Dan, Welcome to Hypography,
Arp's theory is that mass is shrinking over time - on an atomic scale. If an atom such as a hydrogen were to be larger when it emits light then presumably the wavelength of the light emitted would be larger as well.
When we look out into space the further we look the more redshifted light is. This means the light has a larger wavelength than it is expected to have or than it would have if we observed it here in our galaxy.
The key to Arp's theory is that light takes time to get from there to here. If light were emitted some number of billions of years ago when matter was larger and it arrives here when matter is smaller then it would appear redshifted (or so he postulates).
There is no way for sure to test what wavelength light emitted from an atom of different-than-normal size would look like. This is true because we have never seen an atom that has anything but the exact size it should have nor one that emitted light that is anything but the exact wavelength it should emit (in our reference frame). I have not read
Seeing Red so I don't know how Arp gets his distance to redshift scale exactly. Nor does it seem possible for him to claim how to know what rate mass would change size. Such a claim would be speculation - must be speculation.
Most all physicists have ruled out his theories as new evidence gained in the last few decades has favored a relativistic
friedmann-like universe that is expanding. But if your interest is in Arp's theory and I haven't answered well-enough (most likely ture as I know little of his theories), I would recommend you read "Seeing Red" - It's all in there or so I hear.
-modest
