Discordant Redshifts: A Post-Mortem

I've waited many years to accumulate the information I needed to write this series of articles dealing with the claims of discordant redshifts (DZ) so it's only appropriate to create a one-page quick reference of what we've learned. 

I have contacted some of the amateur sites advocating discordant redshifts, so I may be hearing from some of them which may add to a final project list.   I doubt this will be the last I write on this topic as I still have a couple of demonstrations I'd like to complete.  Right now that list includes a demonstration of how extended objects in a field of view can have apparent 'connections' and how it is we can see through galaxies to what is beyond.  

Their 'prime' piece of evidence was that the connections and associations were low probability.  Back at the start of the claims about discordant redshifts, Halton Arp and others claimed that chance alignments were very low probability in the standard cosmological model.

I've found no evidence that anyone amongst that community bothered to investigate, or even ask, if that statement were really true!

As we see in sections (Discord for Discordant Redshifts. I., Discord for Discordant Redshifts. II.), in a universe full of galaxies roughly uniform in space, you will see many more high-redshift objects in a given area of sky, the number increasing as the square of redshift.  The 'low probability of chance alignment' fails based on simple 3-D geometry and projection effects.  

Once that fails, all the other associations and connections become chance alignments and irrevelant (Discordant Redshift Excuses: But the Galaxies Show Connections!).  

Even worse is that this fact was recognized and documented back in 1975 (Reexamination of the correlation of galaxies and QSO's).  With the small catalogs of galaxies and quasars (a few thousand entries) of the 1970s, Noerdlinger's conclusions become pretty definitive with todays catalogs containing on the order of a million of galaxies.  It is no longer statistics of small numbers creating a bottleneck.

To be fair, for researchers who learned cosmology in the 1950s, when values of the Hubble constant were thought to be about five times larger than today (see CfA: The Hubble Constant), and the Universe was consequently much smaller, chance alignments would have had a lower probability.  In that picture of the universe, investigation of discordant redshift pairs made a lot more sense.  But as the value of the Hubble constant was refined, and smaller, the universe got larger, and full of galaxies, and chance alignments became unavoidable.

The only way to rescue discordant redshift claims from the simple geometrical effect is for them to retreat to a small, geocentric universe (which decreases the probability of chance alignments at high-redshift).

There are still a number of motivated amateurs identifying 'discordant' objects in some of the large galaxy surveys.  Of course, as we've seen in this series, it's a rather easy task with the new deep surveys such as SDSS and others.  Not that those results would change any of the facts, and conclusions, of this series.

Although I have heard some stories of advocates of discordant redshifts actually realizing their error, it's sad that a lot of professionals have wasted a large part of their career in pursuit of the claims.  I suspect when the current generation of professional astronomers advocating discordant redshifts are gone, there will be no more, and this notion will move completely into the realm of crank science.
 

Discordant Redshifts: RIP

Some Amateur Sites Advocating Discordant Redshifts

• Quasars, Redshifts and the "accelerating-expansion" Universe.
• Discordancy Report

Update, June 18, 2013:  After some correspondence with the operator of the site Anomalous Redshift Investigator (see correspondence in the comments), I have concluded (preliminary and subject to change) that what they are calling 'discordant' is not the extreme cases pushed by Arp and similar supporters.