Hierarchies of fundamental constants (to items Nos 16, 17, and 27 from Ginzburg's list)

Current understanding of major unsolved problems in particle physics and cosmology suggests that physics is facing serious challenges and that the existing view of how the laws of Nature work may possibly (though not necessarily) be substantially extended in the near future. From this standpoint, experiments at the LHC proton collider due to start shortly at CERN are going to make а crucial impact.