BB theory and preferred frames

DaleSpam

I am assuming the same idealization of the FRW model. In the ideal FRW model we observe a Doppler shift to the CMB, therefore we are not comoving observers.

This is certainly not correct. I have no problem with the FRW model as a very close approximation. What you do not seem to realize is that the FRW model, at each spatial location, identifies one particular worldline as the worldline of a co-moving observer, and it is not our worldline.

DaleSpam

Correct. I said as much back in post 6. It is a very reasonable convention, but a convention nonetheless.

PeterDonis

No, all observers are *not* comoving, not even in an idealized, perfectly homogeneous and isotropic model. Only observers who *see* the universe as homogeneous and isotropic are comoving. Even in the idealized model, there are plenty of observers who do not see the universe as homogeneous and isotropic and so are not comoving.

TrickyDicky

I'm not sure if you like to nitpick for the sake of it, or you don't fully understand what I'm saying or the FRW model itself. I'm perfectly aware that in our universe there is departure from homogeneity at our size scale, the FRW model is an idealization expected for objects hypercluster size, that yet works with little deviation (slightly different measures for the earth in your own words) since we are using this model -it is the concordance model- for objects earth or solar system size. I'll try again, in an perfect idealized FRW model, so that we can consider ourselves and all observers like at least hyperclusters size observers, all observers must be basically comoving since we should see the universe as isotropic and homogeneous.
BTW this also implies that we should be observing that slight deviation from Hubble law in the nearby universe region, but we are actually not observing it, for reference this paradox is known as the "de Vaucouleurs paradox" in honor of the brilliant cosmologist that pointed it out, and has not yet been explained.

TrickyDicky

It is exactly as you say, the FRW model is (like most models) an imperfect idealization since so far at all scales we observe there is departure from homogeneity, but this departure is considered small enough so that the FRW model is considered a valid working model.
For the sake of the better understanding of my argument I'm ignoring the small deviation at small scales, and taking the FRW model idealization as depicting realistically our universe at our scale too, I think it is a liberty I can take, but apparently peterdonis is not catching it.

TrickyDicky

Great, we are getting there. So you would agree (if you have read my last posts) that the reason it is a very reasonable convention is that we (no special observers) are very closely approximating the idealized FRW model in which all observers using those coordinates are comoving and we are expecting perfect homogeneity at a certain scale so all observers of a certain big enough size exactly should share being comoving observers, for those comoving observers the comoving frame must be absolute rather than conventional right?

DaleSpam

No, I would not agree with that. The size of the observer is irrelevant, only it's velocity wrt the CMB determines if it is comoving or not. A cluster sized observer moving relative to the CMB would not be comoving, and a neutrino sized observer at rest wrt the CMB would be comoving.

IMO, the reason it is a very reasonable convention is because it can be applied in the identical fashion at each spatial location.

TrickyDicky

Then you'll have to agree that in GR at certain distances velocity is not well- defined (meaning it is a path dependent parameter, and if you consider the LCDM model a valid one you will have to agree that at a certain scale the universe is homogeneous in the way FRW model predicts, therefore in this context size (or scale) is not irrelevant, there can't be a hypercluster (of whatever the size it is required by the LCDM model that the universe is truly homogeneous) that is not comoving with CMBR, if you don't agree with these two facts let me know.

DaleSpam

Agree.

Agree, meaning the stress energy tensor is homogenous.

Disagree. As long as the observers stress-energy is negligible (usually implied), then you certainly could have a hyper cluster sized non-comoving observer.

my_wan

Q-reeus brings up a point that I would like to see a more complete analysis of. Historically the initial condition problem began with the so called arrow of time issue that arose with the development of statistical mechanics. Poincare showed in 1893 that a time reversible dynamics would return to initial conditions given some impossible large number of years, which technically violates the second law. Long story short this lead to speculations about initial conditions we now call the Big Bang.

Although the FRW metric is certainly a valid solution to the EFE is is not the only possible solution. Such alternative speculations are unwarranted, though we can ask what the standard solution entails observationally. Given that gravitational time dilation is absolute, though not in degree, this implies the issue Q-reeus brought up.

The question is how dependent is the apparent age and size of the Universe on differing gravitational depths of a pair of observers watching the Universe grow and age? If it is entirely independent, as appears likely under under relativistic symmetries, it implies that the age/size factor of the Universe is independent of our local clock rates. This implies that counting out 14 billion years on our local clocks might not properly scale to the beginning of the Universe. If the age of the Universe is dependent on local inertial clock rates, with an isotropic expansion rate of space itself, it implies that the apparent age, density, etc, is dependent on the inertial state or the observer.

Trying to work through all the relativistic transforms for both general and special relativity under different initial and boundary condition assumptions is messy at best. Can anybody point at published work that explicitly compares the effects on comoving observers which do not share a common gravitational depth and/or inertial frame?

PeterDonis

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. If that isn't what you're saying, then I don't understand what you're saying; the only other way I can parse your statements is that you're saying that comoving observers are comoving, which is a tautology.

Edit: It looks like DaleSpam is making similar objections to mine, I agree with his posts.

I'll look it up. Do you have any particular references?

PeterDonis

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

http://www2.phys.canterbury.ac.nz/~d...e/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

TrickyDicky

No, not every worldline, if you read carefully you'll notice I'm talking about a certain sized objects.
In this case the observer stress-energy can't be neglected because it is an important part of the assumption.
Usually it is implied to be negligible precisely because it is understood that the FRW model is an idealization, thus galaxies and clusters are considered "dust" even if we know their stress energy is pretty great in reality.
My set up is just a "cosmological rescaling" so to speak.

my_wan

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:
In the article it states:
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

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

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".