Varying coupling constants and their interdependence

Since Dirac predicted in 1937 the possible variation of gravitational constant and other coupling constants from his large number hypothesis, efforts continue to determine such variation without success. Such efforts focus on the variation of one constant while assuming all others pegged to their currently measured values. We show that the variations of the speed of light Formula: see text, the gravitational constant Formula: see text, the Planck constant Formula: see text, and the Boltzmann constant Formula: see text are interrelated: Formula: see text. Thus, constraining any one of the constants leads to inadvertently constraining all the others. It may not be possible to determine the variation of a constant without concurrently considering the variation of others. We discuss several astrophysical observations that have been explained recently with the concomitant variation of two or more constants. We also analyze the reported and unexplained 35 Formula: see textg decrease of 1 Kg Pt-Ir working standards over 22 years of measurements and show that they can be accounted for by allowing Formula: see text, Formula: see text, and Formula: see text to vary as predicted, provided such mass decrease can be confirmed with a Kibble balance used for determining the Planck constant and weighing test-masses with extreme precision.