# Thread: Comoving distance vs Proper distance?

1. ## Comoving distance vs Proper distance?

When I'm reading articles on Cosmology there always those 2 concepts thrown around. I think they refer to 2 different kind of distances , is that correct? Can somebody provide a basic explanation of the difference?

For example, in the actual standard Cosmology, the Lambda-CDM model, I understand that the Hubble radius is about 13.9 billion light years in lenght, and that the radius of the observable Universe is about 46 billion light years in lenght. Are those quantities in Comoving distance or Proper distance?

2. Comoving distance is easy: it's the distance between two objects which isn't changed by the expansion of the universe. So, if galaxy A is (right now) 10 Mpc from galaxy B in comoving coordinates, and then the universe expands by a factor of 2, the distance between the two galaxies is STILL 10 Mpc in comoving coordinates. If you made a movie of the universe using comoving coordinates, then you wouldn't see the galaxies move away from each other on the screen; you might see galaxies jiggle around a little bit due to motions within their groups and clusters, but overall, the view would be pretty static.

A movie filmed with proper distance WOULD show the galaxies moving away from each other on the screen. To measure proper distance, you need a long, long line of engineers, each holding his own meterstick. If the line stretches from galaxy A to galaxy B, and each engineer measures the distance from him to the guy on his left and his right, and then you add up all those distances ... you get the proper distance. As time passes, you'll need to add engineers to the line to account for the expansion of space.

3. ## Re: Comoving distance vs Proper distance?

So what purpose does comoving distance serve?

Is it to filter out macrocosmological motion when looking at local interactions?

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Originally Posted by Glom
So what purpose does comoving distance serve?

Is it to filter out macrocosmological motion when looking at local interactions?
That's one of the purposes yes. It makes some things easier than using proper distance. For example suppose you want to analyze a sphere around us up to some galaxy. You can either use proper distance and think of the sphere as growing over time, or use comoving distance and think of the sphere as having decreasing density. If you don't need density for whatever you are doing, it's easier to use comoving coordinates.

5. So I assume that the 46 billion ly that is normally given as the radius of our observable Universe is a proper distance, right?

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Originally Posted by iron4
So I assume that the 46 billion ly that is normally given as the radius of our observable Universe is a proper distance, right?
Comoving distance and proper distance are defined as equal for the current time, so it's both. That will change in the future and was different in the past.

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I may be wrong as I'm vauge on comoving verses proper, but I believe both are much less than 46 billion light years. The radius of the not observable universe has been speculated to be about 46 billion light years. That includes the portion that is receding faster than 300,000 kilometers per second = c = the speed of light mostly due to the accellerating expansion of the universe. Neil

8. Originally Posted by iron4
When I'm reading articles on Cosmology there always those 2 concepts thrown around. I think they refer to 2 different kind of distances , is that correct? Can somebody provide a basic explanation of the difference?
Proper distance is dependent on the metric tensor, whereas comoving distance is not. What that means ( in terms of cosmology ) is that proper distance is dependent on the scale factor a(t) while the comoving distance stays constant. The two are related like so :

In the present ( t=0 ) the scale factor a(t) is 1, so proper distance and comoving distance are exactly equal.

9. Originally Posted by neilzero
I may be wrong as I'm vauge on comoving verses proper, but I believe both are much less than 46 billion light years. The radius of the not observable universe has been speculated to be about 46 billion light years. That includes the portion that is receding faster than 300,000 kilometers per second = c = the speed of light mostly due to the accellerating expansion of the universe. Neil
Yes, I'm afraid you're wrong on this. It is the edge of the observable universe that is now ~46 billion lightyears distant. As wiki explains it:

...due to the expansion of space, humans are observing objects that were originally much closer but are now considerably farther away (as defined in terms of cosmological proper distance, which is equal to the comoving distance at the present time) than a static 13.75 billion light-years distance. The diameter of the observable universe is estimated at about 28 billion parsecs (93 billion light-years), putting the edge of the observable universe at about 46–47 billion light-years away...

Of course, we don't know and may never know much about the not-observable universe, and we do not expect there to be an edge to that, but based on certain assumptions, some have calculated our entire universe to be something like 1023 times bigger than the observable universe.

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So in co-moving coordinates are galaxies becoming smaller with time?

11. Originally Posted by Markus Hanke
Proper distance is dependent on the metric tensor, whereas comoving distance is not. What that means ( in terms of cosmology ) is that proper distance is dependent on the scale factor a(t) while the comoving distance stays constant. The two are related like so :

In the present ( t=0 ) the scale factor a(t) is 1, so proper distance and comoving distance are exactly equal.

Sorry if i'm thick-headed, but I'd like to comprehend the second part of your statement a little better

When you say "in the present (t=0) the scale factor a(t) is 1", does that mean some concrete date? Or is self-updating, meaning that every day t gets set to 0 and a(t) to 1?

So, if comoving coordinates don't change with time, am I to understand that for example, a million (or more) years from now, Earth's inhabitants will still say: "the radius of the observable Universe is 46 billions ly away in comoving distance"?

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Originally Posted by iron4
Sorry if i'm thick-headed, but I'd like to comprehend the second part of your statement a little better

When you say "in the present (t=0) the scale factor a(t) is 1", does that mean some concrete date? Or is self-updating, meaning that every day t gets set to 0 and a(t) to 1?

So, if comoving coordinates don't change with time, am I to understand that for example, a million (or more) years from now, Earth's inhabitants will still say: "the radius of the observable Universe is 46 billions ly away in comoving distance"?
Cosmologically speaking things don't change that much over a couple of centuries, so "the present" is not so much a fixed date that needs updating every day. It's more like now, give or take a couple thousand years.

13. When you say "in the present (t=0) the scale factor a(t) is 1", does that mean some concrete date? Or is self-updating, meaning that every day t gets set to 0 and a(t) to 1?
No, it is simply a definition, a convention if you so will, just like ( for example ) the boiling point of water at sea level is 100 degrees. We could have chosen any other arbitrary number - it is simply convention.
Cosmologically there is no absolute reference frame against which time and distance can be measured, so the expansion factor always needs to be relative to a chosen reference point. It is convenient to choose the "now" for that, but one can choose any other point in time as well.

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Originally Posted by iron4
So, if comoving coordinates don't change with time, am I to understand that for example, a million (or more) years from now, Earth's inhabitants will still say: "the radius of the observable Universe is 46 billions ly away in comoving distance"?
The radius of the observable universe does change in comoving coordinates. What is fixed is things moving with the hubble flow, which the radius of the observable universe is not.

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