Cosmological principle paradox?

[AWA]

The cosmological principled as applied to modern cosmology and the standard model concerns only the spatial part of spacetime, this has been criticized based on Minkowski's predicated non-separability of spacetime, that led(among other things) to the "perfect cosmological principle" that applies to both space and time and that was used in the flawed stationary model of Hoyle,Bondi and Gold.

So everybody is pretty confident that, no matter what relativity might appear to indicate ,the cosmological principle only affects the spatial dimensions.

That's why I would like for someone to help me solve this false paradox: When we observe the universe we inevitably not only observe the spatial dimension but (specially at high redshifts) due to the finite nature of light we see a look-back time, we are actually perceiving spacetime, not just space. so if we expect to observe ever more and more homogeneity with distance we a re actually expecting to watch more and more homogeneity the farther in time we look back . But paradoxically this leads to the perfect cosmological principle which is forbidden by a universe with a finite age.

Surely there is a trap in this reasoning, but I can't see it right now.

Any hint would be apreciated.

 

[RLutz]

Hmmm? The cosmological principle just says that we're not special. The observable universe looks roughly the same anywhere you look, the CMB is remarkably uniformly spread, etc. From that, it would make sense that the laws of physics are also the same wherever we look.

Also, the oldest thing we can see is the CMB, and that's pretty darn homogeneous.

 

[AWA]

Hmmm? The cosmological principle just says that we're not special. The observable universe looks roughly the same anywhere you look, the CMB is remarkably uniformly spread, etc. From that, it would make sense that the laws of physics are also the same wherever we look.

Also, the oldest thing we can see is the CMB, and that's pretty darn homogeneous.

It actually follows from what you just said that the universe is spatially isotropic and homogenous at large scales. If you read again my post you might understand the apparent paradox I'm talking about and try to solve it.

 

[George Jones]

That's why I would like for someone to help me solve this false paradox: When we observe the universe we inevitably not only observe the spatial dimension but (specially at high redshifts) due to the finite nature of light we see a look-back time, we are actually perceiving spacetime, not just space. so if we expect to observe ever more and more homogeneity with distance we a re actually expecting to watch more and more homogeneity the farther in time we look back . But paradoxically this leads to the perfect cosmological principle which is forbidden by a universe with a finite age..

How so? These observations are consistent with a scale factor and energy/mass density that evolve with time.

 

[AWA]

How so? These observations are consistent with a scale factor and energy/mass density that evolve with time.

Oh, so you think there's no problem with the "perfect cosmological principle"as defined in http://en.wikipedia.org/wiki/Perfect_Cosmological_Principle in standard cosmology?

Anyway none of what I said in my OP contradicts the consistence of energy/mass density evolving with time.

 

[George Jones]

Oh, so you think there's no problem with the "perfect cosmological principle"as defined in http://en.wikipedia.org/wiki/Perfect_Cosmological_Principle in standard cosmology?

Anyway none of what I said in my OP contradicts the consistence of energy/mass density evolving with time.

Energy/mass density that evolves with time clearly conflicts with the Wikipedia definition of "Perfect Cosmological Principle".

 

[AWA]

Energy/mass density that evolves with time clearly conflicts with the Wikipedia definition of "Perfect Cosmological Principle".

That's my point.

Perhaps I didn't express myself clearly enough.

Let's suppose we had super-advance telescopes (let's forget technical and time limitations for the sake of the argumen) with ultra high deep field that allows us to make a map similar to the SDSS map but up to a redshift z from a little after decoupling, according to standard cosmology, at this scale the map surely would show homogeneity (if we don't find it at this scale I wonder at what scale we might expect to).
But this map is also a look-back time map of the time dimension of the last 13 bly, so it would also be showing us homogeneity in the time dimension.

As a matter of fact we don't need that supertelescope, we are watching an isotropic and homogenous to more than a part in 10^5 map from further time back already, the CMB, so we seem to have homogeneity in time at least up to 13.64 bly which for a universe 13.7 bly old is a good proportion of the total.

Well for me this seems to conflict with this statement from wikipedia:"The Perfect Cosmological Principle is an extension of the Cosmological Principle, which accepts that the universe changes its gross feature with time, but not in space." I mean if it doesn't change in space, it shouldn't change in time to keep congruence with the lookback time we see when we look at the space surrounding us at great distances.

The only solution I find is that our universe follows the "perfect cosmological principle" except at the initial singularity, which could mean that ultimately it doesn't.

 

[Rebound]

The cosmological principled as applied to modern cosmology and the standard model concerns only the spatial part of spacetime, this has been criticized based on Minkowski's predicated non-separability of spacetime, that led(among other things) to the "perfect cosmological principle" that applies to both space and time and that was used in the flawed stationary model of Hoyle,Bondi and Gold.

So everybody is pretty confident that, no matter what relativity might appear to indicate ,the cosmological principle only affects the spatial dimensions.

That's why I would like for someone to help me solve this false paradox: When we observe the universe we inevitably not only observe the spatial dimension but (specially at high redshifts) due to the finite nature of light we see a look-back time, we are actually perceiving spacetime, not just space. so if we expect to observe ever more and more homogeneity with distance we a re actually expecting to watch more and more homogeneity the farther in time we look back . But paradoxically this leads to the perfect cosmological principle which is forbidden by a universe with a finite age.

Surely there is a trap in this reasoning, but I can't see it right now.

Any hint would be apreciated.

I'm not convinced of this statement and I believe therein lies the problem.

 

[Rebound]

<snip>
But this map is also a look-back time map of the time dimension of the last 13 bly, so it would also be showing us homogeneity in the time dimension.
<snip>

I may be wrong, but it would seem to me that red-shift in and of itself contradicts your assertion.

 

[AWA]

I'm not convinced of this statement and I believe therein lies the problem.

Which part of the statement do you find trouble with? I think cosmologists expect homogeneity to be evident the larger the scale, and no one can argue against the fact that the longer distance you observe the farther back in time you are looking.

 

[AWA]

I may be wrong, but it would seem to me that red-shift in and of itself contradicts your assertion.

Well the redgarbage in itself is a constraint to how far we can look, so limits the observable universe, but does not have anything to do with the assumed homogeneity we should find in the observable universe.

 

[Calimero]

There is nothing wrong with cosmological principle. Of course, further we look we see more distant past. We just assume that density is now same there as is it now here.

 

[AWA]

There is nothing wrong with cosmological principle. Of course, further we look we see more distant past. We just assume that density is now same there as is it now here.

"Now there" is an ambiguous expression in relativity as it deals with simultaneity and cannot really be determined in GR. Anyhow, If you admit we are watching the past timeline and what we watch is homogenous, seems like the spacetime is homogenous,not only the space.

 

[Calimero]

Fortunately there is easy way to determine cosmological now. Anyway, if you apply notion of homogeneity to time, then things are not homogeneous over time.

 

[AWA]

Anyway, if you apply notion of homogeneity to time, then things are not homogeneous over time.

can you elaborate on this? without explanation seems a gratuitous statement.
I'm not applying any notion, I'm trying to avoid an apparent contradiction.

 

[Calimero]

Well homogeneity means something like substance uniform in composition. Something that is uniform in composition should have average density just the same in every which sample. If you look at the universe at the early times density is obviosly not the same as it is today.
So, to go back to your first post, static universe would obey perfect cosmological principle.

 

[AWA]

Well homogeneity means something like substance uniform in composition. Something that is uniform in composition should have average density just the same in every which sample. If you look at the universe at the early times density is obviosly not the same as it is today.

That is the starting point of my OP, that is what it should be according to what we know. From there I want to fit the fact that the further we observe the universe the bigger the map we can build of the uniform composition of the uniform is also a map of the past worldline of the universe, so if it is uniform as all cosmologists expect, it informs us also of time homogeneity.

 

[Calimero]

You keep talking about homogeneity of time or spacetime. Homogeneity applies to matter, energy or structures. I am really not sure what are you asking.

 

[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.

 

[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.

 

[AWA]

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.

 

[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.

 

[AWA]

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.

 

[Chalnoth]

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.

 

[AWA]

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.

 

[AWA]

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.

 

[Chalnoth]

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.

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.

 

[Chalnoth]

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.

 

[AWA]

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.

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.

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.

 

[Chalnoth]

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.

 

[Calimero]

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.

 

[AWA]

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 no one has questioned this simple observation.

 

[Chalnoth]

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.

 

[AWA]

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.

 

[Chalnoth]

If you are saying that the universe is not homogenous past redshift z=1, I think that is not only wrong but clearly ATM.

What I'm saying is that the universe at low redshifts (say, z=0.01, for instance) looks very different from the universe at z=1 when you look at the details, such as the separation between galaxies and the sorts of galaxies you see. The differences increase as you go further back.