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This is another common misconception. First, Arp is arguing that quasars are intrinsically low luminosity which means that most of the observed quasars must be local (within 100 Mpc - at least prior to surveys like SDSS) in his model. So you don't have billions of galaxies to choose from. You have the local sample.
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No, this is a common failing of Arp and those who support him. It is the argument of intrinsically low luminosity that is not supported by any of his research to date. These also leads to a failure in logic. Arp contends that QSO's show low luminousity, then shows two-dimensional images which he contends show association between QSO's and low reshift galaxies, then says see, this is why the QSO'as are low luminousity. (Josh, in the EU thread, gave a latin saying for this which fits perfectly) Arp is using his premise to arrive at a conclusion when the premise itself is the thing which is being argued.
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Second, Arp model makes a very specific prediction - active galaxies such as Seyferts and starbursts should dominate the population of low redshift parent galaxies associated with ejected quasars - and that's what his results show. If you read his papers you find that the vast majority of his examples involve active galaxies.
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Yes, but the "vast majority" of his models are based on a very small sampling of the objects in the sky. Furthermore, he does not address many more objects that do not show the association he claims for those objects he does include. Finally, the association he makes is still based on his initial premise, taken as true, that there is an association--a premise that he has not provided convincing evidence to support.
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The mainstream suffers from the opposite failing of what you're accusing Arp of - relying on a assumption (redshift = distance) that creates a 3-dimensional interpretation which may in fact be contradicted by the observations.
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Except that the "mainstream" as you put it, have shown convincing evidence that the redshift = distance correlation is strong. While it does remain a theory, in that the objects discussed are too far away to get a parallax measurement to prove it, the series of "standard candles" used by astronomers to get out to several hundreds of millions of light years do support the redshift contention out to that distance. Arp has no such quantifying support for his theory.