?

You have to take the recession speeds into account in order to understand the picture. By the time that those lower z galaxies emitted the light we see, those high z galaxies were much further away and their light was just passing through that lower z space. The comoving radial distance kind of falls out at you.

If we just consider what we actually see, perhaps we should simply call it the visible universe, but that would include the angular diameter of the objects we observe.

I just don't think that light-travel time can cut it, on its own.

[AndreasJ]

It all comes down to the definitions used in cosmology. The unobservable universe is the parts of the universe from which we have never received light, or information. The parts of the universe from which we have received information, however out of date that information is, are part of our observable universe. That is how it has been defined, due to the cosmological principle that we can apply what we observe over here to what has gone on since, over there.

And my problem is precisely with that definition. It's an abuse of the word "observable".

[speedfreek]

I agree to a certain extent - the term "observable universe" is notorious for the confusion it can cause.

But we need a way to differentiate the parts of the universe we have seen from the parts we will never see. If we call the parts of the universe beyond the particle horizon the unobservable universe, what should we call the parts within it?

If you want to take the current definition of the observable universe and split it up with different definitions it gets very complicated. We have to consider both our past and future light cones if we want a true definition of "observable". Our past light cone is what has been observed and our future light cone is what will be observable.

So what do we do with that large area on the space-time diagram in-between our future light cone (which, in effect, is the cosmological event horizon), and the particle horizon, the most distant point from which we have received information? We should call that in-between part unobservable I suppose, but then how do we separate that from what we currently call the unobservable universe?

As for the comoving distance, well if the current comoving distance is within the cosmological event horizon then it is observable. So, strangely enough, when we say that galaxies with a redshift of z=1.4 were 5.7 Glyr away when they emitted their light, had an apparent recession speed of c and now have a comoving radial distance of around 14 Glyr, we find that we will eventually be able to see the events currently happening 14 Glyr away as they are within our cosmological event horizon.

[Contemptaplator]

The question of the centre of the universe goes with the question of the shape of the universe. How do I imagine the shape of the universe in 4d space-time? What is positive curvature? Alexander Friedman assumed that the universe is homogenous, and that it holds true for any observer in the universe. That means that there is no edge to the universe. How can this be visualized?

[Cougar]

That means that there is no edge to the universe. How can this be visualized?

Well, the simplest example is, suppose your universe is the surface of a sphere. No edge! For 4-D, extrapolate liberally.