What Is the Possibility of Higher Dimensions in the Universe?

[thomate1]

What we humans know about the center of mass of Universe?

 

[blue_sky]

I guess not enough

 

[SpaceTiger]

What we humans know about the center of mass of Universe?

This is partially philosophical prejudice, but I'm going to go out on a limb and say that there is no center of the universe, in any sense of the word.

 

[ohwilleke]

We're not sure if it exists, and definitely don't know where it is if it does.

Note, however, that asking about a "center of mass of the universe" does at least potentially make more sense in the context of GR than asking "where did the Big Bang happen" which clearly doesn't make sense, because Big Bang theory suggest that you can map every point in the universe back to the Big Bang.

Among the big unknown and unknowable parts of answering the question are the question "what exists beyond observed space?" because we can't observe on Earth anything that happened more than the age of the universe time the speed of light away from Earth. When you know you don't know and can't know information that would appear to be necessary to give a correct answer, you are stuck.

 

[Chronos]

The center of mass of the universe has always been everywhere in the universe at all times. The only alternative is to assume we are at the center of the universe. And that is highly improbably. If the universe is spatially finite, it curves around upon itself - a hall of mirrors effect - making it mostly indistinguishable from an infinite universe. We do know this much, if it is finite, it's mighty big - >24 Gpc:
http://arxiv.org/abs/astro-ph/0310233

 

[SpaceTiger]

The center of mass of the universe has always been everywhere in the universe at all times. The only alternative is to assume we are at the center of the universe.

That's not necessarily true. The center could be somewhere else.

 

[Chronos]

If there was a center, it would have observational consequences. For example, objects located in opposite directions at equal distances [relative to us] would have different redshifts.

 

[thomate1]

Does it means that I can say that

I am the centre of Universe

 

[SpaceTiger]

Does it means that I can say that

You are the center of your observable universe...but then so am I.

 

[FifthEngineer]

If there was a center, it would have observational consequences. For example, objects located in opposite directions at equal distances [relative to us] would have different redshifts.

Just as the engineer that I am, this is hard to comprehend.

Could it be that we are just that far away from a presumably centre that differences in redshift between the objects even farther and the objects closer are not measurable?

And does anybody know, since Dr. Hubble, how many objects have been checked for this redshift consistency? I would presume in the order of 10^5 out of the estimated 10^11 galaxies (my bad, I rely on Discovery channel figures). And not a single one of these escapes the statistics?

Yet again based on Discovery, about the Deep Space Hubble Space Telescope experiment. Is there any ideea if they looked towards the universe edge or on a "diagonal" within? Is there any ideea whether a tenfold increase in the experiment resolution would yield,e.g., 10^15 galaxies?

These are just questions. Any enlightment will be highly appreciated, thank in advance.

 

[bcrowell]

Hi, FifthEngineer,

Welcome to Physics Forums!

This thread dates back to 2005. Usually it's better to start a new thread if you want to continue a discussion from this far back. Anyway, modern cosmological models do not have a center. Redshifts only depend on the velocity of one galaxy relative to another, so they can't be used to find a center to the universe.

-Ben

 

[tom.stoer]

In order to discuss the 'center of mass' one has to find a mathematical definition; the first proposal would be

$$\langle\vec{r}\rangle = \frac{1}{M}\int_\text{Universe}d^3r\,\vec{r}\,\rho(\vec{r})$$

which is mathematically nonsense in the context of GR and especially for infinite universes or expanding universes.

Please not that not even the mass itself

$$M = \int_\text{Universe}d^3r\,\rho(\vec{r})$$

is a reasonable concept!

 

[petm1]

Each massive particle is a center connection to the visible universe, after all the connection was started when the universe was local to one clock, relative in time to my present.

 

[phinds]

Each massive particle is a center connection to the visible universe, after all the connection was started when the universe was local to one clock, relative in time to my present.

I have no idea what you are talking about, do you?

 

[petm1]

Right "now" in my present it is 1212 pm 17 December 13,700,002,011, give or take. At the beginning of this "time" our visible universe was local to one clock. Why do you think that one Hydrogen atom looks just like another, why can we use any point as a center of a frame of reference? Isn’t everything connected in time? Thanks to relativity we can plot our connection, using massive points, back to one point in time that appears as a singularity in space.

 

[phinds]

Well, at least this time I understood the first sentence. The rest of it is just words strung together as far as I can make out. I don't know you, don't want to be rude to you, but I really don't get that you're making any sense.

 

[SpecialKM]

I would assume: if the universe started out as a single point with infinite mass and infinite energy and expanded from that single point, that every point in space and time is 'the center'. This assumption, however, is just an assumption. Someone correct me if I am wrong.

 

[phinds]

I would assume: if the universe started out as a single point with infinite mass and infinite energy and expanded from that single point, that every point in space and time is 'the center'. This assumption, however, is just an assumption. Someone correct me if I am wrong.

You are wrong on both counts. First, there was no point and second if there had been a point then NOT every point would be the center.

 

[SpecialKM]

Well that's embarrassing, how did it occur then?

 

[phinds]

Well, the nature of the singularity itself is unknown. Basically "singularity" translates to "we don't know WHAT the heck that was all about", but the current cosomological model says that there was the unbelievably dense matter in an area that may or may not have been infinite but was definitely not a point and it was all of space and time.

Starting at 10E-43 seconds later (one Plank Time) it all started expanding and now there's us.

Read more at:

http://www.talkorigins.org/faqs/astronomy/bigbang.html

 

[tom.stoer]

... and expanded ... that every point in space and time is 'the center'. This assumption, however, is just an assumption. Someone correct me if I am wrong.

As I already said in post #13

In order to discuss the 'center of mass' one has to find a mathematical definition; the first proposal would be

$$\langle\vec{r}\rangle = \frac{1}{M}\int_\text{Universe}d^3r\,\vec{r}\,\rho(\vec{r})$$

which is mathematically nonsense in the context of GR and especially for infinite universes or expanding universes.

Please not that not even the mass itself

$$M = \int_\text{Universe}d^3r\,\rho(\vec{r})$$

is a reasonable concept!

Please note that the integrals above are not well-defined mathematically even if you avoid the singularity at 't=0'

http://relativity.livingreviews.org/Articles/lrr-2009-4/

 

[SpecialKM]

Well, the nature of the singularity itself is unknown. Basically "singularity" translates to "we don't know WHAT the heck that was all about", but the current cosomological model says that there was the unbelievably dense matter in an area that may or may not have been infinite but was definitely not a point and it was all of space and time.

Starting at 10E-43 seconds later (one Plank Time) it all started expanding and now there's us.

Read more at:

http://www.talkorigins.org/faqs/astronomy/bigbang.html

Ahh, It seems I've fallen into the common misconceptions category. Thanks for this!

 

[FifthEngineer]

Now us engineers know of and like to refer to a mass center.
Actually there is no need to bother with integrals in this respect. Refer to a center of the space if you feel more comfortable with it.

Put it another way, the universe is said to have been some X ligth years "across" some Y years after its birth (i do not recolect reasonable figures right now for the ensemble X,Y). One would suppose that it was a sphere of radius X/2.
The big question would be where is the center of that sphere now?

I know you will say that it was not necessarily a sphere, but then what was it?
And then again which is its current size? "Accross" or whatever formulation you prefer...

Of what I read this year after my last post I understood these - or at least i hope i do. There is little idea about the shape of the Universe; there is a large acception that it is flat (and hence it is not a sphere) but it is not unanimously.
There is no evidence about the size of the Universe.

But look here: we are definitey sure it does not have any kind of center.

As i put forward in the start, let alone the mass (which is sparse) and focus on the space itself (which is continuosly created by the expansion of the universe, right?). Whenever physicists integrate the Einstein general relativity equations they do some assumptions, one of which is that the space-time is a continuum.

Then there are only two more options:
Either the space is unbounded, or otherways put infinite; but then what is expanding, the infinite? And when did it got there in those mere 14 bny?

or

The space is bounded. Then certain integrals can be computed theoretically, and a center can be put out.

We simply know too little about it. Based solely on some common sense I think that the human will have the knowledge of a "center of universe" in the future. Based on the current knowledge, i would say this may come as late as 1000 years ahead.

Not that we could not wait that long as a specie.

PS I formulated all the above in the simple engineering friendly 3D understanding of reality. Do not add time in an asnwer - it would not do it for me, as long as no one proves there is no "instant state" of the whole universe. Do not add extra dimensions by no mean unless you have ALL the equations ready.

 

[FifthEngineer]

And another simple dumb question from a simple engineer. We see a galaxy say 10 billions LY from us, and another one say 2 or 5 billions LY from us.

By redshifts we can calculate that the farher one is speeding away from us much faster the the nearest one.

But when? Why is this a prove that the Universe is accelerating its expansion now, and not the other way around - it could be seen that galaxies farther away from us in time recede quicker.

Not to mention that we have no ideea about the other relative velocities than radial, not even for galaxies as near as Andromeda.

Honestly, these are just questions for a passionate theoretical physicist that could spare some time here. No debate here, and a human readable answer would be highly appreciated.

 

[phinds]

Now us engineers know of and like to refer to a mass center.

Indeed we do, and that knowledge applies very nicely to finite things. It does not apply to an infinite universe.

Put it another way, the universe is said to have been some X ligth years "across" some Y years after its birth (i do not recolect reasonable figures right now for the ensemble X,Y). One would suppose that it was a sphere of radius X/2.
The big question would be where is the center of that sphere now?

That is NOT said, at least not by any reputable physicists. It is unknown whether the universe was finite or infinite at its birth. I realize that the "birth" of something infinite doesn't seem to make sense. Welcome to cosmology. Whether it was infinite or finite it does NOT have to have a center and all bets currently are that it did not.

I know you will say that it was not necessarily a sphere, but then what was it?
And then again which is its current size? "Accross" or whatever formulation you prefer...

Unknown and presently unknowable.

Of what I read this year after my last post I understood these - or at least i hope i do. There is little idea about the shape of the Universe; there is a large acception that it is flat (and hence it is not a sphere) but it is not unanimously.
There is no evidence about the size of the Universe.

Good. We can agree on something.

But look here: we are definitey sure it does not have any kind of center.

Again we agree.

Then there are only two more options:
Either the space is unbounded, or otherways put infinite; but then what is expanding, the infinite? And when did it got there in those mere 14 bny?

unbounded and infinite are not the same thing. I'm not clear whether you understand that or not. There are unbounded finite models and unbounded infinite models. Infinite IS unbounded but unbounded is not necessarily infinite.

14 Billion Years is the time since the singulariy as measure by a clock that is comoving with the CMB

or

The space is bounded. Then certain integrals can be computed theoretically, and a center can be put out.

nonsense. Bounded, such as the surface of a sphere, most emphatically does NOT imply a center.

We simply know too little about it. Based solely on some common sense I think that the human will have the knowledge of a "center of universe" in the future. Based on the current knowledge, i would say this may come as late as 1000 years ahead.

If you are going to rely on "common sense" I suggest you stick to engineering. Cosmology and quantum mechanics will just frustrate you, since neither has anything much to do with common sense.

 

[bobc2]

What we humans know about the center of mass of Universe?

Do you have a particular universe model in mind? A particular model must be specified before commenting on its properties. For example, what if you had in mind something like this?

So, then you would need to tell us whether you are interested in the center of mass for a 4-dimensional universe or a 3-dimensional cross-section. Then, which 3-D cross-section? But if the 3-D world is a spherical hypersurface shell, then do you consider the universe embedded in higher dimensions or do you just consider intrinsic 3-D?

So, you must decide whether you're interested in the center of a spherical surface (restricting your search to the surface--not the interior) or else the hyperdimension center, i.e., go to the hyperdimensional interior of the shell (like looking at one of those globe maps of the world and going to the inside center of the globe).

Do you think you could find the center of the circumference of a circle (restricting your search to the circumference--not going to the interior center of the circle)? Nor could you find the center of a spherical surface (confining your search to the surface of the sphere). Nor could you find the center of a hyperdimensional spherical surface.

 

[Dale]

As i put forward in the start, let alone the mass (which is sparse) and focus on the space itself (which is continuosly created by the expansion of the universe, right?). Whenever physicists integrate the Einstein general relativity equations they do some assumptions, one of which is that the space-time is a continuum.

Then there are only two more options:
Either the space is unbounded, or otherways put infinite; but then what is expanding, the infinite? And when did it got there in those mere 14 bny?

or

The space is bounded. Then certain integrals can be computed theoretically, and a center can be put out.

This is correct only for flat spacetimes. You need to learn a little about curvature and manifolds if you hope to understand GR.

The surface of a sphere is a two dimensional space which is unbounded but finite.

An infinite plane can still expand by having all distances increase within the space.

You can calculate certain integrals theoretically over the space formed by the surface of a sphere, but, by symmetry, no point in the space has a better claim than another for being the center. The mere fact that you can calculate certain integrals doesn't mean that you can identify a specific point as being the center.

 

[tom.stoer]

FifthEngineer,

DaleSpam had the idea to focus on simpler examples. So let's see where we will get problems.

Think about a sphere (with two coordinates theta, phi), fixed radius R and mass density rho. Then we get for area A

$$A = \int_{S^2} d\Omega = 4\pi R^2$$

and mass M

$$M = \int_{S^2} d\Omega\,\rho$$

For constant mass density rho we get

$$M = A\rho$$

Now please try to find a definition and a derivation for the center of mass of the sphere.

Note that the embedding of the two-sphere in three-space is mathematically not required; that means that the center if mass of the sphere is NOT at r=0 but on the sphere itself (it would be nonsense to say that the center of mass of the universe is not located in the universe itself but somehere in the 5th dimension ;-)

 

[tom.stoer]

hint: for constant rho


$$\langle\vec{r}\rangle = \frac{1}{M}\int_{S^2}d\Omega\,\vec{r}\,\rho = \frac{\rho}{M}\int_{S^2}d\Omega\,\vec{r} = 0$$

which says that the c.o.m. is located 'at the center r=0'. But r=0 is not a point on any sphere S² for constant radius R, so there is no c.o.m. on S²! In some sense a c.o.m. does not exist. This fact is hidden by the embedding of S² in R³ which are used to. But such an embedding is meaningless when talking about the universe.

 

[bobc2]

hint: for constant rho


$$\langle\vec{r}\rangle = \frac{1}{M}\int_{S^2}d\Omega\,\vec{r}\,\rho = \frac{\rho}{M}\int_{S^2}d\Omega\,\vec{r} = 0$$

which says that the c.o.m. is located 'at the center r=0'. But r=0 is not a point on any sphere S² for constant radius R, so there is no c.o.m. on S²!

True.

In some sense a c.o.m. does not exist. This fact is hidden by the embedding of S² in R³ which are used to.

I'm with you so far.

But such an embedding is meaningless when talking about the universe.

I can understand that higher dimensions are not required (it is not necessary to think of the universe as embedded in higher dimensions). However, do you know of a reference that shows that this would necessarily be true (there is no possibility of higher dimensions)?

 

[tom.stoer]

However, do you know of a reference that shows that this would necessarily be true (there is no possibility of higher dimensions)?

No, I am not aware of such a result.

If the universe can be described (like in GR) as a four-dim. pseudo-Riemannian manifold with signature (-+++) and if it satisfies global hyperbolicity, then a global foliation in spacelike 3-manifolds is possible. The topology is then R*M³ where R corresponds to the 'timelike direction' and M³ are the Riemannian 3-manifolds (slices) with signature (+++). Omitting singularities like black holes in then makes sense to think about the embedding of the 3-manifolds M³ in higher dimensional spaces.

There do exist embeddings in higher-dimensional flat (Euclidean) manifolds which can be described using Nash's embedding theorems. But afaik that is w/o any physical relevance. I haven't seen any paper in physics discussing these embeddings.