An attempt to resolve the astrophysical puzzles by postulating scale degree of freedom

TLDR: In this article, the authors consider the existence of active dilatation as a physical realization of conformal transformations, which transform the rest masses of particles, such as nuclei, atoms, crystals, galaxies, etc.

Abstract: If we assume that scale is a degree of freedom which a physical object, such as a galaxy possesses besides translational and rotational degrees of freedom, we are able to incorporate such diverse phenomena as the systematic cosmological red-shifts, anomalous red-shifts, controversals of quasars, and the expansion of Earth into a single theory. At the same time we can consider the proposed existence of active dilatation as a physical realization of conformal transformations. Active conformal transformations transform the rest masses of particles. The objection that this implies a continuous rest mass spectrum which is not observed is avoided by assuming that particles can form bound systems such as nuclei, atoms, crystals, galaxies, etc., only if ‘discrete’ scale relations are established among the constituent particles. Different galaxies can be dilated relative to each other. (Note the analogy with ‘discrete’ positions of atoms in a crystal. Different crystals can be translated arbitrarily each to the other.) An observer in a contracting galaxy experiences that the universe is expanding.