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Cosmological principle paradox?

  1. Sep 22, 2010 #1

    AWA

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    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.
     
  2. jcsd
  3. Sep 22, 2010 #2
    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.
     
  4. Sep 22, 2010 #3

    AWA

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    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.
     
  5. Sep 22, 2010 #4

    George Jones

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    :confused: How so? These observations are consistent with a scale factor and energy/mass density that evolve with time.
     
  6. Sep 22, 2010 #5

    AWA

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    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.
     
  7. Sep 22, 2010 #6

    George Jones

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    Energy/mass density that evolves with time clearly conflicts with the Wikipedia definition of "Perfect Cosmological Principle".
     
  8. Sep 22, 2010 #7

    AWA

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    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 dmension 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.
     
  9. Sep 22, 2010 #8
    I'm not convinced of this statement and I believe therein lies the problem.
     
  10. Sep 22, 2010 #9
    I may be wrong, but it would seem to me that red-shift in and of itself contradicts your assertion.
     
  11. Sep 22, 2010 #10

    AWA

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    Which part of the statement do you find trouble with? I think cosmologists expect homogeneity to be evident the larger the scale, and noone can argue against the fact that the longer distance you observe the farther back in time you are looking.
     
  12. Sep 22, 2010 #11

    AWA

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    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.
     
  13. Sep 22, 2010 #12
    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.
     
  14. Sep 22, 2010 #13

    AWA

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    "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.
     
  15. Sep 22, 2010 #14
    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.
     
  16. Sep 22, 2010 #15

    AWA

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    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.
     
  17. Sep 22, 2010 #16
    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.
     
  18. Sep 22, 2010 #17

    AWA

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    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.
     
  19. Sep 22, 2010 #18
    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.
     
  20. Sep 22, 2010 #19
    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.
     
  21. Sep 23, 2010 #20

    Chalnoth

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    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.
     
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