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Universe Geometry Puzzlement

  1. Jul 5, 2006 #1
    Here's something I can never get my head around, no matter how hard I try.

    As you look out in space, you look back in time. Fine. No problems yet.

    Further back in time, the universe was smaller.....or at least things were closer together. Hmmm......hold on just a minute. We have a problem......at least I do and I doubt I'm the only one with it.

    As you look outwards......the volume of space becomes larger, not smaller. The further out you look, the larger the apparent volume becomes for each similar increase in distance.....and yet, we're told that the universe was actually much SMALLER when the light from those objects was emitted.

    Now I fully understand how it would be the case that further away the expansion would appear to get greater and greater. That should solve the problem ! But....that's not the real issue. It's a bit trickier than that. My problem is that I can't square this up with the angular size of objects. If the apparent expansion increases exponentially with distance, then there oughtn't to be a linear correlation between distance and size ! In other words......a galaxy 10 billion light years away should not simply appear to be half the size of one the same size at 5 billion light years.

    If the increase in expansion with distance is the answer to the 'volume' problem, then surely distant galaxies ought to appear larger than their true apparent size at that distance. Yet I've never read anything that suggests other than a linear decrease in angular size proportional to distance.
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  3. Jul 5, 2006 #2


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    As you look outward, the volume you see (which is a superposition of a range of time in the universe's history) becomes larger, but that certainly doesn't mean that you're looking at a time when the universe itself was larger. We don't see the entire universe at every point in its history, just the small portion of it from which light has been able to reach us.

    In the recent past, the universe has been accelerating (expansion rate getting greater and greater), but in the distant past, it was decelerating. This is not the resolution to your confusion, however.

    Actually, you're right, it isn't. The expansion of the universe destroys the simple relationship between distance, physical size, and angular size. Only in the local universe is a linear relationship a good approximation.
    Last edited: Jul 5, 2006
  4. Jul 5, 2006 #3
    I think the problem is that despite having copious books on the subject I've never seen anything that suggested the relationship was anything other than linear.......especially with space being generally flat....so I've just assumed that it is, and that someone would have said so if it wasn't.

    If it isn't, then there isn't a problem any more.
  5. Jul 5, 2006 #4


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    The angular diameter distance [itex]d_a[/itex] is defined as the distance that relates the angular diameter of the object in the sky [itex]\theta[/itex] and the actual size of the object [itex]s[/itex], such that [itex]\theta = s / d_a[/itex] as you can read in wikipedia. In the standard cosmological model this distance has a maximum value at about redshift z = 1.7, which means that the angular diameter in sky of objects of same size at different redshifts decreases until z = 1.7 and afterwards increases. In a static space that distance is equal to the actual distance measured with rulers, [itex]d_a = d[/itex], and [itex]\theta[/itex] decreases always with distance (for objects of same size).
    Last edited: Jul 6, 2006
  6. Jul 9, 2006 #5
    No matter how far we look, the maximum distance we can see is limited by the maximum distance light has travelled since the Big Bang, right?
  7. Jul 9, 2006 #6


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    Almost. There's actually a "surface of last scattering" at redshift of ~1100 beyond which the universe is optically thick -- that, is opaque. Of course, if you're "observing" the universe with something other than light (like neutrinos or gravitational radiation), you can see beyond that.
    Last edited: Jul 9, 2006
  8. Jul 9, 2006 #7
    "There's actually a "surface of last scattering" at redshift of ~1100 beyond which the universe is optically thick -- that, is opaque."

    This really intriques me. In terms of the language used to describe various aspects of the observable universe. Is it possible that what we see with optical or radio tools can be recalibrated to penetrate spectral emissions by redefining 'space' itself?
  9. Jul 9, 2006 #8


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    I don't know what that means. Theoretically, we can probe to very early epochs with gravitational radiation, which are fluctuations in spacetime.
  10. Jul 10, 2006 #9
    Geometry of the CMB

    What I was thinking has to do with the concept of 'flat space' in terms of the CMB. Does the perception of 'flat space' indicate a universe imbedded on a 2 dimensional 'plane' or a 1 dimensional 'horizon' line? In other words - is our universe 'on a singularity'? Please keep in mind I only wish to understand the concept of 'space' as separate from energy and time, even though I realize that space and time are inseparable as per Einstein's relativity. Now if space is 'flat', is there another 'side'? (Put another way - is it possible that the CMB functions as a form of 'boundary' to 'flat space'????)
  11. Jul 10, 2006 #10


    A "Flat" Universe has euclidean 3-D space. Hence the planes of a flat universe are flat, and not curved.
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