BB theory and preferred frames

[Q-reeus]

...Hope this helps some, I'm not very good at explaining.

Not at all - I'm just a bit slow on all this. From what I recall deep space surveys show a filamentary type pattern of superclusters tending to be distributed at the boundaries of larger 'void' regions, a bit like bubble walls relative to a bubble froth. And that some cosmologists claim the voids are not much different in density once the supposed underlying 'dark matter' distribution is taken into account. On that view superclusters are a visible condensate much like clouds are in our atmosphere. But there are many competing models and I guess it gets back to explaining at what level CMBR dipole anisotropies should be absent. So is it the case that averaging over all redshifts in a supercluster, appreciable dipole anisotropies have been found to still exist wrt the supercluster center of mass? That I take it is what would define departure from absolute rest for a supersized observer. The other thing I vaguely recall that may relate was claims from some that the size scale of voids and filaments is too great to be naturally explained within a standard inflationary BB model, regardless of any relative motions of such.

 

[TrickyDicky]

But there are many competing models and I guess it gets back to explaining at what level CMBR dipole anisotropies should be absent. So is it the case that averaging over all redshifts in a supercluster, appreciable dipole anisotropies have been found to still exist wrt the supercluster center of mass? That I take it is what would define departure from absolute rest for a supersized observer.

I'm not sure what you mean here, but I don't think that kind of procedure is possible, but I'm no astrophysicist so I might be wrong or not understanding what you meant. The dipole we measure in the CMBR refers to our own peculiar motion wrt the CMB frame. The redshifts of distant objects we measure give us an estimated distance according to the Hubble law. Their state of motion from a certain distance is not reliably obtained due to the limitations GR imposes to curved manifolds.

The other thing I vaguely recall that may relate was claims from some that the size scale of voids and filaments is too great to be naturally explained within a standard inflationary BB model, regardless of any relative motions of such.

Yes there are claims that some of the voids and superclusters observed are too big to be compatible with the BB model, but that is a debate independent of the theoretical problem I raise.

 

[Q-reeus]

I'm not sure what you mean here, but I don't think that kind of procedure is possible, but I'm no astrophysicist so I might be wrong or not understanding what you meant. The dipole we measure in the CMBR refers to our own peculiar motion wrt the CMB frame. The redshifts of distant objects we measure give us an estimated distance according to the Hubble law. Their state of motion from a certain distance is not reliably obtained due to the limitations GR imposes to curved manifolds.

Was trying to figure out the standard procedure one would adopt to figure if a supercluster (or whatever defined supersized observer) was comoving wrt an assumed homogeneous BB Hubble flow. Had though one would work up in a heirarchical manner. We know our Earth centric dipole anisotropy, can figure from local redshift surveys the average motion wrt us within the galaxy, thence within the local cluster and so on. Otherwise I cannot see any other means for determining relative motion at such scales. All this assumes CMBR is the proper yardstick of course. Your remark about limitations owing to curved manifolds I guess is the spanner in the works here; had assumed that could be accounted for pretty well, but maybe not. Anyway I'm definitely no astophysicist/cosmologist!

 

[TrickyDicky]

Was trying to figure out the standard procedure one would adopt to figure if a supercluster (or whatever defined supersized observer) was comoving wrt an assumed homogeneous BB Hubble flow. Had though one would work up in a heirarchical manner. We know our Earth centric dipole anisotropy, can figure from local redshift surveys the average motion wrt us within the galaxy, thence within the local cluster and so on. Otherwise I cannot see any other means for determining relative motion at such scales. All this assumes CMBR is the proper yardstick of course. Your remark about limitations owing to curved manifolds I guess is the spanner in the works here; had assumed that could be accounted for pretty well, but maybe not. Anyway I'm definitely no astophysicist/cosmologist!

Yes that is the limitation, the "speeds" that are attributed to distant objects from their redshifts is based in the Hubble law that assumes they are comoving as valid approximation, so that state of motion estimation cannot be used to ascertain relative motion, it is instead used to assign distances for distant objects.

 

[PeterDonis]

Yes, I agree with this, and it is the way the model should be understood for the universe at scales below the homogeneity threshold size, without the need for any piece of matter in the fluid having to have the average density or move along the average worldline as you say. But I'm not sure if you agree that in the LCDM model there is a certain threshold of size at which homogeneity is no longer an approximation, if one really believes the universe has an average density.

I don't understand what you mean by a "homogeneity threshold"; I don't think there is one in the FRW model, and I don't see why there needs to be one. Average density is just that, an average: you take density numbers from different locations throughout the universe and average them. Increasing the size scale for the averaging just means increasing the spacing between the locations where you take the density numbers; ultimately, I guess, you could just pick some single random location in the universe, measure the density there, and call that the "average" density representing the entire universe. Of course that would be very inaccurate and we don't do that.

Even if you are more inclined to the fractal model (I don't know, I gather it from the way you refer to it) you should understand what is the case in the FRW model, that by the way is completely incompatible with the fractal model (in which to begin with there is no average density at all).

Huh? I can always take an average density over a spacelike slice in any model. The nature of the fluctuations from the average will be different for different models, but the average itself is always well-defined. I think you must be using the term "average density" to refer to something else.

But I'm not claiming that, the FRW model is compatible with a quasifractal-like matter distribution for small and intermediate size scales, but it demands that eventually the inhomogeneities must smooth out if a true average density is to be found.

The FRW model claims no such thing. Consider again an ordinary fluid. It is composed of atoms; but we average over those atoms to come up with macroscopic properties for the fluid like density. Are you saying that this implies that, over a large enough size scale, the atoms somehow turn into a continuous substance, instead of a bunch of individual atoms that are mostly empty space? The inhomogeneities of the fluid are what they are; changing the size scale over which we average does not change them at all.

My claim only affects objects of enough size so that homogeneity holds without approximation, those objects haven't been observed yet , but according to the FRW model they must exist -again the alternative is 0 average density, if the homogeneity threshold keeps getting bigger (in the limit at infinity).

Again, I don't understand what you are calling the "homogeneity threshold"; a similar argument applied to an ordinary fluid would imply, as I said just now, that above some size scale the fluid turns from a bunch of atoms into a continuous substance.

 

[TrickyDicky]

By average density I'm considering the universe average density.
I gues to go on with this discusion at the very least you must agree that according to LCDM model there must exist large-scale homogeneity, what I called the threshold is the specific scale at which the transition between the observed inhomogeneity switches to large-scale homogeneity. It has different implications if that homogeneity is observed at 50 Mpc, 100 , 200 Mpc or greater scales. At the moment there is debate with proponents of fractal cosmology claiming there is spatial inhomogeneity still at 100 Mpc/h scale according to SDSS data and mainstream cosmologists defending we can consider that scale as spatially homogeneous.

 

[PeterDonis]

according to LCDM model there must exist large-scale homogeneity, what I called the threshold is the specific scale at which the transition between the observed inhomogeneity switches to large-scale homogeneity.

I wouldn't say there is a "threshold"; the standard LCDM model does not require that inhomogeneities simply vanish above some length scale.

I think a better way of stating it would be that the standard LCDM model predicts that the magnitude of fluctuations of actual density about the average density should grow smaller as the length scale grows larger, for all length scales. To some extent this is clearly true; after all, on the length scale of the solar system we have densities some 30 orders of magnitude higher than the average density of the universe as a whole; and if we were in the vicinity of a neutron star the density would be some 15 orders of magnitude higher still. But on the scale of a galaxy, say, the density is nowhere near that large relative to the average--the average density in the Milky Way is something like one star per cubic light year, or about 10^30 kg per 10^48 cubic meters, or about 12 orders of magnitude higher than the average density of the universe.

The question is whether this pattern continues as we continue to increase length scales, or whether we reach some length scale where the fluctuations basically become scale-invariant, as in a fractal-type model. I agree this is an open question. It will be hard to resolve since we don't even know how much of the entire universe is visible in our observable universe.

 

[TrickyDicky]

I wouldn't say there is a "threshold"; the standard LCDM model does not require that inhomogeneities simply vanish above some length scale.

Say we had observed homogeneity at the 50 Mpc/h scale, shouldn't a supercluster with radius 70 Mpc be a comoving object with a fixed worldline perfectly orthogonal to the spacelike hypersurface, and no possibility to change its state of motion?

 

[PeterDonis]

Say we had observed homogeneity at the 50 Mpc/h scale, shouldn't a supercluster with radius 70 Mpc be a comoving object with a fixed worldline perfectly orthogonal to the spacelike hypersurface, and no possibility to change its state of motion?

No. At least, not unless you are going to *define* "observed homogeneity at scale x" to mean "every object larger than scale x must be comoving". But that's not the way an FRW-type model defines "homogeneity".

An FRW-type model *does* predict, I believe, that the average deviation of 70 Mpc superclusters from "comoving" motion should be less than, say, the average deviation of 7 Mpc clusters, which should in turn be less than the average deviation of 10 kpc galaxies. But I don't think it requires that the deviation absolutely vanish at any length scale.

 

[TrickyDicky]

No. At least, not unless you are going to *define* "observed homogeneity at scale x" to mean "every object larger than scale x must be comoving". But that's not the way an FRW-type model defines "homogeneity".

Ok, I see, at least identifying the specific point where we disagree is a good step IMO.
I'll try and see if I can find some citation supporting (or discarding) my notion of homogeneity and its consequences on the comoving frame. I would say it naturally follows from the homogeneity and isotropy assumptions.

An FRW-type model *does* predict, I believe, that the average deviation of 70 Mpc superclusters from "comoving" motion should be less than, say, the average deviation of 7 Mpc clusters, which should in turn be less than the average deviation of 10 kpc galaxies. But I don't think it requires that the deviation absolutely vanish at any length scale.

But this is equivalent to saying that homogeneity is never completely achieved, in other words I'd say this describes an inhomogeneous cosmology, not the FRW model.

 

[PeterDonis]

But this is equivalent to saying that homogeneity is never completely achieved, in other words I'd say this describes an inhomogeneous cosmology, not the FRW model.

I'm saying that homogeneity is not *required* to be completely achieved for an FRW model; what is required is that the actual inhomogeneities in the universe are small enough not to affect the dynamics. This is what the LCDM model, for example, actually assumes: not that homoegeneity is perfect above some size scale, but that the dynamics of the scale factor can be calculated, to a good approximation, *as if* homogeneity were perfect. An "inhomogeneous" cosmology would be one in which the model explicitly includes effects of inhomogeneity on the dynamics.

 

[Passionflower]

The FRW model obviously requires perfect homogeneity, it is afteral a model and a solution to the EFEs.

The question is really how much do we have to we divert from perfect homogeneity for the FRW model to become practically useless. And then the second question is, is our universe beyond that level or not.

 

[Dale]

Homogeneity of the dust does not require nor imply that the dust be stationary.

 

[TrickyDicky]

I'm saying that homogeneity is not *required* to be completely achieved for an FRW model; what is required is that the actual inhomogeneities in the universe are small enough not to affect the dynamics. This is what the LCDM model, for example, actually assumes: not that homoegeneity is perfect above some size scale, but that the dynamics of the scale factor can be calculated, to a good approximation, *as if* homogeneity were perfect. An "inhomogeneous" cosmology would be one in which the model explicitly includes effects of inhomogeneity on the dynamics.

What I'm saying has nothing to do with what you seem to be confusingly saying.
When I talk about the large-scale homogeneity that is observed at certain scale threshold I refer to something much simpler than that, and that I would say everyone with certain acquaintance with cosmology understands.
From WP:"The End of Greatness is an observational scale discovered at roughly 100 Mpc (roughly 300 million lightyears) where the lumpiness seen in the large-scale structure of the universe is homogenized and isotropized as per the Cosmological Principle."
http://en.wikipedia.org/wiki/Large-scale_structure_of_the_cosmos#Large-scale_structure
This is of course an averaging process, but it allows us to say that a hypothetical object of that size should have comoving motion and therefore gives us a reference any other motion state can refer to. It would only have a recessional motion due to expansion but no peculiar velocity. In other words the CMB comoving frame is precisely related to the homogeneity of the matter distribution in our universe and it would not be relative in as much as spatial homogeneity is not something relative but an absolute property of the matter distribution. The FRW comoving frame and expansion are precisely built upon the spatial homogeneity assumption(this homogeneity being of course an average and allowing thus certain inhomogeneity at small scales) .

 

[TrickyDicky]

Homogeneity of the dust does not require nor imply that the dust be stationary.

What are you referring to as dust? If you refer to domestic dust you're certainly right, then again domestic dust is not demanded to be homogeneous by the FRW model.
In the FRW model dust refers to objects of a scale such as they only show recessional motion from expansion, that is no peculiar velocities and therefore stationary wrt the comoving frame.

 

[Dale]

What are you referring to as dust?

The standard meaning of dust in GR models is a perfect fluid where the particles interact only gravitationally.

As PeterDonis said above, the fact that a fluid is at rest does not imply that every particle in the fluid is at rest. Do you understand that concept for fluids?

Similarly, a static dust does not imply that the individual dust particles are at rest.

 

[TrickyDicky]

The standard meaning of dust in GR models is a perfect fluid where the particles interact only gravitationally.

As PeterDonis said above, the fact that a fluid is at rest does not imply that every particle in the fluid is at rest. Do you understand that concept for fluids?

Similarly, a static dust does not imply that the individual dust particles are at rest.

Wow, you do master looking up words in wikipedia!

 

[PeterDonis]

This is of course an averaging process, but it allows us to say that a hypothetical object of that size should have comoving motion and therefore gives us a reference any other motion state can refer to.

If we're only talking about hypothetical objects, then of course there's no argument. But there is no requirement that any actual object, that we can actually observe, has exactly the same worldline as any of these hypothetical objects.

In other words the CMB comoving frame is precisely related to the homogeneity of the matter distribution in our universe and it would not be relative in as much as spatial homogeneity is not something relative but an absolute property of the matter distribution.

Agreed, in our actual universe the CMB provides a physical reference for determining whether a given worldline is comoving: observers moving on comoving worldlines see the CMB as isotropic. And the FRW model does not require that any actual object actually move exactly on such a worldline; i.e., it is not required that any actual observers see the CMB as exactly isotropic. All that is required is that whatever deviations from this motion exist are small enough not to affect the overall dynamics of the universe as a whole.

 

[Dale]

Wow, you do master looking up words in wikipedia!

Yes, that's why I don't have to ask questions that are answered in Wikipedia.

 

[TrickyDicky]

If we're only talking about hypothetical objects, then of course there's no argument. But there is no requirement that any actual object, that we can actually observe, has exactly the same worldline as any of these hypothetical objects.



Agreed, in our actual universe the CMB provides a physical reference for determining whether a given worldline is comoving: observers moving on comoving worldlines see the CMB as isotropic. And the FRW model does not require that any actual object actually move exactly on such a worldline; i.e., it is not required that any actual observers see the CMB as exactly isotropic. All that is required is that whatever deviations from this motion exist are small enough not to affect the overall dynamics of the universe as a whole.

Sorry about the late reply, the holiday's uproar kept me busy. (Happy new year's eve by the way!).

It's great you agree with the core of my posts, besides I'm not saying that any actual object or observer is required to have that exact motion only and eternally (for one, no object of that size is required to exist by any law), so we agree about that too.
But I think you get the drift of the conceptual linking I'm trying to stress here between uniform matter distribution comoving frames and absolute velocity.
Because a simple way to obtain absolute motion or velocity is to have as assumption that the spatial distribution of matter be homogeneous or uniform and the same in all directions (isotropic),since by the very definition of (average) velocity as space/time, and given that having the in average equally spaced matter assumption and that all velocities (distances) are in reference to matter, well it seems straightforward that assuming this special matter distribution inmediately gives us a way to define the concept of absolute average speed for the comoving frame (that has synchronous time and must observe the universe as exactly homogeneous and isotropic) in the spatially homogeneous universe: An observer with absolute uniform velocity is the one that is able to perceive exactly the uniform and isotropic matter distribution of our universe so that in average it measures the same distances in the same times between material landmarks.
Of course for all observers that move in reference to inhomogeneous matter at smaller scales they can have different velocities, but all those velocities can be referenced to the absolute velocity and objects at rest wrt the CMB frame are obliged to have an absolute uniform velocity wrt the spatial distribution of matter that is special to the FRW universe.

This would seem to me that is the very thing that the principle of relativity forbids but according to the brilliant Dalespam is not. So everything is fine.

 

[Dale]

a simple way to obtain absolute motion or velocity is to have as assumption that the spatial distribution of matter be homogeneous or uniform and the same in all directions (isotropic),

That is not what is meant by "absolute velocity" in relativity. What is meant by "absolute velocity" is that the principle of relativity is violated, or in other words, that the laws of physics are different in different frames.

Mount Everest is tautologically at rest in Mount Everest's rest frame, but the laws of physics are not different in a frame where Mount Everest is moving. Therefore Mount Everests' rest frame does not constitute an absolute rest frame.

The CMB is tautologically at rest in the FRW coordinates, but the laws of physics are not different in a frame where the CMB is moving. Therefore the CMB frame does not constitute an absolute frame.

If you want to show that the CMB represents an absolute rest frame it is not sufficient to show that the CMB is at rest in some coordinate system nor even that some class of observers is at rest in that same frame, it is necessary to show that the laws of physics are different in that rest frame. That is impossible, I refer you again to post 3.

 

[TrickyDicky]

That is not what is meant by "absolute velocity" in relativity. What is meant by "absolute velocity" is that the principle of relativity is violated, or in other words, that the laws of physics are different in different frames.

Just what I said in the last line of my post.
The laws of physics are generally considered as absolute and universal, and in that case no possible violation of the principle of relativity as you quote it s permitted by definition, turning the principle of relativity into a true tautology. To avoid ambiguities you should define clearly what a physical law is and what constitutes something that in your opinion counts as a difference in a physical law.

Mount Everest is tautologically at rest in Mount Everest's rest frame, but the laws of physics are not different in a frame where Mount Everest is moving. Therefore Mount Everests' rest frame does not constitute an absolute rest frame.

The CMB is tautologically at rest in the FRW coordinates, but the laws of physics are not different in a frame where the CMB is moving. Therefore the CMB frame does not constitute an absolute frame.

If you want to show that the CMB represents an absolute rest frame it is not sufficient to show that the CMB is at rest in some coordinate system nor even that some class of observers is at rest in that same frame, it is necessary to show that the laws of physics are different in that rest frame. That is impossible, I refer you again to post 3.

You have some kind of obsession with tautologies, I wish you well wrt that. Also, you need to address what is actually said in the post you reply to, not what you imagine was said.

 

[Dale]

To avoid ambiguities you should define clearly what a physical law is and what constitutes something that in your opinion counts as a difference in a physical law.

Fair enough. What would count as a difference in a physical law in different frames would be a term in the physical law which depends on the reference frame.

In the case of GR the physical law is the EFE, which contains no term depending on the reference frame. Therefore, anything which is a solution to the EFE (e.g. the FRW metric) cannot depend on the reference frame.

 

[TrickyDicky]

Fair enough. What would count as a difference in a physical law in different frames would be a term in the physical law which depends on the reference frame.

In the case of GR the physical law is the EFE, which contains no term depending on the reference frame. Therefore, anything which is a solution to the EFE (e.g. the FRW metric) cannot depend on the reference frame.

That's my point, no absolute frame is possible for the EFE solutions. Therefore no event can be assigned to a certain "absolute" date.

 

[Dale]

That's my point, no absolute frame is possible for the EFE solutions. Therefore no event can be assigned to a certain "absolute" date.

I agree.

You can, however, adopt any convention that is convenient and use it to assign dates to events. That is all the time coordinate in the FRW metric is.