<p>The 13 billion lightyears distance of the quasar mean 13 billion lightyears <a href="http://en.wikipedia.org/wiki/Distance_measures_%28cosmology%29" rel="nofollow">light-travel distance</a>. In other words, the light took 13 billion years to reach us, independent of the distance the quasar is now away from us.</p>

<p>The current proper distance (a chain of rulers would measure) is called <a href="http://en.wikipedia.org/wiki/Comoving_distance" rel="nofollow">comoving distance</a>; it is much larger than the light-travel distance for large redshifts.</p>

<p>The quasar is moving away from us in an accelerated fashion, and is now moving away faster than light. This means, light which is emitted now (in the sense of <a href="http://en.wikipedia.org/wiki/Cosmic_time" rel="nofollow">cosmic time</a>) by the galaxy, the quasar may have evolved into in the meanwhile, will never reach us.
The light, the quasar emitted 13 billion years ago, left the quasar just in time to leave the regions of the universe which later have been receding faster than light from us, to eventually reach us.</p>

<p>As a thought experiment, imagine walking with 5 km/h (our playground speed of light) on a rubber band which is expanding with a constant rate of 1 km/h per meter actual length of the band. (This leads to an exponential acceleration of the distance between the two marks on the band). If you start closer than 5 meters away from your goal, e.g. from a start mark (our quasar) 4.50 m away, you'll finally reach the goal mark. The start mark will soon be further away from the goal mark than 5 meters, therefore receding with more than 5 km/h from the goal shortly after you left the start mark.
At the moment you arrive at the goal mark, the start mark will be much further away (comoving distance) than the distance you needed to walk (light travel distance). And you've been walking a longer distance than the (proper) distance between the marks was at the time you started walking.</p>

<p>Btw.: Acceleration is only felt as a force, when the velocity to the local rubber band (mataphoric space-time) is changed.</p>

<p><strong>Example</strong> calculations with a protogalaxy of redshift $z=11.9$:
Based on the <a href="http://adsabs.harvard.edu/abs/2006PASP..118.1711W" rel="nofollow">Cosmology Calculator</a> on <a href="http://www.astro.ucla.edu/~wright/CosmoCalc.html" rel="nofollow">this website</a>, the cosmological parameters $H_0 = 67.11$ km/s/Mpc,
$\Omega_{\Lambda} = 0.6825$ provided by the <a href="http://en.wikipedia.org/wiki/Planck_%28spacecraft%29" rel="nofollow">Planck</a> project, and the <a href="http://en.wikipedia.org/wiki/Scale_factor_%28Universe%29" rel="nofollow">scale factor</a> $d(t) = d_0 / (1+z)$, setting $\Omega_M = 1- \Omega_{\Lambda} = 0.3175$, the
age of the universe is $13.820$ Gyr, and the comoving distance of the protogalaxy is $d_0 = 32.644$ Gly.</p>

<p>The age of the universe, we see the protogalaxy (at redshift 11.9), was 0.370 Gyr, light-travel distance has been 13.450 Gly, proper distance was 2.531 Gly.</p>

<p>After the protogalaxy has been emitting light 0.370 Gyr after the big bang, the light travelled towards us through space of redshift beginning with 11.9 shrinking to 0; the light arrived at us 13.820 Gyr after the big bang. The comoving distance (to us) of the space traversed by the light started with 32.644 Gly shrinking to 0. The remaining distance, the light needed to travel, started with 13.450 Gly shrinking to 0. The proper distance between the protogalaxy and us started with 2.531 Gly increasing to 32.644 Gly due to the expansion of spacetime.</p>

<p>Here some intermediate states described by
a couple of tuples, consisting of</p>

<ul>
<li>redshift $z$,</li>
<li>according age $t$ of the universe (Gyr),</li>
<li>comoving radial distance (at age $t$) of the emitted light, we can now detect from the protogalaxy (Gly),</li>
<li>remaining light travel distance of that emitted light (Gly),</li>
<li>proper distance of the protogalaxy at age $t$, according to $d(t) = d_0 / (1+z)$:</li>
</ul>

<p>$$(11.9,  0.370, 32.644, 13.450,  2.531),$$
$$(11.0,  0.413, 32.115, 13.407,  2.720),$$
$$(10.0,  0.470, 31.453, 13.349,  2.968),$$
$$( 9.0,  0.543, 30.693, 13.277,  3.264),$$
$$( 8.0,  0.636, 29.811, 13.184,  3.627),$$
$$( 7.0,  0.759, 28.769, 13.061,  4.081),$$
$$( 6.0,  0.927, 27.511, 12.892,  4.663),$$
$$( 5.0,  1.168, 25.952, 12.651,  5.441),$$
$$( 4.0,  1.534, 23.952, 12.285,  6.529),$$
$$( 3.0,  2.139, 21.257, 11.680,  8.161),$$
$$( 2.0,  3.271, 17.362, 10.549, 10.881),$$
$$( 1.0,  5.845, 11.124,  7.974, 16.322),$$
$$( 0.0, 13.820,  0.0  ,  0.0  , 32.644).$$</p>

<p>The Hubble parameter, meaning the expansion rate of space per fixed proper distance, is decreasing with time. This allowed the protogalaxy to recede almost with the speed of light, although it was just about 2.5 Gly away from us (proper distance) in the time, when it emitted the light we detect now.
Nevertheless distant objects in this space accelerate away from us, since their increasing distance is multiplied with the expansion rate of space.</p>

CC BY-SA 3.0
2014-04-14T19:08:21.407Z
Yeah, I "get" all of that, and thanks for going into it.  But I'm not sure that answers my question, and I'm not sure that I've communicated it well enough.  Here is a list of the most distant objects: http://en.wikipedia.org/wiki/List_of_the_most_distant_astronomical_objects.  One of them is 13.37 billion light years away.  The point is, that's less than 0.5 years from the age of the universe.  You might as well say we were on top of that object when the light left it.  How could it possibly take that long to reach us when we were so close to it when the light left it?
user3355020
CC BY-SA 3.0
2014-07-26T06:39:12.197Z
@user3355020 Because space is expanding. And btw, the Milky Way wasn't born at that time.
Yashbhatt
CC BY-SA 3.0
2014-04-14T00:54:27.520Z
2014-04-15T23:49:35.430Z
2014-04-15T23:49:35.430Z
Gerald
<p>Couldn't comment as I do not have the proper rep yet, but regarding @user3355020 and the answer provided by @Gerald, (and me being far less educated than I ever could have imagined before reading this), I interpret it like this: (and I wouldn't be surprised if this is wrong)
the speed of light is constant, but the expansion rate of the universe is not. The over-simplified observed effect is similar to the feeling of having a dream where you're in a hallway and you're running away from something as fast as you possibly can,focused on the end of the hallway, but the hallway seems to stretch more and more as time goes by. Much in the same way, light is the person running and 'space' is the hallway and earth is the opening at the end. Some light was able to get far enough in the beginning that the stretch did not impact it so much as to make it impossible to reach earth (it's just going to take it 13+ billion yrs), and some light (and from my understanding of the answer given by @Gerald all light after a certain 'time') will never reach earth.</p>

CC BY-SA 3.0
2014-07-24T10:07:37.447Z
2014-07-24T10:07:37.447Z
MegaMark
<p>I was directed here after asking a similar question at <a href="https://astronomy.stackexchange.com/questions/50720/age-of-the-universe-vs-its-size?noredirect=1#comment113015_50720">Age of the universe vs. it&#39;s size</a>.</p>
<p>I'm still confused.  The universe is estimated to be 13.7-13.8 billion years old &amp; that is the observed distance of the Cosmic Microwave Background...which is our cosmic horizon...the furthest we can see.</p>
<p>But the universe has galaxies 46 billion years away.  I can't figure out how those 2 are reconciled.  I would think that the universe would be 46 billion years old if that were true.</p>
<p>Is it that because the universe is expanding at an accelerated rate, a galaxy could be 46 billion light years away, but that it took only 13.7+ years to get there?</p>

CC BY-SA 4.0
2022-10-12T00:01:57.937Z
This does not provide an answer to the question. Once you have sufficient [reputation](https://astronomy.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://astronomy.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/30124)
WarpPrime
CC BY-SA 4.0
2022-10-12T20:08:17.797Z
Sorry, Phil. The Answers section isn't the place to ask questions. If the existing answers here (and on the Linked & Related questions) don't adequately answer your question that we closed, please edit that question. Mention that you've seen these answers, and ask about the specific points that you need further help with. When you edit that question, it will go into a review queue so that people can vote to reopen it.
PM 2Ring
CC BY-SA 4.0
2023-02-18T20:46:56.973Z
I am breaking the rules, but the answer to your question is that the universe can be infinitely big and 13.7 billion years old.  First of all, the universe is not subject to the special relativity rule of no motion greater than the speed of light.  Secondly, an infinitely dense Big Bang does not have to be a point, but the Observable Universe part of it would have been a point.
eshaya
CC BY-SA 4.0
2023-02-20T23:16:42.617Z
Thank you very much for your response.  I now realize that although light has reached us from ~13.8 light years away & the universe is that age, the universe has expanded far beyond our horizon (the CMB).  I also apologize for violating any rules, as this was the very first question I've asked in this forum.
Phil R
CC BY-SA 4.0
2022-10-11T21:45:25.580Z
2022-10-11T21:45:25.580Z
Phil R
<p>I was recently reading about a galaxy or quasar (not sure which, so lets just say quasar) where the estimated distance to this thing was some very significant fraction of the age of the universe.  What I mean is this:  I can't recall the exact particulars, but assuming for argument's sake that the age of the universe is 13.8 billion years old, this thing was like 13 billion light years away.  (Again, some detail here might be slightly off; the thing might have been estimated at 12 billion light years away - so focus on the general principle I am layout out here, not any particulars).</p>

<p>What I don't understand is this.  If the thing is 13 billion light years away, then the light reaching my eyes as I look at it now took 13 billion years to get to me.  Yet the age of the universe is 13.8 billion years old (again if I'm slightly wrong in some of these numbers, just accept them for now for argument's sake).  It means the light must have left this object when the universe was much "smaller" or more compact, and things were much closer together.  Which means the light should have passed my position a long time ago if I have been either "moving" or "expanding" (or some combination) away from the object at anything except some rather large percentage of the speed of light.</p>

<p>To try to boil this down, or restate it in simpler terms:  1) either it seems I am moving/expanding/red-shifting away from this object at some significant fraction of the speed of light (haven't done the numbers, but might be 80% or 90% or so) and have been for a while, or 2) something is "off" (the age of the universe, or the distance of this object).</p>

<p>or 3) there is something I'm not understanding.  Which is why I came here.</p>

<p>I have never seen it stated that we are "expanding" or "redshifting" or [insert whatever term you like] at some significant fraction of the speed of light; I have only ever seen it stated that for some brief period of time after the big bang the universe could have (or did) expand faster than light, but again that was for like less than a second if memory serves.</p>

<p>At any rate, anyone care to explain?</p>

<p>Thanks.</p>

CC BY-SA 3.0
2014-04-13T16:37:47.067Z
in some (strictly incorrect) sense you are indeed expanding at a velocity much larger than the speed of light. The catch is that in an expanding universe, velocity composition is not "Euclidian".
chris
CC BY-SA 3.0
2014-04-13T16:43:16.367Z
you might want to look at this?   (e.g. their figure 2)http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf
chris
CC BY-SA 3.0
2014-04-13T16:59:12.907Z
This one might be easier to read? http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf quoting it: Baffled by the expansion of the universe? You’re not alone. Even astronomers frequently get it wrong !
chris
CC BY-SA 3.0
2014-04-13T21:18:29.880Z
All of that made my eyes glaze over.  I just need a plain-spoken, layman's description of why I'm wrong, and what is correct.  If it is understandable, then it is describable in simple layman's language.  If it isn't describable that way, it probably isn't understandable.
user3355020
CC BY-SA 3.0
2014-04-13T21:31:04.287Z
In a simple language, 1) is correct in some sense.
chris
CC BY-SA 3.0
2014-04-13T21:49:33.733Z
I don't know what velocity composition not being "Euclidian" means, but if he simply means that if we are far enough apart the distance between you and I could be expanding so fast that we, in some sense, are "moving" away from each other faster than the speed of light without breaking any kind of laws... sure, I get that.  It's rather intuitive, actually.  However, I don't think that explains the conundrum I outlined because we'd be too close to each other 14 billion years ago (essentially next to each other) for this to work.
user3355020
<distances><expansion><redshift>
Conundrum involving distance to object, universal expansion, age of universe, etc
user3355020
# Conundrum involving distance to object, universal expansion, age of universe, etc

(Asked by: username_0 on 2014-04-13)

I was recently reading about a galaxy or quasar (not sure which, so lets just say quasar) where the estimated distance to this thing was some very significant fraction of the age of the universe. What I mean is this: I can't recall the exact particulars, but assuming for argument's sake that the age of the universe is 13.8 billion years old, this thing was like 13 billion light years away. (Again, some detail here might be slightly off; the thing might have been estimated at 12 billion light years away - so focus on the general principle I am layout out here, not any particulars).

What I don't understand is this. If the thing is 13 billion light years away, then the light reaching my eyes as I look at it now took 13 billion years to get to me. Yet the age of the universe is 13.8 billion years old (again if I'm slightly wrong in some of these numbers, just accept them for now for argument's sake). It means the light must have left this object when the universe was much "smaller" or more compact, and things were much closer together. Which means the light should have passed my position a long time ago if I have been either "moving" or "expanding" (or some combination) away from the object at anything except some rather large percentage of the speed of light.

To try to boil this down, or restate it in simpler terms: 1) either it seems I am moving/expanding/red-shifting away from this object at some significant fraction of the speed of light (haven't done the numbers, but might be 80% or 90% or so) and have been for a while, or 2) something is "off" (the age of the universe, or the distance of this object).

or 3) there is something I'm not understanding. Which is why I came here.

I have never seen it stated that we are "expanding" or "redshifting" or [insert whatever term you like] at some significant fraction of the speed of light; I have only ever seen it stated that for some brief period of time after the big bang the universe could have (or did) expand faster than light, but again that was for like less than a second if memory serves.

At any rate, anyone care to explain?

Thanks.

**Tags:** distances, expansion, redshift

> **Comments:**
> **username_1**: in some (strictly incorrect) sense you are indeed expanding at a velocity much larger than the speed of light. The catch is that in an expanding universe, velocity composition is not "Euclidian".  
> **username_1**: you might want to look at this?   (e.g. their figure 2)http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf  
> **username_1**: This one might be easier to read? http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf quoting it: Baffled by the expansion of the universe? You’re not alone. Even astronomers frequently get it wrong !  
> **username_0**: All of that made my eyes glaze over.  I just need a plain-spoken, layman's description of why I'm wrong, and what is correct.  If it is understandable, then it is describable in simple layman's language.  If it isn't describable that way, it probably isn't understandable.  
> **username_1**: In a simple language, 1) is correct in some sense.  
> **username_0**: I don't know what velocity composition not being "Euclidian" means, but if he simply means that if we are far enough apart the distance between you and I could be expanding so fast that we, in some sense, are "moving" away from each other faster than the speed of light without breaking any kind of laws... sure, I get that.  It's rather intuitive, actually.  However, I don't think that explains the conundrum I outlined because we'd be too close to each other 14 billion years ago (essentially next to each other) for this to work.  

---

## 3 answers

### Answer by username_2 on 2014-04-14. Score: 2 | Accepted answer

The 13 billion lightyears distance of the quasar mean 13 billion lightyears [light-travel distance](http://en.wikipedia.org/wiki/Distance_measures_%28cosmology%29). In other words, the light took 13 billion years to reach us, independent of the distance the quasar is now away from us.

The current proper distance (a chain of rulers would measure) is called [comoving distance](http://en.wikipedia.org/wiki/Comoving_distance); it is much larger than the light-travel distance for large redshifts.

The quasar is moving away from us in an accelerated fashion, and is now moving away faster than light. This means, light which is emitted now (in the sense of [cosmic time](http://en.wikipedia.org/wiki/Cosmic_time)) by the galaxy, the quasar may have evolved into in the meanwhile, will never reach us.
The light, the quasar emitted 13 billion years ago, left the quasar just in time to leave the regions of the universe which later have been receding faster than light from us, to eventually reach us.

As a thought experiment, imagine walking with 5 km/h (our playground speed of light) on a rubber band which is expanding with a constant rate of 1 km/h per meter actual length of the band. (This leads to an exponential acceleration of the distance between the two marks on the band). If you start closer than 5 meters away from your goal, e.g. from a start mark (our quasar) 4.50 m away, you'll finally reach the goal mark. The start mark will soon be further away from the goal mark than 5 meters, therefore receding with more than 5 km/h from the goal shortly after you left the start mark.
At the moment you arrive at the goal mark, the start mark will be much further away (comoving distance) than the distance you needed to walk (light travel distance). And you've been walking a longer distance than the (proper) distance between the marks was at the time you started walking.

Btw.: Acceleration is only felt as a force, when the velocity to the local rubber band (mataphoric space-time) is changed.

**Example** calculations with a protogalaxy of redshift $z=11.9$:
Based on the [Cosmology Calculator](http://adsabs.harvard.edu/abs/2006PASP..118.1711W) on [this website](http://www.astro.ucla.edu/~wright/CosmoCalc.html), the cosmological parameters $H\_0 = 67.11$ km/s/Mpc,
$\Omega\_{\Lambda} = 0.6825$ provided by the [Planck](http://en.wikipedia.org/wiki/Planck_%28spacecraft%29) project, and the [scale factor](http://en.wikipedia.org/wiki/Scale_factor_%28Universe%29) $d(t) = d\_0 / (1+z)$, setting $\Omega\_M = 1- \Omega\_{\Lambda} = 0.3175$, the
age of the universe is $13.820$ Gyr, and the comoving distance of the protogalaxy is $d\_0 = 32.644$ Gly.

The age of the universe, we see the protogalaxy (at redshift 11.9), was 0.370 Gyr, light-travel distance has been 13.450 Gly, proper distance was 2.531 Gly.

After the protogalaxy has been emitting light 0.370 Gyr after the big bang, the light travelled towards us through space of redshift beginning with 11.9 shrinking to 0; the light arrived at us 13.820 Gyr after the big bang. The comoving distance (to us) of the space traversed by the light started with 32.644 Gly shrinking to 0. The remaining distance, the light needed to travel, started with 13.450 Gly shrinking to 0. The proper distance between the protogalaxy and us started with 2.531 Gly increasing to 32.644 Gly due to the expansion of spacetime.

Here some intermediate states described by
a couple of tuples, consisting of

* redshift $z$,
* according age $t$ of the universe (Gyr),
* comoving radial distance (at age $t$) of the emitted light, we can now detect from the protogalaxy (Gly),
* remaining light travel distance of that emitted light (Gly),
* proper distance of the protogalaxy at age $t$, according to $d(t) = d\_0 / (1+z)$:

$$(11.9, 0.370, 32.644, 13.450, 2.531),$$
$$(11.0, 0.413, 32.115, 13.407, 2.720),$$
$$(10.0, 0.470, 31.453, 13.349, 2.968),$$
$$( 9.0, 0.543, 30.693, 13.277, 3.264),$$
$$( 8.0, 0.636, 29.811, 13.184, 3.627),$$
$$( 7.0, 0.759, 28.769, 13.061, 4.081),$$
$$( 6.0, 0.927, 27.511, 12.892, 4.663),$$
$$( 5.0, 1.168, 25.952, 12.651, 5.441),$$
$$( 4.0, 1.534, 23.952, 12.285, 6.529),$$
$$( 3.0, 2.139, 21.257, 11.680, 8.161),$$
$$( 2.0, 3.271, 17.362, 10.549, 10.881),$$
$$( 1.0, 5.845, 11.124, 7.974, 16.322),$$
$$( 0.0, 13.820, 0.0 , 0.0 , 32.644).$$

The Hubble parameter, meaning the expansion rate of space per fixed proper distance, is decreasing with time. This allowed the protogalaxy to recede almost with the speed of light, although it was just about 2.5 Gly away from us (proper distance) in the time, when it emitted the light we detect now.
Nevertheless distant objects in this space accelerate away from us, since their increasing distance is multiplied with the expansion rate of space.

> **Comments:**
> **username_0**: Yeah, I "get" all of that, and thanks for going into it.  But I'm not sure that answers my question, and I'm not sure that I've communicated it well enough.  Here is a list of the most distant objects: http://en.wikipedia.org/wiki/List_of_the_most_distant_astronomical_objects.  One of them is 13.37 billion light years away.  The point is, that's less than 0.5 years from the age of the universe.  You might as well say we were on top of that object when the light left it.  How could it possibly take that long to reach us when we were so close to it when the light left it?  
> **username_3**: @username_0 Because space is expanding. And btw, the Milky Way wasn't born at that time.  

---

### Answer by username_4 on 2014-07-24. Score: 0

Couldn't comment as I do not have the proper rep yet, but regarding @username_0 and the answer provided by @username_2, (and me being far less educated than I ever could have imagined before reading this), I interpret it like this: (and I wouldn't be surprised if this is wrong)
the speed of light is constant, but the expansion rate of the universe is not. The over-simplified observed effect is similar to the feeling of having a dream where you're in a hallway and you're running away from something as fast as you possibly can,focused on the end of the hallway, but the hallway seems to stretch more and more as time goes by. Much in the same way, light is the person running and 'space' is the hallway and earth is the opening at the end. Some light was able to get far enough in the beginning that the stretch did not impact it so much as to make it impossible to reach earth (it's just going to take it 13+ billion yrs), and some light (and from my understanding of the answer given by @username_2 all light after a certain 'time') will never reach earth.


---

### Answer by username_5 on 2022-10-11. Score: -2

I was directed here after asking a similar question at [Age of the universe vs. it's size](https://astronomy.stackexchange.com/questions/50720/age-of-the-universe-vs-its-size?noredirect=1#comment113015_50720).

I'm still confused. The universe is estimated to be 13.7-13.8 billion years old & that is the observed distance of the Cosmic Microwave Background...which is our cosmic horizon...the furthest we can see.

But the universe has galaxies 46 billion years away. I can't figure out how those 2 are reconciled. I would think that the universe would be 46 billion years old if that were true.

Is it that because the universe is expanding at an accelerated rate, a galaxy could be 46 billion light years away, but that it took only 13.7+ years to get there?

> **Comments:**
> **username_6**: This does not provide an answer to the question. Once you have sufficient [reputation](https://astronomy.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://astronomy.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/30124)  
> **username_7**: Sorry, Phil. The Answers section isn't the place to ask questions. If the existing answers here (and on the Linked & Related questions) don't adequately answer your question that we closed, please edit that question. Mention that you've seen these answers, and ask about the specific points that you need further help with. When you edit that question, it will go into a review queue so that people can vote to reopen it.  
> **username_8**: I am breaking the rules, but the answer to your question is that the universe can be infinitely big and 13.7 billion years old.  First of all, the universe is not subject to the special relativity rule of no motion greater than the speed of light.  Secondly, an infinitely dense Big Bang does not have to be a point, but the Observable Universe part of it would have been a point.  
> **username_5**: Thank you very much for your response.  I now realize that although light has reached us from ~13.8 light years away & the universe is that age, the universe has expanded far beyond our horizon (the CMB).  I also apologize for violating any rules, as this was the very first question I've asked in this forum.  

---

