Non-expanding universe: a cosmological system of units

Abstract

The product of two empirical constants, the dimensionless fine-structure constant (α) and the von Klitzing constant (R k, an electrical resistance), turns out to be an exact dimensionless number. Then the accuracy and cosmological time variation (if any) of these two constants can be tied together. Also this product defines a natural unit of the electrical resistance, the inverse of a quantum of conductance. When the speed of light c is taken away from α, as has been shown elsewhere, the constancy of α implies the constancy of the ratio e 2/h (the inverse of the von Klitzing constant), e being the charge of the electron and h the 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.