James
Some notes about variations of fundamental constants:
In discussion between L. B. Okun, G. Veneziano and M. J. Duff, concerning the number of fundamental dimensionful constants in physics (physics/0110060). They advocated correspondingly 3, 2 and 0 fundamental constants. Why they not considering case,where only 1 constant Planck-Dirac's constant; h/2pi=1,054x10^-27ergxsec?
This will be convincingly, because c not contain mass dimension for triumvir(l,t,m) and G not contain t for triumvir
My be h only dimensionful constant of Nature? Some hint give Planck mass Mp=(hc/G)^1/2 .We simultaneously can decrease or increase c and G, but Mp remains unchanged.
As a consequence only Mp/Me=1836 true dimensionless constant?
Very beautiful symmetric number because 1+8=3+6=9
In binary code 1001
"For practical use Planck length, time and energy are obviously irrelevant."
I am sure Planck mass(energy) eternal relevant.
I am not sure about Planck length and Planck time.
I will try why:
My be h only dimensionful constant of Nature? Some hint give Planck mass Mp=(hc/G)^1/2 .We simultaneously can decrease or increase c and G, but Mp remains unchanged.I think that the speed of light and speed of gravity the same independently the are luminal or superluminal.
In the formula Planck length G/c^3 no linear link.
In the formula Planck time G/c^5 no linear link.
All the best