by AWA
 P: 11 AWA, here is the resolution of your 'false paradox': The way to avoid the confounding of variables (the varying of both space and time when we simultaneously look far away in distance and far back in time) is this: When we try to verify the homogeneous and isotropic nature of space we must do so by holding time constant, which means that we will look in many directions but always at the SAME distance! Thus we may decide to check first at 10 billion light years of distance. So we study the terrain at that distance, let's say in 1000 different directions--imagining a sphere surrounding the earth, our telescopic gaze would penetrate that sphere at 1000 different points, with 10 random points in each of 100 sectors of sky. If the results in each sector were very similar to the other sectors, we could declare the universe homogeneous and isotropic at 10 billion light years of distance (10 billion years ago). We repeat the process for 5 billion light years of distance. Similar results. We declare the universe homogenous and isotropic at 5 billion light years (5 billion light years ago). Do it at 50 other distances and get similar results, and you can confidently declare the universe generally homogeneous and isotropic in space throughout its history. Importantly, we can conclude that this is true even for "out of sync" objects--i.e. if we're considering 10 billion light years of distance (and 10 billion years ago) we can also conclude that 10 billion years ago, objects that happen to be 3 or 7 or 12 billion light years away from us now were configured similarly to the objects that we studied at 10 billion light years away. That is, 10 billion years ago, objects in every direction from us were similarly configured to one another, at ANY distance from us, not just at the 10 billion light year distance that we observed. Why is this true? Because our observations of objects as they were 10 billion years ago were constrained in a manner (i.e. being a given distance from earth) that provides no basis for a skewing of the results--there'd be no reason that objects 7 or 9 or 12 billion light years from earth would give different results if, in 2010, we could see light from them that originated 10 billion years ago. With that conclusion safely tucked under our belts, we can now proceed to the second half of the proof. Knowing that 10 billion years ago space in every direction from us and at every distance from us was similar, and knowing that 5 billion years ago the same was true, if we compare the configurations at 5 and 10 billion years, we can conclude that any differences must be a function of time and not space. And indeed there are significant differences, and thus we know that the universe does not vary with space, but does vary with time.
 Sci Advisor P: 4,596 The emission of the CMB would not be possible in a universe that is homogeneous in time as well as space, as the CMB was emitted due to a phase transition of the universe as a whole from a plasma to a transparent gas. Such a phase transition involves a drop in temperature, which cannot happen in a universe that is homogeneous in time.
P: 134
 Quote by echoing song AWA, here is the resolution of your 'false paradox': The way to avoid the confounding of variables (the varying of both space and time when we simultaneously look far away in distance and far back in time) is this: When we try to verify the homogeneous and isotropic nature of space we must do so by holding time constant, which means that we will look in many directions but always at the SAME distance! Thus we may decide to check first at 10 billion light years of distance. So we study the terrain at that distance, let's say in 1000 different directions--imagining a sphere surrounding the earth, our telescopic gaze would penetrate that sphere at 1000 different points, with 10 random points in each of 100 sectors of sky. If the results in each sector were very similar to the other sectors, we could declare the universe homogeneous and isotropic at 10 billion light years of distance (10 billion years ago). We repeat the process for 5 billion light years of distance. Similar results. We declare the universe homogenous and isotropic at 5 billion light years (5 billion light years ago). Do it at 50 other distances and get similar results, and you can confidently declare the universe generally homogeneous and isotropic in space throughout its history. Importantly, we can conclude that this is true even for "out of sync" objects--i.e. if we're considering 10 billion light years of distance (and 10 billion years ago) we can also conclude that 10 billion years ago, objects that happen to be 3 or 7 or 12 billion light years away from us now were configured similarly to the objects that we studied at 10 billion light years away. That is, 10 billion years ago, objects in every direction from us were similarly configured to one another, at ANY distance from us, not just at the 10 billion light year distance that we observed. Why is this true? Because our observations of objects as they were 10 billion years ago were constrained in a manner (i.e. being a given distance from earth) that provides no basis for a skewing of the results--there'd be no reason that objects 7 or 9 or 12 billion light years from earth would give different results if, in 2010, we could see light from them that originated 10 billion years ago. With that conclusion safely tucked under our belts, we can now proceed to the second half of the proof. Knowing that 10 billion years ago space in every direction from us and at every distance from us was similar, and knowing that 5 billion years ago the same was true, if we compare the configurations at 5 and 10 billion years, we can conclude that any differences must be a function of time and not space. And indeed there are significant differences, and thus we know that the universe does not vary with space, but does vary with time.
Nice try. But it misses to fully explain the "false paradox". Just look at a picture of the Sloan Sky Survey map from "the telescope as a Time machine":

We are expecting to find homogeneity from this map at much larger scale. Now, the SDSS map is intended to be a 3D map of spacetime. and this kind of map integrates time thru time snapshots like you were talking about, it does not concentrate in 5 billion years ago or 10 billion years ago(well at the moment much less than that of course), it shows(or it should show if standard cosmology assumptions are correct) the time dimension as homogenous if it is to show spatial homogeneity, too.
 Sci Advisor P: 4,596 The "distance" axis of that plot, AWA, is not time or distance, but redshift. There couldn't even be any redshift if the universe was homogeneous in time as well as space.
P: 134
 Quote by Chalnoth The emission of the CMB would not be possible in a universe that is homogeneous in time as well as space, as the CMB was emitted due to a phase transition of the universe as a whole from a plasma to a transparent gas. Such a phase transition involves a drop in temperature, which cannot happen in a universe that is homogeneous in time.
Right, in one of my first posts I hinted at such a resolution, as certainly the paradox would only affect the observable universe and what is behind the LSS is obviously not observable, and even more obvious is the fact that the initial singularity destroys the time isotropy and homogeneity (as well as the spatial). But since we lack the physics to deal with that point I wanted to leave it out of my setting.
P: 4,596
 Quote by AWA Right, in one of my first posts I hinted at such a resolution, as certainly the paradox would only affect the observable universe and what is behind the LSS is obviously not observable, and even more obvious is the fact that the initial singularity destroys the time isotropy and homogeneity (as well as the spatial). But since we lack the physics to deal with that point I wanted to leave it out of my setting.
I don't get what you're saying here. The last scattering surface is most definitely part of the observable universe, and could not exist in a time-homogeneous universe.
P: 134
 Quote by Chalnoth The "distance" axis of that plot, AWA, is not time or distance, but redshift. There couldn't even be any redshift if the universe was homogeneous in time as well as space.
Strictly speaking you are right, but if you tell me that we can't interpret redshift as a distance marker and therefore as look-back time you are undermining the very basic assumptions of modern cosmology.
As for your second statement, that is our initial assumption, yes. And that is what seems to be contradicted by the homogenous map of look-back time+ space we expext from the SDSS. Otherwise there wouldn't be any "paradox" to begin with.
P: 134
 Quote by Chalnoth I don't get what you're saying here. The last scattering surface is most definitely part of the observable universe, and could not exist in a time-homogeneous universe.
As I said the "paradox" can only affect the observable universe, we don't strictly observe the LSS but photons scaping from there after decoupling. And these give us a mostly homogenous map.
P: 4,596
 Quote by AWA Strictly speaking you are right, but if you tell me that we can't interpret redshift as a distance marker and therefore as look-back time you are undermining the very basic assumptions of modern cosmology.
Well, when you presume a static universe, you are undermining the interpretation of redshift itself. There is no redshift either from intervening gravitational curvature or from relative velocities if there's no expansion. So unless you can come up with a completely different mechanism for producing the redshift, then redshift cannot be a proxy for distance. This is what the static universe promoters have repeatedly tried, and failed, to do.

 Quote by AWA As for your second statement, that is our initial assumption, yes. And that is what seems to be contradicted by the homogenous map of look-back time+ space we expext from the SDSS. Otherwise there wouldn't be any "paradox" to begin with.
Uh, what? The further-away galaxies just aren't the same as the more nearby ones. Galactic populations evolve dramatically over time.
P: 4,596
 Quote by AWA As I said the "paradox" can only affect the observable universe, we don't strictly observe the LSS but photons scaping from there after decoupling. And these give us a mostly homogenous map.
We observe the last scattering surface in the exact same way that we observe anything else that emits light. All that we observe from stars, after all, are those photons escaping from the outer layers of the star.

Now, you can always try to propose a different sort of source for the CMB than the last scattering surface, but it's going to be massively difficult to find a model that both predicts a nearly perfect black body spectrum along with the specific power spectrum of deviations from isotropy we observe.
P: 134
 Quote by Chalnoth Well, when you presume a static universe, you are undermining the interpretation of redshift itself. There is no redshift either from intervening gravitational curvature or from relative velocities if there's no expansion. So unless you can come up with a completely different mechanism for producing the redshift, then redshift cannot be a proxy for distance. This is what the static universe promoters have repeatedly tried, and failed, to do.
Never, not even once have I presumed a static universe, much less promoted it. I only put forward what I called a "false paradox" with an easy solution actually(the Big Bang), as an educational kind of game, since I am assuming and promoting standard cosmology.

 Quote by Chalnoth Uh, what? The further-away galaxies just aren't the same as the more nearby ones. Galactic populations evolve dramatically over time.
Never talked about any galaxy evolution specifically either. I talked about homogeneity at large scales.

 Quote by Chalnoth Now, you can always try to propose a different sort of source for the CMB than the last scattering surface, but it's going to be massively difficult to find a model that both predicts a nearly perfect black body spectrum along with the specific power spectrum of deviations from isotropy we observe.
See above.
 Sci Advisor P: 4,596 Now you're really confusing me as to what you're trying to talk about here. We see a universe that changes in time, but is consistent with a particular set of equal-time slices being approximately homogeneous on large scales. We see a thin cone through this universe stretching backwards in time and outwards in space. All of our observations are consistent with the nearby universe stemming from a different realization of the same underlying statistical distribution of homogeneities as the far away universe.
 P: 256 AWA, universe evolves through time. It means that it is not same today as it was earlier, and that it will be in the future. Universe with scale factor, say, 0.5 is not homogeneous (same in composition) with universe with scale factor 1. Now, I know that you get this, but still you are talking about false paradox. I fail to see what that paradox is.
P: 134
 Quote by Chalnoth We see a universe that changes in time, but is consistent with a particular set of equal-time slices being approximately homogeneous on large scales. We see a thin cone through this universe stretching backwards in time and outwards in space. All of our observations are consistent with the nearby universe stemming from a different realization of the same underlying statistical distribution of homogeneities as the far away universe.
This is all correct here, my point was only to remark that when we look around with our telescopes we see not only space but due to the finite value of c, we see spacetime, and in as much as what we observe is homogenous it would seem that spacetime is homogenous in the past direction. It is as simple a remark as this. If this has nothing to do with the perfect cosmological principle or with cosmology, or it's irrelevant, fine. But so far noone has questioned this simple observation.
P: 4,596
 Quote by AWA This is all correct here, my point was only to remark that when we look around with our telescopes we see not only space but due to the finite value of c, we see spacetime, and in as much as what we observe is homogenous it would seem that spacetime is homogenous in the past direction.
Except this just isn't true. The universe changes quite dramatically as we move to higher and higher redshift.

I mean, sure, if you stay at very low redshifts, it all looks fairly homogeneous in both time and space. But once you head to higher redshifts (say, greater than 1)., really dramatic changes start to become apparent. The further out you go, the more dramatic the changes become.
P: 134
 Quote by Chalnoth Except this just isn't true. The universe changes quite dramatically as we move to higher and higher redshift. I mean, sure, if you stay at very low redshifts, it all looks fairly homogeneous in both time and space. But once you head to higher redshifts (say, greater than 1)., really dramatic changes start to become apparent. The further out you go, the more dramatic the changes become.
If you are saying that the universe is not homogenous past redshift z=1, I think that is not only wrong but clearly ATM.