# About the size of the Universe and distance between galaxies

1. Nov 17, 2014

### tonyxon22

I have heard and read many times and I’ve also seem many pictures about galaxies that are 13.000 million light years away. One of my favorites (actually I have it as my cell phone’s wallpaper) is the famous “Hubble Space Telescope Ultra Deep Field”.

The doubt that I’ve always had is related to when “they” state that given the distance of those galaxies, it took 13.000 million years to their light to reach us. At the same time, it think about the fact that the Universe is approximately only 700 million years older than that light, and that it has been continuously expanding.
So every time I look at those pictures (which is essentially every 10-15 minutes ‘cause I have it on the cell phone) if find myself asking these questions:
1) How far away could those galaxies be from us at that moment (13.000 million years ago)?
2) It is possible to have a Universe bigger than 13.000 million light years only 700 million years after the Big Bang?
3) Have they always been at that distance from us? (that does not makes much sense for me since the universe is expanding, so I would expect them to be farther away now)
4) Were they closer back then? If so, how come the light took that amount of time to reach us?
Maybe these are very basic concepts, but I have a hard time understanding the facts considering the limit of the speed of light and the young age of the universe when this light was emitted.

Thanks and best regards,

2. Nov 17, 2014

### Orodruin

Staff Emeritus
The redshift 700 million years after the big bang is about 7.5, which means the Universe was ca 8.5 times smaller at that time. Thus:

1) They would have been a factor 8.5 times closer, so ca 1500 million light years away.
2) Yes, although it will not be in causal connection.
3) No. See above. Yes, they are further away now (the comoving distance is ca 30000 million light years).
4) Yes, they were closer. The time the propagation takes is not set by the distance when the light was emitted. It depends on the history of the expansion of the Universe.

3. Nov 17, 2014

### tonyxon22

So, may I understand that they where 1.500 million light years away from us when the light was emitted, and yet the time that light took to reach us was 13.000 million light years? The relation between these two numbers is very similar to the factor of 8.5 that you mention.
This makes me think about that other phrase that you find a lot when reading about the Big Bang, "the expansion of the space itself". Is this related to what happened here? Something like the light, even though it was emitted at what was then a distance of 1.500 million light years, began to travel but the space between us was expanding at a much more larger rate (8,5) than the speed of light?

4. Nov 17, 2014

### PeroK

Here's a simplistic explanation. As light moves through the universe, the space being the galaxies is expanding. So, over very long distances, the light takes longer than the initial distance would suggest. Light travels at c throughout its journey, but it ends up travelling more distance than the original separation of the galaxies. Also, while the light has been travelling the universe has continued to expand and the galaxies are now much, much further away.

This means that you have three distances to consider:

a) The distance between the galaxies when the light set out.
b) The distance the light eventually travelled (b > a).
c) The current distance between the galaxies when the light arrives (c > b).

Last edited: Nov 17, 2014
5. Nov 17, 2014

### Orodruin

Staff Emeritus
Yes, sorry, I was thinking too fast. It should be the current distance divided by 8.5, so 3500 million light years.

6. Nov 17, 2014

### tonyxon22

The specific ratio is not what is important for me but the actual concept. Is my statement correct?

Also, what do you mean by this?

7. Nov 17, 2014

### Orodruin

Staff Emeritus
You cannot compare the speed of light with the expansion rate of the universe, they have different units. PeroK put it quite neatly, while the light started propagating, the Universe continued to expand, meaning that distances both behind and in front of a light signal increase. This is also why a signal from something that is now 30000 light years away has already reached us - the light propagated a significant fraction of the way when the Universe was smaller.

The Universe may very well be (and always have been) infinite. However, then parts of the Universe cannot have had time to communicate with each other since light will not have had sufficient time to do so. It is possible to distinguish the part we can see as the observable universe.

8. Nov 17, 2014

### tonyxon22

Ok I understand now that the expansion rate of the universe also affects the space behind the signal. However, it’s still no clear to me how with a light signal we can say that the light was emitted at a certain distance from us (say 3500 Mly), which now corresponds to another distance (13.000 Mly) and that current object is now at even another distance (30.000 Mly) farther away than the observable universe (since the observable universe can be, at most, a sphere with a radius of 13,8 Mly). I’m not quite sure of what I’m looking at anymore.
Regarding your comment about the universe being infinite, you are referring to an infinity of empty space that has always been there even before the Big Bang? Because we know that at some point, shortly after the BB (enough time for the condensation of matter) all the atoms where very close together. So how can it be that there are parts of the universe that could not communicate with each other?

9. Nov 17, 2014

### Orodruin

Staff Emeritus
There is a very common misconception that the expansion of the Universe is an expansion away from some central point or explosion. This is not the case. When I am saying that the Universe may be infinite, I am talking about the Universe itself and the BB happened everywhere in the Universe at once. It is simply that the Universe was expanding so fast that distances grew at a tremendous rate. This expansion is not limited to increase distances at a speed of the speed of light or slower. Since it is space itself that is expanding, this does not break any of the postulates of general relativity.

The light from the CMB that is reaching us now originated from a point in space that is currently about 46000 million light years away. Thus, the current diameter of the observable universe is around 92000 million light years. Again, this is because the Universe used to be smaller and the light travelled a lot during that time.

10. Nov 17, 2014

### Staff: Mentor

The first and last distances (3500 Mly and 30,000 Mly) are "comoving" distances, which means they are coordinate distances in comoving coordinates--coordinates in which observers who are "moving with the flow" of the expansion are at rest, keeping the same spatial coordinates at all times. These observers can be distinguished physically by the fact that they observe the universe to be homogeneous and isotropic. In these coordinates, all "changes in distance" are contained in a single function of time, the "scale factor"; if the universe is 8.5 times larger now than it was when the light was emitted, that means the scale factor has increased by a factor of 8.5. All distances between comoving objects (we assume that the object that emitted the light and we ourselves are both comoving for purposes of this discussion) will increase by the same factor.

The second "distance" (13,000 Mly) is a different kind of distance: it is the time (in comoving coordinates) that the light has traveled, multiplied by the speed of light. You should not expect to be able to compare this distance directly with the other two and have the comparison be meaningful; they are physically different kinds of things.

No, he's referring to the universe itself being infinite in spatial extent. There are models (arising from inflation theory) that postulate that the universe we observe is a "bubble" within a pre-existing infinite space, but that's a whole different subject.

Because even though the individual particles were close together, they were moving apart so fast, and the time since the BB had been so short, that light emitted by one particle just after the BB had not had enough time to catch up with another. The further apart the individual particles were shortly after the BB, the longer it would take for light emitted by one to catch up with the other; and if the particles were far enough apart shortly after the BB, light from one would not have been able to catch up with the other even 13.7 billion years later (i.e., now).

11. Nov 17, 2014

### Chronos

12. Nov 17, 2014

### tonyxon22

Well, thanks to everyone! My four original questions have been actually answered. It will take some time until the idea properly cooks and settles in my brain but I feel I'm on the track considering all the information you gave me.

Of course, more questions aroused from all this, but I supose that is normal in the process of learning new things and answering questions. I'll take my time to shape them and come back with other threads.

That cosmological calculator looks very interesting but there are a lot of variables in there that I don't have the faintest clue of what they are. I see the comparison between some characteristics of the system at the observation date and the characteristic of the system at the time the "image" was sent, and putting it together with all that was explained here, it makes a little more sense to me now.

Thanks again!
Kind regards,

13. Nov 17, 2014

### Orodruin

Staff Emeritus
I would actually not pay much attention to the calculator until you are more familiar with the very basic concepts behind cosmological expansion and understand how the different distances fit together. Once you do, it can be interesting to play around a bit or to use it for reference.