Halton Arp brings to my mind redshift quantization along lines, which has been considered also by Fang-Sato, who talked of "God's fingers". I have considered several explanations for the quantization.
- To my opinion, the most convincing explanation is in terms of lattice-like structures, tessellations, in hyperbolic space H3, which corresponds to cosmic time a= constant hyperboloid of future light-one (see this).
- H3 allows an infinite number of tessellations, which correspond to discrete subgroups of Lorentz group SO(1,3) having as covering SL(2,C) (spinors). In E3 only 17 lattices are possible. The so called icosa-tetrahedral tessellation is in a key role in TGD model of genetic code realized at a deeper level in terms of dark (heff=nh0>h) proton triplets and flux tubes of magnetic body (see this).
- For lattices in the Euclidean space E3, the radial distance from origin is quantized. For H3 redshift proportional to H3 distance replaces Euclidian radial distance and the tessellation gives redshift quantization. Astrophysical objects would tend to be associated with the unit cells of the tessellation.
- The tessellation itself could be associated with the magnetic (/field) body carrying dark matter in the TGD sense as heff=nh0>h phases: this is a prediction of number theoretic vision about physics as dual of geometric vision. Very large values of heff =hgr= GMm/v0 (Nottale hypothesis for gravitational Planck constant, see this) assignable to gravitational flux tubes are possible, and this makes these tessellations possible as gravitationally quantum coherent structures even in cosmological scales. This is a diametric opposite to what superstring models where quantum gravitation appears only in Planck length scale, suggests.
For a summary of earlier postings see Latest progress in TGD.