BB theory and preferred frames

[my_wan]

Not only that but if the data does not match up there is always invisible dark energy and invisible dark matter that comes to the rescue.

That that is equivalent to insisting that a theory is right but that the discrepancies are caused by invisible pink unicorns is something that seems to go right over the heads of many.

If the CERN-Grasso experiment turns out to be correct I would not be surprised that it is posed that the theory still stands but that the discrepancies are caused by undetectable dark spacetime fluxes or something like it, with the key being that it must be undetectable.

The dark matter/energy issue is not that big a deal to me. Unknowns are a part of science. On the face of it, it's really no worse than MOND, which pulls a form fitted to specs equation out of their... What bugs me about MOND is that if it was simply designed to specs to fit a certain empirical data curve why is it so effective with such a large variety of disparate data on so many scales? So MOND suffers from a similar non-explanation. Yet the dark matter people can't justifiable just hand wave and simply say there's no point in answering this because we already know it's wrong without looking! So the whole thing just reaks of a battle of models rather than how to actually ask real questions.

As far as the CERN-Grasso experiment, I wouldn't hold my breath. But hey, at least their asking rather than defending a model turf.

 

[TrickyDicky]

Not only that but if the data does not match up there is always invisible dark energy and invisible dark matter that comes to the rescue.

That that is equivalent to insisting that a theory is right but that the discrepancies are caused by invisible pink unicorns is something that seems to go right over the heads of many.

If the CERN-Grasso experiment turns out to be correct I would not be surprised that it is posed that the theory still stands but that the discrepancies are caused by undetectable dark spacetime fluxes or something like it, with the key being that it must be undetectable.

Good points.

 

[Dale]

Well, certainly, my observers are not physical, this is more like a gedanken experiment, very often observers are considered massless and nobody sees any problem with that.

Never massless, that would require them to follow null geodesics. They are practically always considered massive with negligible mass and negligible spatial extent. In fact, I have never seen anyone besides you speak of observers with non-negligible mass in the FRW spacetime.

I think you are missing the important point, their velocity, their motion, is absolute.

Agreed, except for the assertion that it is an important point.

Btw, there is no need to do anything other than say "comoving observers". The velocity and motion of standard comoving observers is also tautologically absolute. Just as with your super-massive observers in the exact FRW spacetime, but without requiring either exactness in the metric nor your unusual usage of the term "observer".

That is not related to whether they are free to do calculations in any frame , the fact is that their state of motion is fixed.

Their state of motion is indeed fixed as one of the givens in your setup. So what?

The point is that as you agree, they can do their physics calculations in any frame using any simultaneity convention and obtain correct predictions of the results of any physics experiments without changing the form of the equations. If simultaneity were absolute then this would not be possible, the only way to get correct physics predictions would be to do your calculations using the absolute simultaneity coordinate system. That is what is meant by absolute simultaneity.

Also the fact that a model is a solution of the EFE doesn't guarantee that the model is physical, and it only guarantees general covariance, not Lorentz covariance which is what here is being discusses.

What is being discussed is absolute simultaneity. General covariance guarantees an even more general form of the relativity of simultaneity than Lorentz covariance.

 

[TrickyDicky]

The FRW solution is a spacetime that is assumed to be an approximate model of our spacetime.
I have serious reservations about that since we clearly do not see the matter distribution as homogeneous and isotropic. The assumption that it is homogeneous and isotropic on a large enough scale it is I think is sheer speculation. Matter clutters due to gravity even at large scales.

I see what you mean here and it is in part what suggested me the scenario I present for the hypothetical scale in which matter distribution is perfectly homogeneous as the LCDM model based in the FRW solution expects. But there's where some problems arise,objects of that scale size (hyperclusters to name them some way) must have a fixed or stationary state of motion(perfect comoving frame of the FRW model) if the homogeneity of the model is to be taken seriously, so they can act as a stationary reference for all other moving objects. Certainly so fa rwe haven't observed that kind of homogeneity, the clusters we observe are still colliding (i.e. Bullet cluster), but according to the LCDM model we should be very close to observing the scale at which true homogeneity appears. How is the problem above mentioned avoided?

 

[TrickyDicky]

Never massless, that would require them to follow null geodesics. They are practically always considered massive with negligible mass and negligible spatial extent. In fact, I have never seen anyone besides you speak of observers with non-negligible mass in the FRW spacetime.

Actually that is what I meant, sorry about my clumsy wording, I was referring to negligible mass and extent.

Agreed, except for the assertion that it is an important point.

Well, importance is something subjective, I can't expect you to find important the same things I do.

Btw, there is no need to do anything other than say "comoving observers". The velocity and motion of standard comoving observers is also tautologically absolute. Just as with your super-massive observers in the exact FRW spacetime, but without requiring either exactness in the metric nor your unusual usage of the term "observer".

I've been trying to stress at all times the size, not the mass, and there is a reason for that , I was trying to be graphic in this sense because I wanted to relate my set up with the realcosmological search of the homogeneity scale.
Otherwise you are right that I could have said just comoving observers or better comoving objects, the diference is in the homogeneous or inhomogeneous context. Objects comoving that have the size at which homogeneity is found can only have that state of motion, that is not the case for the other smaller comoving objects.

Their state of motion is indeed fixed as one of the givens in your setup. So what?

So what? I take that question as funny understatement.

The point is that as you agree, they can do their physics calculations in any frame using any simultaneity convention and obtain correct predictions of the results of any physics experiments without changing the form of the equations. If simultaneity were absolute then this would not be possible, the only way to get correct physics predictions would be to do your calculations using the absolute simultaneity coordinate system. That is what is meant by absolute simultaneity.

I didn't agree that they should obtain "correct" results

What is being discussed is absolute simultaneity. General covariance guarantees an even more general form of the relativity of simultaneity than Lorentz covariance.

This is just not correct, I'll find you a reference.

 

[TrickyDicky]

The first and the fourth papers in this site are relevant.

http://www.tc.umn.edu/~janss011/

 

[Dale]

I've been trying to stress at all times the size, not the mass,

If you are talking about super-large but negligible-mass then there is no reason that they need to be comoving. The size is irrelevant, only the mass (or rather stress-energy). Large, negligible mass observers may move without disrupting the isotropy and homogeneity of the FRW metric.

I didn't agree that they should obtain "correct" results

As long as the laws of physics can be formulated in a covariant manner they will.

 

[TrickyDicky]

If you are talking about super-large but negligible-mass then there is no reason that they need to be comoving. The size is irrelevant, only the mass (or rather stress-energy). Large, negligible mass observers may move without disrupting the isotropy and homogeneity of the FRW metric.

No, I'm not considering their mass negligible, only saying that size was important because of the homogeneity issue, when I previously spoke about negligible mass I was clarifying my previous comment on people using unphysical "massless" observers that was (rightly) corrected by you.

As long as the laws of physics can be formulated in a covariant manner they will.

Nope, you are ignoring my last post and the last comment in the previous post, you are mixing Lorentz covariance with general covariance, the former is not guaranteed by being a solution of the EFE. To be more precise Lorentz covariance is only guaranteed by general covariance at infinitesimal size points. See post #10 in this https://www.physicsforums.com/showthread.php?p=3679704#post3679704

 

[Dale]

No, I'm not considering their mass negligible, only saying that size was important because of the homogeneity issue

The size is not important, only the mass (stress-energy). Consider, for example, an observer consisting of a black hole containing 90% of the mass of the universe. The size is negligible, but due to the immense mass the homogeneity and isotropy of the FRW spacetime is clearly violated. Consider, for a second example, an observer of immense hyper-cluster size of mass 1 mg. Such an observer would not distort the FRW spacetime at all, despite being hyper-cluster size. The size is not important, only the stress-energy.

you are mixing Lorentz covariance with general covariance, the former is not guaranteed by being a solution of the EFE. To be more precise Lorentz covariance is only guaranteed by general covariance at infinitesimal size points. See post #10 in this https://www.physicsforums.com/showthread.php?p=3679704#post3679704

I agree, but again, that is not what we have been discussing. We are discussing absolute and relative simultaneity, which is a feature of Lorentz covariance. Although you cannot do a global Lorentz transform* in a curved spacetime you can do essentially arbitrary changes in simultaneity in general diffeomorphisms. Thus the relativity of simultaneity is also a feature of general covariance. So proving general covariance is sufficient to prove relativity of simultaneity.

*Actually, you can do a global Lorentz transform on any set of coordinates where all four coordinates range from -∞ to ∞. However, unless the spacetime is flat the components of the metric will change.

 

[TrickyDicky]

The size is not important, only the mass (stress-energy). Consider, for example, an observer consisting of a black hole containing 90% of the mass of the universe. The size is negligible, but due to the immense mass the homogeneity and isotropy of the FRW spacetime is clearly violated. Consider, for a second example, an observer of immense hyper-cluster size of mass 1 mg. Such an observer would not distort the FRW spacetime at all, despite being hyper-cluster size. The size is not important, only the stress-energy.

I keep saying this is not about distorting or violating the FRW model but about sticking to it.
Size (or scale) is strictly a deman of reality, at the scales we observe there is no homogeneity, but the current mainstream model expects it at bigger scales, that is why size is important in the FRW model set up.
OTOH, if you really think super massive BH's clearly violate the FRW spacetime you are not in line with mainstream cosmology, unless you believe BHs don't exist since they haven't been observed. In which case you are also not mainstream anyway.

Sure, but again, that is not what we have been discussing. We are discussing absolute and relative simultaneity, which is only one feature of Lorentz covariance. Although you cannot do a global Lorentz transform in a curved spacetime you can do essentially arbitrary changes in simultaneity in general diffeomorphisms. Thus the relativity of simultaneity is also a feature of general covariance and proving general covariance is sufficient to prove relativity of simultaneity.

Simultaneity of relativity is a feature of SR, and is realized in GR locally (at infinitesimal points), a cluster is not an infinitesimal point.
Besides the fact that there is absolute simultaneity for a class of observers doesn't mean that there isn't relativity of simultaneity for the rest of observers.

 

[Dale]

I keep saying this is not about distorting or violating the FRW model but about sticking to it.

Right, and as long as you do not distort or violate FRW then you are sticking to it.

Size (or scale) is strictly a deman of reality, at the scales we observe there is no homogeneity, but the current mainstream model expects it at bigger scales, that is why size is important in the FRW model set up.

Scale is important in the assumption of homogeneity, but size is irrelevant for specifying a class of observers.

Remember, your goal with that stipulation was merely to obtain a class of observers where it was logically necessary that they be comoving. If you have observers that are super-large but of negligible mass then they need not be comoving, and their motion will not distort FRW.

Simultaneity of relativity is a feature of SR

It is not exclusive to SR, as I have already described.

TrickyDicky, we are going in circles. In post 5 you agreed with my post 4. Therefore, the big bang does not imply a preferred frame nor absolute simultaneity. QED.

In the intervening posts you have introduced a lot of unnecessary concepts. With all of these irrelevancies bouncing around in your mind I am not surprised that you are confused, but I don't think that there is anything I can do about it. All I can say is that the schizophrenia you worry about is in your head, not in GR.

 

[TrickyDicky]

Right, and as long as you do not distort or violate FRW then you are sticking to it.

Scale is important in the assumption of homogeneity, but size is irrelevant for specifying a class of observers.

Remember, your goal with that stipulation was merely to obtain a class of observers where it was logically necessary that they be comoving. If you have observers that are super-large but of negligible mass then they need not be comoving, and their motion will not distort FRW.

It is not exclusive to SR, as I have already described.

TrickyDicky, we are going in circles. In post 5 you agreed with my post 4. Therefore, the big bang does not imply a preferred frame nor absolute simultaneity. QED.

In the intervening posts you have introduced a lot of unnecessary concepts. With all of these irrelevancies bouncing around in your mind I am not surprised that you are confused, but I don't think that there is anything I can do about it. All I can say is that the schizophrenia you worry about is in your head, not in GR.

Hilarious reply, (I agreed in post 4 so QED) if a bit pathetic and completely devoid of physics.

Thanks. Hopefully peter donis or someone else could look into this.

 

[Q-reeus]

I see what you mean here and it is in part what suggested me the scenario I present for the hypothetical scale in which matter distribution is perfectly homogeneous as the LCDM model based in the FRW solution expects. But there's where some problems arise,objects of that scale size (hyperclusters to name them some way) must have a fixed or stationary state of motion(perfect comoving frame of the FRW model) if the homogeneity of the model is to be taken seriously, so they can act as a stationary reference for all other moving objects. Certainly so fa rwe haven't observed that kind of homogeneity, the clusters we observe are still colliding (i.e. Bullet cluster), but according to the LCDM model we should be very close to observing the scale at which true homogeneity appears. How is the problem above mentioned avoided?

TrickyDicky; Most of the GR jargon in this thread is over my head, but am I right in supposing the above distills your key issue - FLRW/BB model is somehow wrong because homogeneity should be evident at the supercluster scale indicated, but observationally isn't? So is this suggesting say a fractal cosmology model as nearer the truth, or something else (or I've misunderstood the issue)?

 

[TrickyDicky]

TrickyDicky; Most of the GR jargon in this thread is over my head, but am I right in supposing the above distills your key issue - FLRW/BB model is somehow wrong because homogeneity should be evident at the supercluster scale indicated, but observationally isn't? So is this suggesting say a fractal cosmology model as nearer the truth, or something else (or I've misunderstood the issue)?

Not exactly, I'm just trying to expose a problem that might arise with a key prediction of FRW/BB model, not judging it in terms of wrong vs. correct model.
The homogeneity at large scales is hard to discern with the observational data at this moment with some groups claiming it has already been reached and other groups (those who suggest a fractal cosmology model) saying it hasn't indeed been observed based in a different statistical treatment of redshift data and slightly different definition of the cosmological principle (see for instance http://arxiv.org/abs/1012.5624).
I see problems with the fractal cosmology, the main one that it doesn't really have a solid mathematical and physical model that is consistent with what we already know (GR).
I'm basically following strictly FRW/BB model (not interested right now in debating whether empirically we have observationally reached the homogeneity scale or not or if in my opinion such transition occurs at some point) and showing how this key prediction produces some problem related to the existence of an absolute frame of motion for objects of the size at which the homogeneity is reached and bigger, they define an stationary frame,they are perfect comoving objects (invariant in time since they can't change their motion or else homogeneity is not achieved) all the smaller objects can refer their motion to.
It's just this, it might be solved easily because maybe I'm missing something very obvious, but so far no one has come up with it.

 

[Q-reeus]

I'm basically following strictly FRW/BB model...and showing how this key prediction produces some problem related to the existence of an absolute frame of motion for objects of the size at which the homogeneity is reached and bigger, they define an stationary frame,they are perfect comoving objects (invariant in time since they can't change their motion or else homogeneity is not achieved) all the smaller objects can refer their motion to.

As I understand it in a truly homogeneous BB universe, every point can be considered 'the centre', and uniform Hubble expansion about it follows. But that being true for any location, neglecting 'real universe' inhomogeneities of density and peculiar velocities, I'm not getting this bit about absolute motion/rest beyond a certain scale. Assuming this is not an averaging issue of some sort, is there a specific scenario of what it would mean to be otherwise? Sorry for dumb question - this absolute rest thing is throwing me.

 

[TrickyDicky]

As I understand it in a truly homogeneous BB universe, every point can be considered 'the centre', and uniform Hubble expansion about it follows. But that being true for any location, neglecting 'real universe' inhomogeneities of density and peculiar velocities, I'm not getting this bit about absolute motion/rest beyond a certain scale. Assuming this is not an averaging issue of some sort, is there a specific scenario of what it would mean to be otherwise? Sorry for dumb question - this absolute rest thing is throwing me.

Ok, the thing is FRW model demands spatial homogeneity as one of its main assumptions (along with isotropy), to make more precise those assumptions a set of fundamental observers are introduced to define better mathematically how that homogeneity must be understood , that is to make clear it must be only spatial and therefore define a synchronous coordinate time. These observers have a state of motion (comoving frame) that allows them to define the flow of the cosmological fluid (the Hubble flow) as being at rest wrt them.
Obviously the FRW model is an idealized model, and we don't observe homogeneity at the scale size of the solar system or galaxies. When this model was proposed in the 30's galaxies as differentiated entities had just been confirmed by Hubble. At the beginning it was thought that the scale of homogeneity would be at the galactic group, so it came as a surprised when progress in technology allowed us to make cosmological maps of certain size in the 70s/80s that ever bigger clusters and voids without appearance of homogeneity were found. Nevertheless the model needs that homogeneity to be reached at some point.
To give an example if we had found it at the clusters level that would have meant these clusters should be following perfect worldlines orthogonal to the spatial hypersurfaces, so no collision like the Bullet cluster would be possible. It would also mean clusters and any bigger object, couldn't change their state of motion in time, so they would define a sort of stationary absolute frame that all the rest of smaller objects with the capacity of changing state of motion could use as reference.
Hope this helps some, I'm not very good at explaining.

 

[PeterDonis]

Obviously the FRW model is an idealized model, and we don't observe homogeneity at the scale size of the solar system or galaxies. When this model was proposed in the 30's galaxies as differentiated entities had just been confirmed by Hubble. At the beginning it was thought that the scale of homogeneity would be at the galactic group, so it came as a surprised when progress in technology allowed us to make cosmological maps of certain size in the 70s/80s that ever bigger clusters and voids without appearance of homogeneity were found. Nevertheless the model needs that homogeneity to be reached at some point.

One thing to point out here: it is possible that, even if the universe today is *not* homogeneous enough to make an FRW model a useful approximation, it may still have been in the past. For example, the isotropy of the CMBR indicates that at the time of "last scattering", the universe was homogeneous to about one part in 100,000. So it could still be that an FRW model would be a good approximation for some portion of the universe's history, even if it isn't for the current universe. A full model could then "patch" an FRW model for the portion of the universe's history where it was a good approximation, onto something else like a fractal model for later times when the size of structures had become large enough to make homogeneity no longer a good approximation even on large scales.

To give an example if we had found it at the clusters level that would have meant these clusters should be following perfect worldlines orthogonal to the spatial hypersurfaces, so no collision like the Bullet cluster would be possible.

Another thing to point out: even if homogeneity is a good approximation on the largest scales, that does not mean that any actual objects we observe have to be comoving. All that is required is that the *average* motion of the actual objects we observe is comoving. The FRW model treats the matter in the universe as a fluid, with the objects we actually observe viewed as "particles" of the fluid. The average motion of a fluid does not have to match up exactly with the individual motion of any of its particles.

 

[TrickyDicky]

even if homogeneity is a good approximation on the largest scales, that does not mean that any actual objects we observe have to be comoving. All that is required is that the *average* motion of the actual objects we observe is comoving. The FRW model treats the matter in the universe as a fluid, with the objects we actually observe viewed as "particles" of the fluid. The average motion of a fluid does not have to match up exactly with the individual motion of any of its particles.

The problem with this is that an inhomogeneity to homogeneity transition scale cannot be reached as an average, it is either there (spatially homogeneous model) or not there (spatially inhomogeneous model), and if it's there, like the FRW model demands, the scale at which the transition occurs is not an average, there will be objects above that scale size which will be obliged to have a certain motion state without possibility of changing it, they will be following the worldlines exactly orthogonal to spacelike hypersurfaces and therefore they'll define an apparently absolute frame for all objects under that size.

Of course there is a backdrop problem in all this, GR only deals with "test particles" when talking about motion, so I'm not sure this can even be treated properly within GR since my comoving objects are huge, i.e. their extent and stress-energy can't be neglected the way is demanded in GR.

 

[PeterDonis]

The problem with this is that an inhomogeneity to homogeneity transition scale cannot be reached as an average, it is either there (spatially homogeneous model) or not there (spatially inhomogeneous model), and if it's there, like the FRW model demands, the scale at which the transition occurs is not an average, there will be objects above that scale size which will be obliged to have a certain motion state without possibility of changing it, they will be following the worldlines exactly orthogonal to spacelike hypersurfaces and therefore they'll define an apparently absolute frame for all objects under that size.

This is not how I understand the FRW model; as I said, it models the matter in the universe as a fluid, and all assertions about homogeneity (to some scale of approximation), isotropy, "comoving" worldlines, etc., refer to the fluid, not to any individual pieces of matter that compose it. A fluid can have an average property, such as density, that is constant to within some scale of approximation, and can have "average" worldlines assigned to it, without any actual piece of matter in the fluid having to have the average density or move along the average worldline.

It is true that the matter in the universe is unlike that in an ordinary fluid because of the fractal-like structure we now know it to have. Some cosmologists appear to be claiming that this is enough to invalidate FRW-type models (at least at the current epoch, though not necessarily in past epochs--see my earlier post), but I don't think that claim requires one to assert that FRW models require that the largest bound systems we see (superclusters) must be comoving (so that evidence that they're not invalidates the FRW model). The way I would expect an inhomogeneous structure to affect the dynamics is through the equation of state: a "lumpy" fluid where the particles tend to clump together will have a different equation of state (relationship of pressure to density) than an ideal gas-type fluid, which is basically what the FRW models assume.

 

[TrickyDicky]

This is not how I understand the FRW model; as I said, it models the matter in the universe as a fluid, and all assertions about homogeneity (to some scale of approximation), isotropy, "comoving" worldlines, etc., refer to the fluid, not to any individual pieces of matter that compose it. A fluid can have an average property, such as density, that is constant to within some scale of approximation, and can have "average" worldlines assigned to it, without any actual piece of matter in the fluid having to have the average density or move along the average worldline.

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. 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).

It is true that the matter in the universe is unlike that in an ordinary fluid because of the fractal-like structure we now know it to have. Some cosmologists appear to be claiming that this is enough to invalidate FRW-type models (at least at the current epoch, though not necessarily in past epochs--see my earlier post), but I don't think that claim requires one to assert that FRW models require that the largest bound systems we see (superclusters) must be comoving (so that evidence that they're not invalidates the FRW model).

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. 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).
At this moment superclusters not exactly comoving invalidate nothing since we know at that scale homogeneity hasn't been reached yet, I was just talking hypothetically if the transition to homogeneity had alredy been reached at that scale.

 

[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.