The fundamental scales of structures from first principles

Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe, clusters, galaxies, stars and the nucleon. The fundamental scales form naturally a self-similar hierarchy, generating new relationships among the parameters of the nucleon,the cosmological constant and the Planck scale. There is implied a sixth fundamental scale thatcorresponds to the electrostatic force within an atom. Identifying the implied scale as such leads to new relationships among the fundamental charge, the mass of the electron and cosmological parameters. Theseconsiderations also suggest that structures on the scale of galaxies and larger must be bound by non-Newtonian forces.