BB theory and preferred frames

[TrickyDicky]

I can't manage to understand the quasi-schizofrenic way we should believe that our universe started at a certain time point called Big-bang while at the same we must never admit that in order to say that it follows that an absolute time (and an absolute frame) must be distinguished, (the CMB rest comoving frame). We at most can call it "preferred" frame-even if many people uses "preferred frame" as the one where physics is different, which is a notion forbidden by reativity.
I think it is one way or the other, if we must think something extraordinary happened exactly 13.7 bly (with fractions of a second precision) ago then we are using an absolute clock, and therefore we shoud admit an absolute frame. If no such frame exists and that frame is only preferred in an arbitrary way, those 13.7 bly are also an arbitrary number and there's not anything absolute associated to that "age" and we could as well say something singular happened an infinite (if our universe was infinite) time ago or yesterday or an infinite number of different ages ago fom some other point in the universe.
Please someone take me out this interpretational swamp.

 

[Dale]

I can't manage to understand the quasi-schizofrenic way we should believe that our universe started at a certain time point called Big-bang while at the same we must never admit that in order to say that it follows that an absolute time (and an absolute frame) must be distinguished, (the CMB rest comoving frame). We at most can call it "preferred" frame-even if many people uses "preferred frame" as the one where physics is different, which is a notion forbidden by reativity.

There is nothing schizophrenic about it. It is straight out of the Einstein Field Equations and differential geometry. The problem is trying to describe the math in english.

If you are frustrated and confused by the verbal descriptions then you really need to learn the math. Otherwise you are "blind" to the overall picture.

http://en.wikisource.org/wiki/The_poems_of_John_Godfrey_Saxe/The_Blind_Men_and_the_Elephant

 

[TrickyDicky]

There is nothing schizophrenic about it. It is straight out of the Einstein Field Equations and differential geometry. The problem is trying to describe the math in english.

If you are frustrated and confused by the verbal descriptions then you really need to learn the math. Otherwise you are "blind" to the overall picture.

http://en.wikisource.org/wiki/The_poems_of_John_Godfrey_Saxe/The_Blind_Men_and_the_Elephant

Thanks for the poem but I don't think the confusion comes in this case from the verbal description, I know the math and is precisely from the math that I gather the verbal description of my last post, in any case you could try and describe (in english or mathematically) which way of the two I described in the second paragraph do you think is the correct one.

 

[Dale]

If you know the math then what is the problem?

1) The big bang is a feature of the FRW metric.
2) The FRW metric is a solution of the EFE.
3) The EFE are manifestly covariant.
4) Covariance implies the lack of a preferred frame.
5) Therefore, there the big bang does not imply a preferred frame.

 

[TrickyDicky]

If you know the math then what is the problem?

1) The big bang is a feature of the FRW metric.
2) The FRW metric is a solution of the EFE.
3) The EFE are manifestly covariant.
4) Covariance implies the lack of a preferred frame.
5) Therefore, there the big bang does not imply a preferred frame.

I agree with those 5 points, that's the problem.
So is the "age" of the universe just an arbitrary figure?

 

[Dale]

The "age of the universe" refers specifically to the proper time experienced by an observer which is passing next to us now and has been at rest in the FRW coordinates since the big bang. It is arbitrary, but well-defined.

 

[TrickyDicky]

The "age of the universe" refers specifically to the proper time experienced by an observer which is passing next to us now and has been at rest in the FRW coordinates since the big bang. It is arbitrary, but well-defined.

Two things, if t=0 is a real singularity, that is "outside physical theories realm", an exact age can't be that well-defined since we can't know how our theory behaves at the limit when t tends to zero, as far as we ñnow time could behave weirdly there and became asymptotic or...whatever, that what a true singularity does.
Second, I agree with the " refers specifically to the proper time experienced by an observer which is passing next to us now and has been at rest in the FRW coordinates since the big bang", but a proper time in relativity is a purely local measure (with the caveat I referred to above on top of it), it can never be generalized to a "universe age" in any sense other than our local non-centric or non-special location in any way, right? (if you respect the cosmological and Copernican principles at least).

 

[Dale]

Two things, if t=0 is a real singularity, that is "outside physical theories realm", an exact age can't be that well-defined since we can't know how our theory behaves at the limit when t tends to zero, as far as we ñnow time could behave weirdly there and became asymptotic or...whatever, that what a true singularity does.

Agreed, similar issues happen with defining the proper time of an observer falling to the singularity of a black hole. Usually the singularity is simply excluded from the manifold, which makes the limits all behave nicely (and is actually required mathematically). This is what is meant by the proper time of an observer going into or coming out of a singularity.

Of course, GR probably diverges from reality well before reaching the singularity.

Second, I agree with the " refers specifically to the proper time experienced by an observer which is passing next to us now and has been at rest in the FRW coordinates since the big bang", but a proper time in relativity is a purely local measure (with the caveat I referred to above on top of it), it can never be generalized to a "universe age" in any sense other than our local non-centric or non-special location in any way, right? (if you respect the cosmological and Copernican principles at least).

Science is full of bad terminology that persists despite good reasons for it to be dismissed. It sounds like you actually understand everything, and simply object to the terminology. Your objection is reasonable, but changing common terminology is nearly impossible.

However, I personally don't think that the terminology is as bad as you seem to feel it is. The above definition certainly can be generalized to a "universe age" simply by adopting the same convention at every point in the universe. Since the FRW metric is homogenous it is reasonable to do, IMO.

 

[TrickyDicky]

However, I personally don't think that the terminology is as bad as you seem to feel it is. The above definition certainly can be generalized to a "universe age" simply by adopting the same convention at every point in the universe. Since the FRW metric is homogenous it is reasonable to do, IMO.

As I said I disagree that it is simply a terminology issue, it is about logical consistency and avoiding contradictions.
The FRW metric is homogeneous only spatially and to adopt the same convention at every point in te universe wrt a "universe age" i.e, sharing the same clock for the BB event, it would be necessary to either have a not FRW universe spatially and temporally homogeneous which seems not to be the case or do without the relativity of simultaneity (you are basically demanding absolute simultaneity for the BB event for every point in the universe no matter how distant).

 

[Q-reeus]

As I said I disagree that it is simply a terminology issue, it is about logical consistency and avoiding contradictions.
The FRW metric is homogeneous only spatially and to adopt the same convention at every point in te universe wrt a "universe age" i.e, sharing the same clock for the BB event, it would be necessary to either have a not FRW universe spatially and temporally homogeneous which seems not to be the case or do without the relativity of simultaneity (you are basically demanding absolute simultaneity for the BB event for every point in the universe no matter how distant).

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.

 

[PeterDonis]

The FRW metric is homogeneous only spatially and to adopt the same convention at every point in te universe wrt a "universe age" i.e, sharing the same clock for the BB event, it would be necessary to either have a not FRW universe spatially and temporally homogeneous which seems not to be the case or do without the relativity of simultaneity (you are basically demanding absolute simultaneity for the BB event for every point in the universe no matter how distant).

The FRW model does not say that every observer sees the same "universe age" regardless of their state of motion. It only says that *comoving* observers all see the same "universe age". We here on Earth are not comoving observers, so the universe age we measure will actually be slightly different than the universe age that would be measured by a comoving observer just passing through the Solar System right now. Our instantaneous hypersurface of simultaneity on Earth right now is also not the same as the hypersurface of constant comoving time passing through Earth right now.

 

[Dale]

(you are basically demanding absolute simultaneity for the BB event for every point in the universe no matter how distant).

Huh? Any event (including the BB) is in fact simultaneous with itself absolutely. So yes, I am demanding that, and that is noncontroversial.

I think I must be severely misunderstanding your point.

 

[TrickyDicky]

Huh? Any event (including the BB) is in fact simultaneous with itself absolutely. So yes, I am demanding that, and that is noncontroversial.

I think I must be severely misunderstanding your point.

Ok, I guess you mean that the BB is supposed to have occurred not in a single location but in every location, and that's what you find noncontroversial. So it's no problem for you to do without the relativity of simultaneity for this particular event.
You do realize that all this implies an absolute frame, right?

 

[TrickyDicky]

The FRW model does not say that every observer sees the same "universe age" regardless of their state of motion. It only says that *comoving* observers all see the same "universe age". We here on Earth are not comoving observers, so the universe age we measure will actually be slightly different than the universe age that would be measured by a comoving observer just passing through the Solar System right now. Our instantaneous hypersurface of simultaneity on Earth right now is also not the same as the hypersurface of constant comoving time passing through Earth right now.

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".

 

[Dale]

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".

We are observers and we are not comoving.

Let me describe a slightly different way of constructing this coordinate system. First, recall that in order to define a geodesic you need an event and a tangent vector (i.e. velocity). So, take any event in the universe, and at that event find the one unique velocity at which there is no CMB Doppler shift. Using that event and tangent vector construct a geodesic that goes back in time to the BB, called the comoving geodesic. At each event along the geodesic calculate the length of that geodesic from the BB to the event (with the aforementioned caveats). Assign that number as the t coordinate of each event along the geodesic. Because the universe is spatially homogenous you can do this procedure at every point in the universe, assigning 3 different coordinates to identify the different comoving geodesics. This will result in the standard FRW coordinate system, with corresponding hypersurfaces of simultaneity.

However, there is nothing that requires you to use that procedure. You could just as well choose a different method for assigning coordinates. You can have simultaneity without having absolute simultaneity.

 

[TrickyDicky]

We are observers and we are not comoving.

I said I'm assuming the idealization of the FRW model, the universe age we as observers measure will actually be slightly different than the universe age that would be measured by a comoving observer, if that is a problem for you here I guess you wouldn't accept the FRW model because we as observers are not comoving and therefore the universe must not be homogeneous. Frankly, that's feeble, we are looking at the big picture here.

 

[TrickyDicky]

However, there is nothing that requires you to use that procedure. You could just as well choose a different method for assigning coordinates. You can have simultaneity without having absolute simultaneity.

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?

 

[Dale]

I said I'm assuming the idealization of the FRW model

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.

if that is a problem for you here I guess you wouldn't accept the FRW model because we as observers are not comoving and therefore the universe must not be homogeneous. Frankly, that's feeble, we are looking at the big picture here.

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.

 

[Dale]

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]

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]

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]

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]

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?

 

[Dale]

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]

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.

 

[Dale]

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.

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.

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]

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]

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.

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]

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/~dlw24/universe/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]

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

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]

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.