MadSci Network: Astronomy
Query:

Re: How can we see a galaxy 13 billion light years away

Date: Tue May 31 14:33:26 2011
Posted By: Nial Tanvir, Faculty, Astrophysics
Area of science: Astronomy
ID: 1305740876.As
Message:

Good question, and a very common source of confusion to people trying to understand the expanding universe! It would, of course, be great to be able to give a really simple answer, but unfortunately the issues are rather tricky -- and I think the best I'll be able to do is give you an indication of the nature of this trickiness, and then some partial explanations which I hope will at least give you some new insight.

So, the first thing to realise is that when we are talking about the Universe on very large scales, our normal notions of distance and time quickly become insufficiently precise. What do I mean by this? Well, if I ask you how far away it is to the Moon, say, then you can look up the answer which comes from the laser ranging experiments -- where light from a laser is shone up to a retroreflector on the Moon, and the distance determined by the time the reflected ray takes to travel there and bounce back. What if we were to try this to estimate the distance to some remote galaxy? Of course, you see straight away that the situation is more complicated (even ignoring practical difficulties), because the light would take so long to reach the galaxy and return, that in the mean-time the galaxy would have moved further away. So we have to be more precise (if we used a method like that) and state specifically at what time we regard the distance estimate to apply (and maybe account for the extra recession).

Now, this may still not sound very profound, but let's take it a step further and remember that the Special Theory of Relativity tells us that for objects moving fast relative to us, their time appears to be running slowly. Thus if I look at a distant galaxy I see it "in the past", not just because light has taken time to reach me, but also because of this slow time effect. So now if I try to measure a distance I'm faced with a further potential confusion -- am I saying that distance refers to the time on my clock, or on the clocks in the distant galaxy. In fact, the situation gets more complicated still when we use the General Theory of Relativity, where the passage of time is also determined by space-time curvature.

Anyway, of preference you'd probably say you'd rather keep everything relative to your clock here on Earth, but actually that doesn't make use of the fact that the Universe on large scales seems very symmetrical (ie. similar densities of galaxies). For that reason, in Cosmology it is conventional to define something called the comoving distance to any distant galaxy "Z" in a way which roughly corresponds to the following: measure the distance to a nearby galaxy "A" which is along the same direction as "Z", now, at the same time (by which we mean the same time after the Big Bang) measure the distance from "A" to another nearby galaxy "B", and so on from "B" to "C" etc. all the way to "Z". Now simply add these distances up. This may seem reasonable (if a little long-winded), but actually it will give you a different answer to that you would get if you tried to stretch a tape-measure from "A" to "Z".

Where does that leave us? Well, for one thing, the galaxy you refer to at 13 billion light years has a comoving distance of more like 30 billion light years. The 13 billion light years really just corresponds to the amount of time we believe we are looking back -- and this kind of distance is typically only used by Cosmologists when they are describing discoveries for "public consumption". Furthermore, it seems the problem of how it got so far away in the age of the Universe has become even more acute! (I'll remark in passing that the comoving distance isn't necessarily more fundamental than other ways of defining distances, but it is the most mathematically convenient and natural way).

Okay, so how are we to understand this? One way (which is part of the story, although not the whole story) is to think back to what we said above, that when we look at distant galaxies we see their time running slowly, and hence it is perfectly possible (although hard!) to see galaxies as they were just a few hundred million years after the Big Bang.

Another way to think about it is to realise that the amount of the Universe we can see has increased with time through the age of the Universe. The galaxy now at 13 billion light years was not within our observable Universe for much of its age, and so there is certainly no impediment to it travelling faster than the speed of light (before it came into existence, from our point of view!). However, even once within our observable Universe, if we take speed as being comoving distance divided by time, then in fact the answer will come out to be considerably larger than c for this galaxy. Do you need to worry about this apparently breaking the Universal speed limit? The answer is no, essentially because of the way we defined comoving distance. None of the hypothetical observers on galaxies B, C, D... etc. would measure their neighbour to be exceeding c, and really what Special Relativity tells us is that two things can't pass each other at a speed greater than c, and clearly that isn't happening in this case. This explanation is sometimes phrased as saying "the galaxies aren't getting further apart, it's just that space is expanding between them, and that's allowed to happen faster than c".

So, these various "explanations" all contain some element of the truth, but aren't the whole story. You may be wondering how cosmologists deal with these kinds of conceptual problems on a daily basis in their work. I guess the answer is that most of them do carry visualisations in their heads, of the sort I've tried to describe; but for the most part, the true answer to such questions comes from the equations of the theory. These equations incorporate these phenomena of curved space-time (time dilation etc.) that I've mentioned, and quantitative understanding comes from solving them (or more usually, some simplified version of the equations).


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