Metrological constraints on the variability of the fundamental constants $e$, $\hbar$, and $c$

We set up a framework for a model-independent analysis of the time variation of $e$, $\hbar$, and $c$ indiviually. It is shown that the time-evolution of each constant can be determined uniquely from the time evolution of the fine structure constant $\alpha$ provided that the choice of basic time-independent units (i.e., the clock and ruler) is fixed. Realistic systems of units are considered as examples and implications for metrology are discussed.