To expand on the difference between Chronos’ #1 and #3 and apply it to what the good Dr. Arp is talking about:
If the redshift were due to the various non-Local-Group galaxies moving away from the Milky Way, which would make it the center of the Universe, then if we were able to tgransport ourselves to one of these other galaxies, the Milky Way would appear redshifted, but some other galaxies in that direction that happened to have a net velocity toward us would appear blue-shifted.
This does not seem to be what is happening. The only galaxies that are blue-shifted relative to us (moving toward us are fairly local, and the shift is explainable by gravitational effects. Never mind the low possibility that we just happen to be at the center of the Universe.
What we believe is happening is the expansion of the space of the universe as described in previous posts. In this scenario, if were in that distant galaxy, all galaxies not local to it would appear redshifted as well.
Now as long as we are there, let’s imagine viewing the Milky Way galaxy in one direction, and another galaxy with an equivalent redshift in the opposite direction. If we hop back to the Milky Way, that further galaxy would appear to have a greater redshift than the one we just visited. Because we believe that the Universe is expanding uniformly in all directions, we can guess the distance of a far-off galaxy by its redshift.
If we know the distance, we can use the speed of light to figure out how old the light from that object reaching us is, and when we figure out which are the farthest objects we can see, we can guess at the age of the Universe. A good-if-somewhat-dense-for-the-layman-but-nowhere-near-as-dense-as-it-could-be treatment of the current state of our understanding of all of this as of a couple of years ago can be found in Ken Croswell’s book, The Universe At Midnight.
What Arp is suggesting, therefore, is that he has evidence that two objects whose redshifts suggest they are thousands or even millions of light years away from each other are displaying some sort of interaction that their apparent relative disntances would suggest is possible. This would suggest that our belief that redshifts are caused by cosmological expansion are incorrect, and that everything we think we know about the Universe as a result of those beliefs is wrong.