Register to reply

BB theory and preferred frames

by TrickyDicky
Tags: frames, preferred, theory
Share this thread:
DaleSpam
#19
Dec19-11, 05:42 PM
Mentor
P: 17,344
Quote Quote by TrickyDicky View Post
Ok, so if we can choose a different methd for assigning coordinates, you then admit there is nothing special about the age (13.7 bly) we usually assign to the universe right?
Correct. I said as much back in post 6. It is a very reasonable convention, but a convention nonetheless.
PeterDonis
#20
Dec19-11, 06:40 PM
Physics
Sci Advisor
PF Gold
P: 6,179
Quote Quote by TrickyDicky View Post
Sure, since we are using the FRW model I'm idealizing a little and assuming perfect homogeneity (wich is expected anyway at certain scale) so that "all observers are basically comoving".
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
#21
Dec20-11, 03:15 AM
P: 3,043
Quote Quote by PeterDonis View Post
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.
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
#22
Dec20-11, 03:23 AM
P: 3,043
Quote Quote by Q-reeus View Post
I'm no cosmologist but the only maybe useful observation I can make is that as real universe is lumpy not spatially homogeneous, temporal 'lumpiness' is also present to some extent. So higher gravitational potential inside a cosmic void region implies experiencing more relative total time since BB than inside a clumped region. And of course considerably less time has passed at the surface of an ancient neutron star say. But guessing that is not your concern here, as it seems from your earlier remarks we are assuming homogeneity.
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
#23
Dec20-11, 03:33 AM
P: 3,043
Quote Quote by DaleSpam View Post
Correct. I said as much back in post 6. It is a very reasonable convention, but a convention nonetheless.
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
#24
Dec20-11, 06:19 AM
Mentor
P: 17,344
Quote Quote by TrickyDicky View Post
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?
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
#25
Dec20-11, 07:42 AM
P: 3,043
Quote Quote by DaleSpam View Post
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.
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
#26
Dec20-11, 07:55 AM
Mentor
P: 17,344
Quote Quote by TrickyDicky View Post
Then you'll have to agree that in GR at certain distances velocity is not well- defined (meaning it is a path dependent parameter
Agree.

Quote Quote by TrickyDicky View Post
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,
Agree, meaning the stress energy tensor is homogenous.

Quote Quote by TrickyDicky View Post
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.
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
#27
Dec20-11, 08:43 AM
P: 863
Quote Quote by Q-reeus View Post
I'm no cosmologist but the only maybe useful observation I can make is that as real universe is lumpy not spatially homogeneous, temporal 'lumpiness' is also present to some extent. So higher gravitational potential inside a cosmic void region implies experiencing more relative total time since BB than inside a clumped region. And of course considerably less time has passed at the surface of an ancient neutron star say. But guessing that is not your concern here, as it seems from your earlier remarks we are assuming homogeneity.
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
#28
Dec20-11, 09:04 AM
Physics
Sci Advisor
PF Gold
P: 6,179
Quote Quote by TrickyDicky View Post
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.
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.

Quote Quote by TrickyDicky View Post
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.
I'll look it up. Do you have any particular references?
PeterDonis
#29
Dec20-11, 10:10 AM
Physics
Sci Advisor
PF Gold
P: 6,179
Quote Quote by TrickyDicky View Post
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.
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:

SANDAGE-DE VAUCOULEURS PARADOX

... In the standard way of thinking about cosmological averages, if you take a box of the size of average homogeneity, then you should expect galaxies to have large peculiar velocities if you average on scales much smaller than the homogeneous box, which I mentioned before was of order 170 Mpc. In particular, if you look at very small scales the statistical scatter of peculiar velocities should be so great that no linear Hubble law between redshift and distance can be extracted. Yet Hubble discovered his law on nearby scales of 20Mpc, 10% of the scale of homogeneity. By standard thinking this does not make sense.
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 far as the argument of Sandage and de Vaucouleurs is concerned; if we measure the Hubble constant in an ideal "bubble wall" where the average clock rate is close to ours, we will get a low value of the Hubble constant, 48 km/s/Mpc. If we measure it to the other side of a void of the dominant size of 48Mpc across, we will get a higher value, 76 km/s/Mpc - because space appears to be expanding faster there by our clocks - which are going slower than the clocks in the voids. Once we average on the scale of apparent homogeneity, our average includes as many bubble walls as voids as the average in the observable universe, then we converge to a "global average" Hubble constant between the two extremes, of 62 km/s/Mpc.
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
#30
Dec20-11, 11:31 AM
P: 3,043
Quote Quote by DaleSpam View Post
Disagree. As long as the observers stress-energy is negligible (usually implied), then you certainly could have a hyper cluster sized non-comoving observer.
Quote Quote by PeterDonis View Post
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;
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
#31
Dec20-11, 11:48 AM
P: 863
Quote Quote by PeterDonis View Post
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:
Quote Quote by http://arxiv.org/abs/astro-ph/0703556
Based 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:
Quote Quote by http://arxiv.org/PS_cache/astro-ph/pdf/0703/0703556v1.pdf
The 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
#32
Dec20-11, 11:51 AM
P: 3,043
Quote Quote by PeterDonis View Post
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
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
#33
Dec20-11, 12:44 PM
P: 863
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
#34
Dec20-11, 01:45 PM
P: 3,043
Quote Quote by my_wan View Post
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".
DaleSpam
#35
Dec20-11, 07:49 PM
Mentor
P: 17,344
Quote Quote by TrickyDicky View Post
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
#36
Dec20-11, 10:42 PM
Physics
Sci Advisor
PF Gold
P: 6,179
Quote Quote by my_wan View Post
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.


Register to reply

Related Discussions
What are valid Preferred Frames? Special & General Relativity 2
Evidence for preferred frames? Special & General Relativity 49
String theory and reference frames HELP Beyond the Standard Model 6
Preferred Frames not in SR are used in Astrophysics Special & General Relativity 27
Frames of reference & Inertial frames Classical Physics 2