How far can we see?

[sman]

I'll try to state my problem with parsimony:

When we look a Barnards star (for example, ~15 light years out) we see it as it was 15 years ago. When we look 1 million ly out we are looking at a scene from 1 million years ago. So I think I understand it when astronomers say that looking very far away is equivalent to looking very far into the past.

I've heard of telescopes that see BILLIONS of light years away. Here's my problem: the universe is only ~15 billion years old. So if we are looking at something 15 billion ly away, we are looking 15b years into the past - at that time when whatever we are looking at should've been RIGHT HERE.

Maybe we just can't see that far, but still, the farther we look the closer we come to the point where all mater was in the same spot. This is the paradox: the FARTHER it is away from us, the CLOSER everything sould be to everything else.

I'm sure I'm missing something here that someone can fill in. I'd appreciate any comment.

[sanctus]

It is based on the common misconception that the big bang was an explosion in one point (had that too until a little while ago and still often find myself thinking like that), but the big bang was an explosion everywhere since it is assumed to have created space-time...there is more to say, but not much time now...

[modest]

Originally Posted by sman

I've heard of telescopes that see BILLIONS of light years away. Here's my problem: the universe is only ~15 billion years old. So if we are looking at something 15 billion ly away, we are looking 15b years into the past - at that time when whatever we are looking at should've been RIGHT HERE.

Close, but not quite. There are two different kinds of distance that are important here. Light travel time is the distance you're thinking of. If we see a galaxy and the light took 10 billion years to reach us then you might think it is 10 billion lightyears away. But, the universe is expanding, so while the light from that galaxy traveled for 10 billion years the galaxy from which it came moved away from us.

The comoving distance is how far the galaxy is from us today which can be more than 13.7 billion lightyears because of expansion. If the light travel time is 10 billion years then the comoving distance is about 16.4 billion lightyears. The furthest back we can see is to when the universe was filled with opaque plasma which is today viewed as the cosmic microwave background.

That was more than 13 billion years ago. The light that we see as the CMB today was only 36 million lightyears from us (or from the matter that would eventually become the Milky Way) when it was released. The universe has expanded about 1300 times over since that happened meaning the matter which emitted that light which we see today is currently about 46 billion lightyears from us.

So, in general, your post is correct. The further back we look the closer everything was. The only reason it seems like a paradox is because you're mixing up the two different types of distance. A comoving distance of 20 or 30 billion lightyears does not mean the light was emitted 20 or 30 billion years ago.

~modest

[sanctus]

Ok, modest I think what I said was not relevant at all...and then you are scared to read my article :-)

[modest]

Originally Posted by sanctus

...and then you are scared to read my article :-)

Well, scared to discuss it at least

~modest

[sman]

Originally Posted by modest

If the light travel time is 10 billion years then the comoving distance is about 16.4 billion lightyears.

So this particular galaxy has put 16.4 billion light years between us in 15 billion years? This kinda throws up a flag for me.

[sman]

My instinct here (and this maybe my fallacy) is to lay cartesian coordinates over it and just do the math. This produces kindof an "event horizon" at comoving distance=15bly. I think the cosmos is bigger than that & I don't think spacetime is expanding faster than the speed of light.

[modest]

Yes, Sman, If you're talking in terms of light travel time distance then there's a cosmic horizon somewhere between 13 and 14 billion lightyears. No light can have taken longer to reach us. But, this is not the only distance cosmologists speak in terms of. In an expanding cosmos it is sensible to speak of distances which are greater than the light travel time.

Ned Wright's cosmology tour under the heading Many Distances explains:

Cosmology Tutorial - Part 2

And here's one of many Hypo threads on the topic:

Distance to the Furthest Visible Objects

~modest

[sman]

Thank you for the references and thank you both for the feedback - all of which is very relevent.

I think this is just a product of my inability to wrap my mind around the concept of spacetime. I'll keep trying - there's no deadline.

[modest]

Originally Posted by sman

I'll keep trying - there's no deadline.

Fantastic outlook!

Believe me when I say, you are not alone in your confusion. The different ways of expressing distance have generated a lot of confusion. The following link shows one astronomer who appears more than a little irritated by the way the popular press expresses cosmic distances:

Light Travel Time Distance

You must imagine that this galaxy which you're looking at is moving away from you. By the time we absorb light from that galaxy it is no longer in the spot where it emitted the light which we just received. It has expanded away from us by the time we receive the light. So, how far is the galaxy really? There's more than one answer.

Let's say the galaxy has a redshift of 1.815. This will mean light traveling from that galaxy to the milky way took 10 billion years. When the light was emitted the universe was much younger than it is today (the universe was about 3.7 billion years old). So this is not a very sensible distance. Light travel time distance is comparing how far apart a young galaxy is to an old galaxy. We're looking at two different time periods.

The comoving distance looks at how far that other galaxy is *today* compared to the Milky Way today. This distance is necessarily going to be greater than the light travel time because these two galaxies have been moving apart during the time the light has been traversing the distance. In this case of redshift 1.815 and light travel time of 10 billion years the comoving distance is 16.165 billion light years.

Just as there is more than one measure of distance, so too there is more than one measure of velocity. The velocity that goes into Hubble's law is not the same as you would figure in special relativity. The link I gave yesterday gets into that.

But, yeah, this can get confusing quick—your puzzlement is quite understandable.

~modest