Today, I asked some people interested in Electromagnetics the following question:

Harry, All:

Do you have a clear idea how the values of epsilon and mu are obtained/measured for mediums? Are they obtained from measuring the velocity of light in the medium and from measuring the characteristic impedance of the medium, and then solving the two equations for c and Z0? 

Alex

Harry Ricker’s reply was:

Alex,
No! Do you?
Harry

Followed by me:

No, I don’t, Harry. What I see on wiki is a sort of dead circle. Plus it involves the use of electron charge and other constants.Alex

Then Harry continued as follows:

Alex,
Regarding your second question. If we are talking about SI units, they are defined units. The mu is defined and  then the epsilon is defined by using the velocity of light. The ratio is the velocity of light. I think the definitions were established so as to keep the previous definitions of the ohm voltage and current. Frankly I am not up on this. My view is that free space impedance ought to be 1 ohm and the rest of the units based on that. But that is only my opinion. 
The subject of units and measurement is very highly specialized and is fixed based upon international treaties. That has a long history behind it. The main idea being to try to keep the common units in use the same while bringing in new definitions of units based upon more stable reference standards. 
I am sure you know more about this than I do.
Harry

And this has led me to proposing the idea of establishing some precedence order between various key notions in Electromagnetics:

Harry,

I agree units and measurements are connected. But, putting various notions of constants and parameters, such as epsilon and mu ‘on the table’ along with c and Z0, as well as electron charge, etc, could be done in some order of precedence, and that precedence could be aligned with the order in which the relevant physical notions are put into theory. 

The latter (order of precedence of physical notions) should follow (at least) two key principles:

– experimental evidence, and

– Occam’s razor.

Perhaps also some basic geometric relationship of space and time, such as velocity will need to be used as a guide.

I don’t want to get deeper into natural philosophy here. But, to me, Ivor’s notion of energy current being most fundamental in EM, which has the two key attributes, the velocity of light (or generally, of EM energy current) and impedance (analogous to some sort of viscosity or friction, or some counter-action to progressive action) is most natural, and meets the above principles. So, the order of precedence seems to originate in first having c and Z0, which can be measured by existing equipment, is also natural. Those are then split into two principal components, epsilon and mu, which are in some sense are more primary if we talk about Electrical and Magnetic as the two key aspects of Electromag. So from the experimental point of view our “Adam and Eve” are c and Z0, which we can measure. From the theory point of view, our “Adam and Eve” are epsilon and mu.

That’s how I see it to myself in some logical order.

Alex