What you would need to determine is whether a dimensionless quantity is changing. https://en.wikipedia.org/wiki/Fine-structure_constant#Is_the_fine-structure_c

What you would need to determine is whether a dimensionless quantity is changing. https://en.wikipedia.org/wiki/Fine-structure_constant#Is_the_fine-structure_constant_actually_constant https://en.wikipedia.org/wiki/Fine-structure_constant#Is_the...? If the fine structure constant α is found to change, then would only be able to say that the relationship among the speed of light c, the elementary charge e, and the Planck constant ħ are changing, but IMO if we discovered that (say) α changed from .007300… to its present value of .007297…, we would not be able to then say "the speed of light changed (and the elementary charge and Planck constant remained the same)" …but as a matter of practicality, scientists could feel free to use a different value for c in the past (and the present value for the elementary charge and Planck constant), if that is the most convenient way to accommodate a change in α. It wouldn't surprise me in the least if holding c and ħ constant is better for astronomers and holding e and ħ constant are better for particle physicists. (Saying that ħ changes would be similar to saying that mass changes, or at least, the units of ħ include mass, and the Planck constant "is the basis for the definition of the kilogram." in the SI system [well, technically, this is not the case until next month. Right now the kilogram is still defined by the physical "international prototype kilogram" object, but the above quote is from wikipedia]) However, while the best experiments are consistent with changing α, the change in α is constrained to be WAY less than it would need to be to explain cosmological red shift observations.