Thanks czeslaw, I am familiar with most of the material in wikipedia on this.

Matt.o, I am interested in doing some analysis of these surveys (or small parts of them), and have asked some questions elsewhere on getting such data (with some success).

My main interest in this thread is to discuss some of the issues. I think the most important one is that I suspect that the latest methods of analysis might not be sensitive to the methods used by Tifft, Arp and the USA-Australian project shown in the above graph. I would like someone who understands the methods used to discuss that with me if possible. But I will explain what I understand of ideas that I arrived at independently of Arp which agree with his as I understand them.

Consider the possibility that the masses of particles are not constant over time, but experience increases of certain amounts at intervals of time. The result would be that all spectral frequencies would increase in steps at intervals of time. When we look at distant galaxies, we would see them as they were long ago when all galaxies had lower frequencies, so comparing them to the laboratory frequencies we would see them as red shifted.

For the pattern to be seen it seems sufficient to reduce all redshifts to the CMBR rest frame. There is no problem when observing a small area of sky (so called pencil beams like the above example) because the correction for our motion is essentially the same for all the galaxies in the sample. Once reduced to this rest frame the pattern should be visible over the whole sky. This does not mean that we are at the centre of the Universe, because all locations see the same pattern of steps of frequency.

The large surveys done over the whole sky will not show these effects if they do not correct for our motion relative to the CMBR. Also, I am unsure if some surveys also do comparison between pairs of galaxies other than ours and another. If they do, they will use vector differences based on the redshift being a true measure of distance and it being a vector field. If Arp and I are right then it is not a vector field. For example consider two galaxies that are seen from here and are exactly 90 degrees apart in the sky. let us say that we see each as having a 72 km/s red shift. It is natural to assume that if the two galaxies have no random motions that they will see each other as having sqrt(2)*72 km/s red shifts. But that would not be the case. They would either see a 72 km/s or a 144 km/s difference because the frequencies are changing in steps of 72 km/s and no actual motion is involved. We cannot tell which of those two would be the answer.

Does this make sense?