- #26

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Both permittivity and permeability were first experimentally measured "electrically", that is completely independently of any speed of light concept. Units have nothing to do with the fact that vacuum has specific permittivity and permeability whose relation is directly proportional to the speed of light. You can set those numbers to equal one, but you can not change the relation they have with the speed of light.That equation has to be true because it's derived by solving Maxwell's equations for a particular set of boundary conditions. Permeability and permittivity appear in that solution if and only if you chose to write Maxwell's equations in a form in which they appear - and to make that choice is to choose a system of units.

We got into this mess in the first place because many systems of units were developed before Maxwell's equations were discovered. Using these systems in Maxwell's equations is perfectly legitimate, but it complicates the formulas without adding any new insight - just as doing relativity problems in the mks system so that the speed of light is ##2.998\times{10}^8## m/sec is harder but no more informative than using light-seconds for distance and seconds for time.