What does homogeneity mean (in the cosmological context)?

[Lino]

First, I must stress that I am not asking this question in relation to the proof, or disproof, of any form of rotating Universe. I am only asking in order to understand the meaning of “homogeneity” in the cosmological context.

Secondly, I know that there are many threads that reference homogeneity, some asked by myself, and I thank everyone for your previous comments and answers. However, I don’t think a question from this perspective has been addressed (or at least I couldn’t find it).

Consider a model of the Universe, like a basic spiral galaxy (isotrophic, no black holes, no other complications) – again, I am not suggesting that this model is valid, I just want to use the model to frame a question. From my God-like perspective I can see the centre of rotation and therefore I know that the model is not homogenous. However, if I reside within the model, at any point – centred or off-centre – I see the motion of other objects in the Universe relative to me, so things appear to rotate around me (kind-of-like Earth in pre-Copernican days), and so this is homogenous (I think).

So my question is: which perspective is correct (in relation to the way the word homogenius is used in a cosmological context)?


Thanks, in anticipation, for all your help,


Noel.

 

[bcrowell]

Homogeneity means that the properties of the universe are the same at every point in space, at a given time (with time measured this way: https://www.physicsforums.com/showthread.php?t=506990 ).

Rotation in general relativity is different from rotation in Newtonian mechanics. You can have rotation in GR with no center of rotation.

Have you looked at our FAQ on rotation of the universe? https://www.physicsforums.com/showthread.php?t=506988

-Ben

 

[Lino]

Thanks Ben.

In relation to rotation, between GR, papers on max value for angular rotation, deSitter space, etc., I still have a lot that I'm trying to get through. I continue to revert to the FAQ to help work through the logic ... and ... I am getting there, but very, very slowly! But all references are, as always, greatly appreciated (thanks again).

In relation to homogeneity, thanks for the reference to the thread on measurement of time / distance, but I'll have to spend some time thinking about this. I was trying to use as simple a model as possible, but obviously, time / distance still have an impact so I will have to work through that.

If you forget about the model that I mentioned, at a very basic level, my question is: when homogeneity is measured ("... properties ... are the same at every point ...") does it matter if the observer is within the space, or not?


Regards,


Noel.

 

[Cosmo Novice]

If you forget about the model that I mentioned, at a very basic level, my question is: when homogeneity is measured ("... properties ... are the same at every point ...") does it matter if the observer is within the space, or not?


Regards,


Noel.

Hello Noel,
Is this what you are trying to ask:

Does homogeneity exist only when veiwed from within the homogeneous space/time manifold - by extension if you were to view the space/time manifold not from within itself - would it still be homogeneous and isotropic?

I think the questin is unanswerable and to me a little bit invalid, but was this what you are trying to ask?
Is that correct?

 

[WannabeNewton]

If you forget about the model that I mentioned, at a very basic level, my question is: when homogeneity is measured ("... properties ... are the same at every point ...") does it matter if the observer is within the space, or not?


Regards,


Noel.

Homogeneity is an intrinsic property of the manifold. The thing is, in GR we don't assume or even think of space - time as being embedded in higher - dimensional space. Any and all measurements must be made in the 4 - manifold in question such as that representing the observable universe. I don't know if this is what you meant by "within space".

 

[Cosmo Novice]

Homogeneity is an intrinsic property of the manifold. The thing is, in GR we don't assume or even think of space - time as being embedded in higher - dimensional space. Any and all measurements must be made in the 4 - manifold in question such as that representing the observable universe. I don't know if this is what you meant by "within space".

I think that's exactly what he meant.

 

[Chalnoth]

Here's the definition of homogeneity that I like:

There exists a set of observers at different points in space that see the same average properties of the universe (e.g. density, expansion rate).

 

[Lino]

Thanks everyone.

Cosmo Novice & WannabeNewton, I think that's what I meant ... it sounds right, but I'm afraid I'm not sure that I understand it ... yet. I'll work on it and get there.

Chalnoth, That's exactly the (type of) definition that started me off on this train of thought! I'm trying to work the other elements (mentioned by other people) into this but it seems there are many folds on the journey!

 

[Lino]

I think that I understand the basics.

GR Homogenity: a set of observers at different points in space that see the same average properties of the universe (e.g. density, expansion rate), an intrinsic property of the manifold ... [not] embedded in higher - dimensional space. Therefore it doesn't make sense to ask the "outside" question. Is that correct?

Are there any non-GR models that allow (?again forgive the clumsy language?) the "outside" question ... just in the theoritical sense?

Regards,

Noel.

 

[Chalnoth]

Are there any non-GR models that allow (?again forgive the clumsy language?) the "outside" question ... just in the theoritical sense?

Sorta kinda. In string theory, one possibility (among many) is that the 4 dimensions of space-time that we observe are a 4-dimensional brane that moves in some higher-dimensional space. There are, in principle, other directions of motion than forward/backward, up/down, left/right, but we can't move in those directions because we are stuck on this brane. In that sense, there could be a very real "outside" of our universe, it's just that we could never point in that direction (in the same way you can't draw an arrow on a piece of paper that points out of the piece of paper).

 

[Tanelorn]

This is probably too much to ask but is it possible to write down all the properties of the universe in order that the universe could be decribed as homogeneous (and isotropic)? and perhaps also a range of values for these properties which would still satisfy the definition of homogeneity?

 

[Chalnoth]

This is probably too much to ask but is it possible to write down all the properties of the universe in order that the universe could be decribed as homogeneous (and isotropic)? and perhaps also a range of values for these properties which would still satisfy the definition of homogeneity?

Total matter density and spatial curvature. That's about it. There are other things we strongly believe are the same from place to place (e.g. dark energy density, baryon/dark matter ratio, primordial helium abundance), but dark + baryon matter density combined with spatial curvature are the only ones that have much of a chance of actually varying from place to place.

 

[Lino]

Wow! The last couple of posting are very deep ... and interesting. I'll have to send sometime on it.

In the meantime, thanks again for everyones help.

Regards,

Noel.

 

[Tanelorn]

Thanks Chalnoth