Comment Re:What exactly is varying? (Score 2, Interesting) 105
Writing as an outside critic of academic physics, I am still very appreciative of the old paper by Max Planck on the constants of physics. The paper is a prime part of relativity theory (the theory of invariants as it is better termed).
The speed of light, the Planck constant, the gravitational constant, the magnetic constant, and the Boltzmann constant serve to define units of measurement. So any variation of those constants only reduces to some weird physical observation that is correctable by fixing the calibration, not to a provable variation of the constants.
If the charge of the electron changes, then you have nonconservation or nonlocal transfer of charges to deal with. These alternatives are mathematically intractable; the Bianchi identities that apply to conservation are very hard to dispose of.