Non-expanding universe: a cosmological system of units

The product of two empirical constants, the dimensionless fine structure constant and the von Klitzing constant (an electrical resistance), turns out to be an exact dimensionless number. Then the accuracy and cosmological time variation (if any) of these two constants are tied. Also this product defines a natural unit of electrical resistance, the inverse of a quantum of conductance. When the speed of light c is taken away from the fine structure constant, as has been shown elsewhere, its constancy implies the constancy of the ratio e2/h (the inverse of the von Klitzing constant), e the charge of the electron and h Planck constant. This forces the charge of the electron e to be constant as long as the action h (an angular momentum) is a true constant too. From the constancy of the Rydberg constant the Compton wavelength, h/mc, is then a true constant and consequently there is no expansion at the quantum mechanical level. The momentum mc is also a true constant and then general relativity predicts that the universe is not expanding, as shown elsewhere. The time variation of the speed of light explains the observed Hubble red shift. And there is a mass-boom effect. From this a coherent cosmological system of constant units can be defined.Comment: 8 page