BB theory and preferred frames

[my_wan]

No, it is *not* true that all observers see the universe as homogeneous and isotropic, even in the perfect idealized FRW model. Only a particular set of observers does, the set whose worldlines are orthogonal to the set of spacelike hypersurfaces which are homogeneous and isotropic. Are you trying to claim that *every single worldline* in the spacetime is orthogonal to that set of hypersurfaces? That's absurd.

This is related to the question I asked. In what way do you support this claim of absurdity? My cosmology may be weak but I know that as you get farther out the peculiar motions settle out and and the isotropy begins to dominate. Though here is a 2007 New Astronomy paper that claims to have observed some anisotropy in the overall Hubble expansion the first sentence in the abstract says:

Based[/PLAIN] on general relativity, it can be argued that deviations from a uniform Hubble flow should be thought of as variations in the Universe's expansion velocity field, rather than being thought of as peculiar velocities with respect to a uniformly expanding space.

In the article it states:

The[/PLAIN] Cosmological Principle—that the Universe is homogeneous and isotropic—is generally assumed to hold, since averaged over large enough scales the Universe will appear homogeneous. However, general relativity is needed to understand not only small dense systems, but large diffuse systems such as the Universe, and according to Einstein’s field equations, the spacetime corresponding to a homogeneous universe can not be used to represent a spatially averaged inhomogeneous universe.

Qualitatively it is not hard to see how under special relativity maintains a homogeneous expansion under a boost. If you have two equidistant galaxies some light years away in opposite direction they share essentially the same Hubble shift. Now boost an observer in the direction of one of the galaxies, say A. The redshift of galaxy A is decreased while the other increases. However, under SR this observer now measures the distance to galaxy A as shorter, hence galaxy A has proper distance as defined by that observer that warrants labeling the decreased redshift as a constant indicator of that proper distance. Visa versa for galaxy B. Hence under boost the Hubble law remains a valid constant. The homogeneity of the Hubble constant is not frame dependent under special relativity.

Under GR, under a change of gravitation depth, the observational effects are essentially the same for both galaxies. Given that light speed defines both time and distance for each observer, contains the very definition of relativistic simultaneity, the isotropy remains even more generally. This doesn't conflict with the quoted paper since this does not entail a statement of how homogeneous the Universe actually is, only how boost and gravitational depths can effect an observers measure of that homogeneity.

So I ask, how do you empirically justify that only a particular set of observers see the universe as homogeneous and isotropic? It seems to me that if what you claim is actually true then we should be able to measure distances just by the amount of anisotropy we can induce with a local boost. Not seeing that go anywhere. So explain?

 

[TrickyDicky]

Found this web page by David Wiltshire at the University of Canterbury in New Zealand:

http://www2.phys.canterbury.ac.nz/~dlw24/universe/general.html

Here's how he describes the paradox:



As he describes it, the paradox is that on scales small compared to the size of the universe, we should not be able to see a Hubble law at all. However, he goes on to say that, while we do observe a Hubble law even on small distance scales, the Hubble constant we observe on those scales is *smaller* than the one we observe on larger scales:



As he goes on to note, the value of the Hubble constant has been an area of some dispute; the current "consensus" value is around 72 km/s/Mpc, but the Sandage team claims a value of around 62 km/s/Mpc, the "global average" value given above. But a variation of the "expansion rate" of the universe with size scale would remove the apparent discrepancy. The reason for the apparent variation in "expansion rate", he says, is simply that galactic clusters are bound systems, and we are inside one: so our local clocks run slower than clocks in the voids, outside the bound systems, for the simple reason that we are inside the gravity well of our local cluster and the voids are not.

Wiltshire has a paper on arxiv in which he claims to be able to account for the observations currently attributed to "dark energy" by this method:

http://arxiv.org/abs/0809.1183

I don't know if others on PF have seen this paper and can give any input. In particular, I don't know if his proposed model fits the other observations that have led to the current consensus Lambda-CDM model, which are well described, for example, by Ned Wright in his cosmology tutorial here:

http://www.astro.ucla.edu/~wright/cosmo_01.htm

Wiltshire is a bit controversial and certainly his "solutions" (to the paradox or to dark energy) are not considered mainstream. AFAIK is an open problem in cosmology, one that is rarely discussed or known though.

 

[my_wan]

I would find it far easier to deal with these kinds of questions and learn far more about the science involved without all the model specific assumptions built in. Unfortunately wading through this or that model trying to explain the observations produces a large work load to try and separate out the observations from the model specific assumptions.

So, although I am not terribly interested in particular model specific description, I will expand my original question of how do you "empirically justify that only a particular set of observers see the universe as homogeneous and isotropic". Expand this to: How can you even theoretically justify that only a particular set of observers see the universe as homogeneous and isotropic, under empirical constraints.

 

[TrickyDicky]

How can you even theoretically justify that only a particular set of observers see the universe as homogeneous and isotropic, under empirical constraints.

This would require reading a few books about cosmology and GR, but you can start looking up "Weyl's postulate" in wikipedia( and possibly "cosmological principle" and "FRW metric".

 

[Dale]

In this case the observer stress-energy can't be neglected because it is an important part of the assumption.

Then it isn't about the size of the observer, it is about the stress-energy of the observer. Obviously if the observer is so massive that it significantly distorts the metric then the metric will be significantly distorted. That tautology hardly implies any of the schizophrenia you mentioned in the OP.

 

[PeterDonis]

So I ask, how do you empirically justify that only a particular set of observers see the universe as homogeneous and isotropic?

*We* don't see the universe as homogeneous and isotropic, and we are observers. I think that counts as empirical.

Only observers who are at rest in the "comoving" frame used in the FRW models see the universe as homogeneous and isotropic. Observers who are not at rest in that frame don't. Earth is not at rest in that frame, because we see a dipole anisotropy in the CMBR. We don't have reports from astronomers in other galaxies, but based on what we can see of their motions, it appears that at least some of the nearby ones are not at rest in the "comoving" frame either (that is, their observed relative velocity to us is different from what it would need to be to cancel the dipole anisotropy we see in the CMBR). AFAIK it gets harder to tell as you go farther out.

 

[TrickyDicky]

Then it isn't about the size of the observer, it is about the stress-energy of the observer. Obviously if the observer is so massive that it significantly distorts the metric then the metric will be significantly distorted. That tautology hardly implies any of the schizophrenia you mentioned in the OP.

You didn't understand the set up I guess, the stress-energy of the observer is idealized in such way in the FRW metric so that it doesn't distort the metric. The whole point was to explain that what is "dust" in the FRW metric refers in fact to objects of a very big size, so yes, it is about size, we haven't found so far objects of that size, up to now the biggest objects we can see are still at inhomogeneous scale (but it is expected that at some size scale we should find true homogeneity), and their distortion of spacetime doesn't significantly distort the FRW metric at all, on the contrary those objects are still considered as dust in FRW models. So it seems you might have have some confusions about the FRW cosmological model. Of course for observers below that size all kind of deviations from comoving motion should be observed (although if you take a look at the previous post about "de Vaucouleurs paradox", those deviations are only significantly observed at much smaller size scales (of a few Mpc).
And after all you already admitted that the age of the universe is purely conventional and arbitrary in a previous post, but very "reasonable" convention.
So you seem to have no problem to think two contradictory things at the same time , relativity of simultaneity and absolute simultaneity (all observers in the same space hyperslice share simultaneity of BB event no matter their spatial separation) can both coexist. Hey, if you see no problem with that who am I to drag you from your comfortable conviction.

 

[Dale]

You didn't understand the set up I guess

I understand the setup. You deliberately make your observer so super-massive that it would distort the metric if it were not comoving and then, under the assumption that the metric is not distorted, you reach the tautological conclusion that your super-massive observer must be comoving.

What I don't understand is why you think that kind of a setup is at all important. Why do you want to go out of your way to use your super-massive observers in this scenario when in most other GR discussions observers are considered to have an insignificantly miniscule amount of mass?

So you seem to have no problem to think two contradictory things at the same time , relativity of simultaneity and absolute simultaneity (all observers in the same space hyperslice share simultaneity of BB event no matter their spatial separation) can both coexist.

I am not thinking two contradictory things. There is no absolute simultaneity. As we agreed above it is simply an arbitrary convention. "Arbitrary convention" explicitly implies that it is not absolute.

Only the comoving observers in the space hyperslice agree on the proper time from the BB. Not all observers are comoving, and the non-comoving ones disagree about the proper time from the BB. All of your super-massive observers are (tautologically) comoving, but clearly not all observers are super-massive.

 

[TrickyDicky]

I understand the setup.

I'm not so sure, or maybe it is the FRW model you find problem with?
My "super massive" observers don't distort the metric, they are treated as "dust" in the FRW model.Tautologically or not they are comoving. My point is that for them the there is absolute simultaneity wrt the BB event and this observers can not change their state of motion or else the homogeneity assumption is lost, so for them certainly their frame is absolute and defines an absolute state for all the others observers, all non-comoving (smaller) observers refer their state of motion to that comoving frame. The fact that there is an absolute state of motion doesn't mean absolutely all objects and observers must have that motion (be comoving) but that they refer their state of motion to that comoving frame.

I am not thinking two contradictory things. There is no absolute simultaneity. As we agreed above it is simply an arbitrary convention. "Arbitrary convention" explicitly implies that it is not absolute.

Only the comoving observers in the space hyperslice agree on the proper time from the BB. Not all observers are comoving, and the non-comoving ones disagree about the proper time from the BB. All of your super-massive observers are (tautologically) comoving, but clearly not all observers are super-massive.

See above

 

[Dale]

My "super massive" observers don't distort the metric, they are treated as "dust" in the FRW model. Tautologically or not they are comoving.

Understood. In your setup we are given that they do not distort the metric, and we are given that they are sufficiently super-massive that they would distort the metric if they were not comoving. Therefore the super-massive observers are comoving. What specifically do you think I am not understanding about the setup?

My point is that for them the there is absolute simultaneity wrt the BB event and this observers can not change their state of motion or else the homogeneity assumption is lost, so for them certainly their frame is absolute and defines an absolute state for all the others observers, all non-comoving (smaller) observers refer their state of motion to that comoving frame.

This is incorrect. While all non-comoving observers may adopt the reasonable convention of referring their state of motion to that comoving frame. Nothing physical forces them to do that. Furthermore, the super-massive observers may decide to adopt the strange convention of referring their state of motion to some non-comoving frame. Nothing physical prevents them from doing that. The simultaneity in the FRW coordinates is still relative, not absolute.

 

[my_wan]

This would require reading a few books about cosmology and GR, but you can start looking up "Weyl's postulate" in wikipedia( and possibly "cosmological principle" and "FRW metric".

I understand Weyl's postulate, and the difficulties with trying to define the physical meaning of Weyl gauges in general. I don't really buy Penrose's Weyl curvature hypothesis either or the entropy argument in general. Due to the relational character of entropy and the nonsense of talking about what's outside the Big Bang when defined as a closed system. Yet if we have an observable metric that is internally expanding from an internal perspective, such as the FRW metric, does this not imply that these internal degrees of freedom where supplied from an outside source? Yet in both the BB conception of enclosed system and relativistic symmetries this notion of degrees of freedom "from the outside" is nonsense. In what way then does the FRW metric expansion decouple itself from the spacetime metric under GR such that this metric is an observable expansion not tied to local clocks under GR?

So don't tell me that I only need to read "a few books" to grok what's happening when the debates on which those books are based can't comes to terms with even the basic physics. Fundamentally this is defined by conceptual split between classical thermodynamics and statistical mechanics. Most obviously in the "arrow of time issues" with time reversible foundations of both classical and quantum physics.

So my question stands, and handwaiving it with "read a few books" buys nothing.

 

[TrickyDicky]

So my question stands, and handwaiving it with "read a few books" buys nothing.

I didn't sell you anything. Your question is too broad and you need to start your own thread.

 

[TrickyDicky]

This is incorrect. While all non-comoving observers may adopt the reasonable convention of referring their state of motion to that comoving frame. Nothing physical forces them to do that. Furthermore, the super-massive observers may decide to adopt the strange convention of referring their state of motion to some non-comoving frame. Nothing physical prevents them from doing that. The simultaneity in the FRW coordinates is still relative, not absolute.

You see nothing physical in the fact that super-size observers can only have one motion state (whether you want to call it "rest frame" or "ether frame" or "CMB frame")?

 

[Dale]

Your question is too broad and you need to start your own thread.

I agree. It feels like you are trying to hijack TrickyDicky's thread on a tangential question.

 

[Dale]

You see nothing physical in the fact that super-size observers can only have one motion state?

No, I don't. It is a direct result of using super-massive observers and I see nothing physical about your super-massive observers.

The super massive observers are comoving, but even comoving observers are free to do physics calculations in a frame where they are not stationary if they wish. Simultaneity is not absolute. Refer back to post 4, your super-massive observers do not change that line of reasoning.

 

[my_wan]

*We* don't see the universe as homogeneous and isotropic, and we are observers. I think that counts as empirical.

That is rather obvious, though my description did not depend on any model containing and homogeneity or nonhomogeneity.

Only observers who are at rest in the "comoving" frame used in the FRW models see the universe as homogeneous and isotropic. Observers who are not at rest in that frame don't.

Ok, here's the problem once again. If we think in terms of the distribution of galaxies (CMBR aside) and their Hubble law relation to distance, then my description explain exactly why this same Hubble law would apply under all relativistic boost.

Earth is not at rest in that frame, because we see a dipole anisotropy in the CMBR. We don't have reports from astronomers in other galaxies, but based on what we can see of their motions, it appears that at least some of the nearby ones are not at rest in the "comoving" frame either (that is, their observed relative velocity to us is different from what it would need to be to cancel the dipole anisotropy we see in the CMBR). AFAIK it gets harder to tell as you go farther out.

Now you bring in the CMBR. Here it is unique from the Hubble law of galaxies since the source is presumed to be at some equidistant boundary condition from a particular frame. In the galaxy distance/redshift case this merely corresponds to a frame in which both galaxies have the same redshift in opposite directions. Now I can't even count the number of things that can go wrong with this assumption, and the claim that a frame in which two redshifts from opposite directions exists such that the redshifts are equal is a tautology of any and all of those possibilities.

Therefore I'll ask for more detail on what you suppose this "prefered" isotropic frame means.
1) Does this mean the Universe is effectively older or younger for our frame, given our anisotropic frame with respect to CMBR?
2) Does this mean that the time since the BB is effectively older when in our frame it's measured in one direction and younger when measured in the other direction?

Now the major point from an earlier reference in this thread, but I'm only interested what Martin Rees is purported to have said here:

But[/PLAIN] there is also a more compelling argument for the standard interpretation that I learned when I was first taught cosmology by Martin Rees in Cambridge in 1984, which I have now also taught students for 15-odd years, which goes as follows. Apart from our small local motion (which we can account for) we see an isotropic CMB.[...]

Now, here Martin Rees's justification was the "isotropic CMB". We see that it is not isotropic. We then choose a "preferred" frame in which it is isotropic and call that justification for isotropic. Yet for any two galaxies or rocks in the Universe, irrespective of any homogeneity or lack of, a "preferred" frame tautologically exist to define their redshifts as equal. Yet, due to the way relativity defines the spacetime metric, the Hubble law is generally valid for all galaxies irrespective of which frame you choose, no "preferred" frame needed. Hence defining a tautology that such a "preferred" frame exist is not evidence of squat.

This compounding of tautologies as if it was "the" evidence is aggravating. The only thing more aggravating is crackpots that remodel their own interpretation, not leaving much left where you can actually learn much about the raw empirical data without all the baggage.

 

[TrickyDicky]

No, I don't. It is a direct result of using super-massive observers and I see nothing physical about your super-massive observers.

The super massive observers are comoving, but even comoving observers are free to do physics calculations in a frame where they are not stationary if they wish. Simultaneity is not absolute. Refer back to post 4, your super-massive observers do not change that line of reasoning.

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. I think you are missing the important point, their velocity, their motion, is absolute, stationary (time invariant since it can't change his motion state) with respect to any other state of motion.
Otherwise you have to break the homogeneity assumption. 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.
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 discussed.

 

[Passionflower]

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.

 

[my_wan]

I am significantly more interested in how to ask empirically answerable questions than in how such questions fit into this or that model, standard or otherwise. So the comfy chair is not for me and my issues are about how uncomfortable I am. Yet it seems to me that so long as the data is wrapped around a particular model a lot of people sit in comfy chairs with little concern about empirically askable questions. Especially those that are not explicitly formatted for their model of choice.

The notion that some idealization of a metric, such as the "stress-energy of the observer", can technically be chosen to validly justify a particular picture is a non-point to me. I can technically choose a valid frame and say that all observer must transform observations to this frame to see "the" valid picture of what is really happening to. So what. The technical validity is blindingly myopic. Before Einstein the ether played the same role the idealized metrics play in cosmology.

 

[Passionflower]

I am significantly more interested in how to ask empirically answerable questions than in how such questions fit into this or that model, standard or otherwise. So the comfy chair is not for me and my issues are about how uncomfortable I am. Yet it seems to me that so long as the data is wrapped around a particular model a lot of people sit in comfy chairs with little concern about empirically askable questions. Especially those that are not explicitly formatted for their model of choice.

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.

 

[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.