Varying Coupling Constants and Their Interdependence
  Since Dirac predicted in 1937 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 $c$, the
gravitational constant $G$, the Planck constant $h$, and the Boltzmann constant
$k$ are interrelated: $G\thicksim c^{3}\thicksim h^{3}\thicksim k^{3/2}$. 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 micro-gram decrease of 1 Kg Pt-Ir working standards over 22
years of measurements and show that they can be accounted for by allowing $G$,
$c$, and $h$ 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.
