Hi Jorrie,

Interesting, but I do not quite know what to make of your blue "teardrop" shape. Does it mean we can only see things as they were when passing the sides of the teardrop? I can understand that we cannot see things as they were outside of the teardrop, because that is presumably the limits of the observable universe. But what about things inside the teardrop? Somewhat confusing.

I hope you see what is bothering me, otherwise I'll try again.

SL

Hi SL, you wrote: "Does it mean we can only see things as they were when passing the sides of the teardrop?"

In a way, yes. But remember that the teardrops are the spacetime paths of photons that arrive at our telescopes 'now'. If we have observed these same galaxies long ago, it must have been a different set of photons and they would have represented a smaller teardrop path - shorter and thinner. Likewise, if the same galaxies were to be observed far into the future, the photon paths will follow a bigger teardrop path - taller and fatter.

In this sense, certain things inside and outside of the present teardrop are observable - but they still have to sit on the 'now-teardrop' of the time under consideration. Each different teardrop spans the whole history of our observable universe, from t~300 thousand years till the present of that time.

The teardrop is compatible with the simple fact that we can observe very distant things only as they were very long ago - and nearby things we can observe only as they were recently. In reality, the teardrops are 4-dimensional, three space and one time, but that's impossible to visualize. :(

I hope this clears the 'bother' - else, feel free to ask again. :)

-J

Hi Jorrie,

OK, you say that in the past the teardrop was smaller, which sounds reasonable - I presume that the observable universe was smaller then? What happened to the hyperbolas - were they also smaller/narrower? After all, the galaxies could not have been as far away as they are now and the two galaxies must still start on both curves.

Thanks for your trouble,

SL

Hi SL, you asked: "What happened to the hyperbolas - were they also smaller/narrower? After all, the galaxies could not have been as far away as they are now and the two galaxies must still start on both curves."

A good observation and not at all obvious from the scale of the original teardrop. It looks as if the teardrop and the hyperbola originally follow the same path.

The teardrop initially sits below the hyperbola and then crosses it. To the right is a picture of the origin, zoomed in. What happens for an earlier observation time is that the red/purple hyperbola remains the same size, while the blue 'teardrop' gets shorter/thinner. (Smaller observable cosmos, as you said). Hence, the crossing points, where the two galaxies were when the photons left them, shift inward (and lower), as shown below.

The original galaxy coordinates were D~±3.3, T~0.6 for the present observations. For 'prehistoric' observers at a cosmic age of 12 Gy,¹ the coordinates of the galaxies would have been D~±2.8, T~0.45. The position of the galaxies at T=12 Gy would indeed have been closer than the present ~30 Gly. They would have been around 27 Gy from us, as you can see on the original 'Teardrop'.

You are welcome (I haven't investigated the case for earlier observation before, so this was interesting).

-J

1. We are pretty sure there were no astronomers on Earth at T=12 Gy (1.7 billion years ago), but nothing says there could not have been astronomers on another planet somewhere in the Milky Way at that time. If so, they would essentially have measured those remote galaxies to have the same characteristics as what we would have observed if we were around.

Hi Jorrie,

I have tried to work out some things for myself from the information you gave above, but it does not quite want to jell. Example: you have shown the galaxies as observed at 12 billion years to be at D2=27 Gly from the origin and when the light left them, they were D1=2.8 Gly. This gives an expansion factor of 27/2.8=9.64, which I think translates to a redshift of z=8.64. If anything, this is larger or at least equal to the z=8.6 that was measured recently.

I've read up some more and here are my main problems.

1. By t=12 Gy, the cosmos must have expanded less than it has by now. How is it that the expansion factor is the same, or perhaps higher? Should your "prehistoric" astronomers not have measured a redshift smaller than 8.6?

2. I do not understand the relationship between your blue teardrop and the hyperbolas (in the zoom) - why does the teardrop start out below the hyperbolas (galaxy paths)? And what is the significance of them crossing?

3. The galaxy paths are not quite hyperbolas, are they? They seem to be visually (and by the recession speeds you described) flaring out at the top, I assume because of the expansion that accelerates.

Sorry for the load of questions; I will be happy with a reply whenever you have the time. (You said it is an interesting case and I agree )

SL

Hi SL, you wrote in 1: "By t=12 Gy, the cosmos must have expanded less than it has by now. How is it that the expansion factor is the same, or perhaps higher?"

The first sentence is correct. However, due to the relatively rapid expansion rate around time 0.45 Gy (recession rates ~ 4c), the earlier start of the "Age=12 Gy" photons make them suffer a greater expansion than the "Age=13.7 Gy" photons, which started out later. In prehistoric times the observed redshift of those galaxies would indeed have been higher than they are today (actually close to z=9 at 12 Gy age).

2: "- why does the teardrop start out below the hyperbolas (galaxy paths)? And what is the significance of them crossing?"

This is rather difficult to explain, but here goes. Firstly, the 'blue teardrop' represents photon positions and the hyperbolas represent galaxy positions. Photons can come from the 'edge' of observable space, practically at the origin of my graphs (present z>1000). The galaxies under consideration were never that far away (present z~8), so they started on the 'inside' of the teardrop. Since the teardrop photons are trying to move in our direction and the galaxies not, the galaxies eventually find themselves 'outside' of the teardrop. So, their paths must cross.

Secondly, the galaxies were never near the origin (they haven't formed yet), but the particles that eventually made them, must have been there all along. This is the reason why one can extend the galaxy hyperbolas to almost, but not quite, meet the teardrop near the origin.

Thirdly, we can only observe the galaxies as they were when the two paths crossed. The teardrop shape represents all that we can presently observe and the galaxies only crossed the 'present teardrop' once. Somewhere in the past we could theoretically have observed those galaxies when they were inside the present teardrop, as illustrated by the '12 Gy observations', but that was a different teardrop.

3. "The galaxy paths are not quite hyperbolas, are they?"

Correct - they are distorted hyperbolas, caused by the accelerated expansion. Only without the pesky 'dark energy' could they have been perfect conical sections (elliptic, parabolic or hyperbolic), depending on the energy balance between the kinetic and potential energy of expansion.

I hope this clears at least some of your questions...

-J

Tx Jorrie, I'll have to think more about some of the issues. Will possibly come back with more questions. Time is limited atm.

SL