I stumbled upon this text which illustrates and says:

We find that as the object is moved to higher redshifts its angular size first decreases (as naively expected) but soon begins to increase after passing through a minimum value.

Is this correct for the mainstream standard model? What would an English language explanation be?


Yes this is correct for the standard model. I believe the English language explanation would be that the angular size of a galaxy does not depend on its current distance to us, but its distance when the light we currently see from it was emitted (here using "distance" synonymous with "proper distance"). Though I also believe there are other complicating factors such as the spatial geometry of the Universe.

Look at the first diagram in Figure 1 in this paper, notice how the size of the past light cone in terms of proper distance firstly increases as we go back in time, before reaching a maximum and decreasing to zero at t = 0.

  • $\begingroup$ Aaargh! I've actually read that paper, but didn't realize this implication. The universe is so strange. I understand Chris Impey who in a public lecture series kind of mumbled to himself: "- I should just make up mad stuff to say in these lectures. I would get away with it." $\endgroup$ – LocalFluff Jan 25 '15 at 16:16
  • $\begingroup$ Those diagrams are immensely useful, there's a lot of hidden information in them! Another way of looking at it perhaps is that, though the size of gravitationally bound objects like galaxies is not hugely affected by expansion, the light as it travels from the galaxy to us will be affected by expansion causing the angular size to expand. In a Universe with a particle horizon there will always come a point where the expansion of the angular size due to cosmological expansion overwhelms the decrease in angular size due to distance. $\endgroup$ – John Davis Jan 25 '15 at 16:44

Here's a drawing that may help understand (edited to take into account the fact that the Universe expands not only along the line of sight, but in all directions — thanks to @Ed Shaya):

  1. In the distant past, at $t = t_1$, you (or your ancestors, or the Milky Way seed) was close to the other galaxy, and photons were emitted from the edges in the shown direction (as well as all other directions). If the Universe didn't expand, the paths of the two photons would cross at the point $p_1$, at an angle $\theta_1$.
  2. At a later time, $t = t_2$, while the Universe is expanding, those photons are traveling in your direction, but still haven't caught up with you. At the same time, the expansion have pulled the photons farther apart, so that their linearly extended point of crossing $p_2$ lies farther away, and their angle of cross is $\theta_2 > \theta_1$.
  3. At present time, $t = t_3$, you receive the photons at the point $p_3$. The galaxy is now far, far away (and has evolved significantly), but the angle you measure between the photons has $\sim$nothing to do with the present size of the galaxy. Rather, it is given by its original angular size, plus a further expanded angle $\theta_3$, so that it now spans a large angular diameter (and looks as it did at $t = t_1$).

Angular size time evolution slices

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    $\begingroup$ Great illustration, thumbs up! I have no trouble understanding this logically. But... intuitively this is ridiculous! $\endgroup$ – LocalFluff Jan 26 '15 at 19:33
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    $\begingroup$ As drawn, it does not explain why a galaxy at z > 1 would appear bigger than one of the same size at z < 1. You need to add that the distance between the two photons is also affected by the universe expanding, so the lines widen even more. It is like lines of constant longitude on a globe that is being inflated. $\endgroup$ – eshaya Jan 27 '15 at 18:42
  • $\begingroup$ Good point, @EdShaya. I hadn't thought of that. $\endgroup$ – pela Jan 28 '15 at 22:02
  • $\begingroup$ I edited the drawing. It's a bit more messy now, though… $\endgroup$ – pela Jan 28 '15 at 22:40
  • $\begingroup$ Okay, now I understand nothing again. I suppose I'm sane after all. $\endgroup$ – LocalFluff Jan 29 '15 at 2:43

This is an interesting thought,but red shift was a theory that could be answered by assuming near light velocities.The belief in,this unproven idea,invokes argument of"If it is coming toward us then we will already have seen it"


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