Scaling in Cosmology and the Arrow of Time

A new type of scaling applicable to a variety of physical parameters in the universe is proposed here. This utilizes a relation linking the fundamental masses and fundamental constants in nature and an axiomatic approach is developed for the relations between microscopic and macroscopic found by Eddington and Dirac. In this approach, the fundamental constants are changing with time and the variation is related to the changing of the scale of the universe. The variation of the fundamental constants leads to an arrow of time in the present universe as well as scale-invariant relationships linking all scales. All lengths in the universe are proportional to the scale of the universe R, and similar relations exist for other physical parameters.