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The big bang's optical paradox

  1. Apr 21, 2013 #1
    Optics would predict that objects appear bigger in size as higher the redshift and the density should be the same independent of the galaxys redshift.
    As far I know this is not supported by observations. Anybody has an explanation please?

  2. jcsd
  3. Apr 21, 2013 #2


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    there is an effect like that, google "wright cosmo calculator"
    for each redshift he gives both the proper distance and the "angular size distance".
    It is a very interesting discrepancy.

    But I am interested to know how you came to the conclusion that there should be an effect.

    Why do you think that at higher redshift objects should have larger angular size in the sky?

    (It is true after a certain point! But maybe you could think that for a wrong reason, so please explain.)
  4. Apr 22, 2013 #3
    If we look back in time (higher redshift) we see the universe within a smaller volume (because it is expanding since the light departed its origin). Lets forget about the 3rd dimension for the sake of simplicity. Lets say we look back at a smaller surface. Now this smaller surface (then) is projected on to a bigger surface (now). The projection is homogen - is is evenly distributed over our sky. The only way to do such a projection is either tiling or scaling. Tiling would be observable so we exclude this. Scaling would mean that every object would appear bigger.
    Let for example take the CBM, it is radiated from an volume (surface) that was small in size compared to our observable universe still it covers the whole sky. It is the biggest visible object in the sky! It is of course scaled. So should be all early galaxys.
    I hope its clearer now, it just simple optics.
    Anyway question i how much the observations agree.

    Last edited: Apr 22, 2013
  5. Apr 22, 2013 #4


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    Yes! To me this seems like a very good explanation! This effect is very much taken into account. It is essential to the way data is analysed.
    I have talked about this in some past threads, but long enough ago that I don't remember how to find them. Out to a certain redshift, or distance, the angular size gets less and less, but from that point on as you go farther away the angular size (of a standard object) increases!

    I think you would be interested to look at Ned Wright's calculator. It has a separate output that illustrates this effect. Google "wright calculator" or "wright cosmo calculator"

    I just went there and put in 67.9 for Hubble, .30 for OmegaM, .70 for Omegavac,
    (more in line with recent Planck model parameters)
    and I found that the MAXIMUM ANGULAR SIZE DISTANCE is for objects with redshift 1.6.
    In fact if you put in z=1.6 you get an angular size distance of 5.8754 Gly
    But if you put in z=1.58 or 1.62 you get smaller angularsize distance!

    So as you increase redshift out to 1.6 the angularsize distance increases (a standard object looks smaller and smaller, its angle width in sky diminishes). This is "normal behavior" in a rough qualitative sense.

    But then beyond that the farther away the standardsize object is, the BIGGER it looks, the more angle in the sky it occupies.
    Last edited: Apr 22, 2013
  6. Apr 22, 2013 #5


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    Cat, here is something you might like.

    You realize there must be a threshold distance where this "paradoxical" reversal begins to take effect. Within that range objects there has not been enough time for expansion to occur, so far away things look tiny---no paradox. Beyond that range there has been sufficient time and expansion for the counterintuitive thing to occur.

    This threshold is around z=1.6. That means an enlargement factor of S=z+1=2.6.
    Distances have been enlarged by a factor of 2.6 since that time. Wavelengths from that time have been expanded by that same 2.6 factor while in transit.

    It's an interesting fact that in proper distance terms (distance as if measured by conventional means with the expansion process frozen at some instant) the past lightcone is teardrop shaped, or pearshaped.

    The maximum girth and maximum radius of the past lightcone come at S=2.6.
    So the threshold for the funny optical effect which you figured out would occur, that threshold corresponds to the widest point of the past lightcone.

    A galaxy on our past lightcone whose light we are getting with S=2.6 (or if you prefer z=1.6), when it emitted the light it was receding at the speed of light and so the light at first did not make any progress. It was coming towards us at speed c thru space which was getting farther from us at speed c, so the net gain was zero.

    To visualize, look at the top figure here:

    The maximum girth comes where the side of the teardrop is vertical, as you see. And it is also the point where the Hubble sphere radius intersects the lightcone radius, just another way of saying that the emitter galaxy at that point is receding at c. As you know that is just the definition of the Hubble radius.
    Last edited: Apr 22, 2013
  7. Apr 22, 2013 #6


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    Another thing to try--go to:
    and put in S=2.6 for the upper S value
    and steps=0

    You should get that Hubble radius and the proper distance "then" (at time of emission) are approximately the same. That is R ≈ Dthen.

    To make the equality more exact, set S = 2.5987
    (put that in for the upper S value and set steps=0)
    then you should get that both R and Dthen were 5.837 billion lightyears at that time,
    and that the year was 4.047 Gy, that is around year 4 billion.

    The precision is overstated, you can round the numbers to suit yourself, but the main idea is that your intuition is right about older things looking bigger.
    this is true about galaxies that we see as they were before year 4 billion.
    with a wavestretch factor of 2.6 or more.
    Beyond that point, the older their light is, the bigger they look.

    And the farthest any galaxy we can see ever was at the time of emission was 5.8 billion lightyears.
    Such a galaxy would "look the smallest" (have smallest angular width) relative to its actual real size.

    The calculator will also tell you the present-day proper distance (what you would measure by conventional means if you could halt expansion process at the present day long enough to measure.)
    Last edited: Apr 22, 2013
  8. Apr 22, 2013 #7
    First of all thanks for the very detailed response.
    I have been trough all these calculators and I found it was Einstein who suggested that it would be the best disprove of all steady state theories if this behaviour would be observed. Question is where can I look up the relevant observations? Any Images with z and angular size parameters? I am googling and will post any results.
    Still it is a spooky effect.

  9. Apr 22, 2013 #8
    Last edited: Apr 22, 2013
  10. Apr 22, 2013 #9


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    I'm not sure what is meant by "no reliable observations". Correct me if I'm wrong but the measurement and interpretation of the acoustic peaks of the CMB involves this angular size effect to an intense degree and it is seeing a huge amount of activity these days. Another important contributor to determining the cosmic model parameters is the "BAO" study based on galaxy redshift surveys, which, as I understand it, necessarily involves correcting for this effect.

    Maybe we are misunderstanding each other because of a distinction between direct and indirect measurement. One fits massive amounts of data to a model, which then says that the CMB stretch factor S=1090. Distances have expanded by that factor since last scattering. And the model tells us the last scatter surface radius is NOW 45 Gly and back THEN at emission time was 42 Mly. And we see the effect of ACOUSTIC waves in this small area of hot gas. We estimate the distance between acoustic peaks. This is like a yardstick which was placed at a distance of 42 million ly. Now the yardstick appears 1090 times bigger.

    And folks have to see if this is all consistent. Is the implied speed of sound in the gas consistent with the temperature and density which the model predicts?

    It seems to me that we are immersed in calculations in which recognizing this effect on the apparent angular size of stuff plays an essential role.

    BAO means "baryon acoustic oscillation" and it is something different, detecting ripples in the large-scale structure, the distribution of baryonic matter as shown by clusters of galaxies. It does not involve the CMB but I believe it also involves correcting for this kind of effect.

    I can't speak at all authoritatively about this but I'm puzzled by the claim of "no observation".

    Maybe what we don't have is DIRECT observation of the variation of angular size, say around S=2.6. It would be very interesting to determine the minimum observationally, instead of fitting the standard model to all sorts of data and then calculating it.

    Charles Hellaby had an interesting idea along these lines in 2006 and URGED MAKING DIRECT observational determination a priority in future.

  11. Apr 22, 2013 #10


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    Again this is something that might intrigue you, and perhaps other readers (if anyone is curious).

    The Mass of the Cosmos
    Charles Hellaby
    (Submitted on 23 Mar 2006)
    We point out that the mass of the cosmos on gigaparsec scales can be measured, owing to the unique geometric role of the maximum in the areal radius. Unlike all other points on the past null cone, this maximum has an associated mass, which can be calculated with very few assumptions about the cosmological model, providing a measurable characteristic of our cosmos. In combination with luminosities and source counts, it gives the bulk mass to light ratio. The maximum is particularly sensitive to the values of the bulk cosmological parameters. In addition, it provides a key reference point in attempts to connect cosmic geometry with observations. We recommend the determination of the distance and redshift of this maximum be explicitly included in the scientific goals of the next generation of reshift surveys. The maximum in the redshift space density provides a secondary large scale characteristic of the cosmos.
    6 pages, 9 graphs in 3 figures, published in Monthly Notices of the Royal Astronomical Society.

    This guy Hellaby is at Cape Town University. Here is a paragraph excerpt from the introduction.
    It is well known in observational cosmology that our past null cone (pnc) has a maximum in its areal radius, ˆRm, where the angular size of sources of a given size is minimum. Beyond this point, more distant images, though dimmer, subtend larger angular sizes [3, 4]. It is also known in relativistic cosmology that this maxi- mum occurs where the observer’s pnc crosses the apparent horizon. What hasn’t been realised is that a measure- ment of this maximum is equivalent to a measurement of the mass within a sphere of areal radius ˆRm, and that this relationship is quite general, not requiring the assumption of homogeneity for example.
  12. Apr 23, 2013 #11
    Thanks, still I hope someone can come up with some study which beyond the CBM shows the effect. What I like to have beyond theories is the hard currency of proves and the angular size would be an important one. It came to my mind and now I see that is an old suggestion. I have read different explanations about cosmological phenomena with the Big Bang as one of them and I thought it would give any other theory a very hard time if the angular size phenomenon could be observed. I am very careful to make any decision which theory is best, remember the corpuscular theory of light? Particle, then wave, then particle again and finally it was decided it is both of it.
    Anyway I hope somebody can point me to some study which researched it further. Would be very helpful. I keep looking and post any results here.

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