In addition, since the brightness drops as the square of the distance, these far objects must also be very bright. From this it follows that the most distant objects we see are necessarily very bright and very young.
In order to determine the distances with any degree of accuracy we need to know the brightness at a distance of 1 l.y., but here we hit a stone wall: the only objects we see are much older than the ones we are interested in, and we do not have a reliable theory of the way in which these things evolve, we have no way of calibrating our observations using any near-by objects.
It is here, in the observation of the universe at large, that the General Theory of Relativity must be used to measure distances. How this is done is described in the next section.