In Classical Mechanics, one of the possible foundations is based on three concepts aka mass(equivalent to energy), length and time. This is a foundation because we can model everything ( pressure, position, volume, acceleration, velocity, temperature ) from those, even if the description of more complex things ( like temperature ) in terms of the foundations might be a bit complicated and further abstractions/definitions would prove to be useful.

So, it seems like the other big part of classical physics is Classical Electromagnetism and i was looking for a possible foundations there that is able to model everything in Electromagnetic Theory ( from electrostatic, to electrodynamics, to maxwellian equations to electromagnetic waves, to optics ),

Could a canditate 3-uple for a simple foundations of Classical Electromagnetism be charges ( or difference in charge ), length and time. This would be just substituting mass ( equivalent to energy ) for differences in charge ( which is equivalent to energy ).

Is this a good enough simple foundations for Electromagnetic Theory ?

If not, can anyone suggest me one ( preferably a simple one in terms of math ) ?

Thanks a lot in advance

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    $\begingroup$ Do you have a proper definition for "derivable concept"? As it stands, this question is in danger of being opinion-based since everyone has their favorite views about what is fundamental and what is derived. $\endgroup$ – ACuriousMind Feb 12 '15 at 18:02
  • $\begingroup$ Is it really a question of opinion ? For instance, in Classical Mechanics i think the majority of physicists would agree that the fundamental stuff is mass ( equivalent to energy ), length ( which can derive space ) and time. Don't you agree ? I'm looking for the same thing, inside Electromagnetic Theory, if it is possible there. $\endgroup$ – nerdy Feb 12 '15 at 18:06
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    $\begingroup$ Well, I'd say the "fundamental stuff" of classical mechanics is a phase space with a Hamiltonian flow on it. You don't need to talk about spacetime or mass at all (though they will figure in most applications, of course)! This is what I mean by opinion based - there's a sliding scale of abstraction from where you can start, and no one tells where that is - you could also start from Newton's laws, or do Lagrangian mechanics. It's all equivalent in classical mechanics. $\endgroup$ – ACuriousMind Feb 12 '15 at 18:09
  • $\begingroup$ Hmm, now i see what you mean. So maybe what i'm looking for is a possible "foundation" for Electromagnetic Theory that is simple to understand ( just like mass, time and space is ) . I'm gonna edit the question $\endgroup$ – nerdy Feb 12 '15 at 18:16
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    $\begingroup$ @nerdy I think that a fundamental system of concepts should be parallel to the fundamental system of units. In c.g.s. we have cm, gram, sec., s.t. length, mass, time are enough for mechanics. Though I don't understand why you separate electromagnetism. So you should add to c.g.s. the statC, s.t. the system of concepts becomes length, mass, time, charge. But what about magnetic field? Well, the unit of magnetic flux, Wb = V $\cdot$ s, s.t. no additional unit should be introduced, and no additional basic concept. $\endgroup$ – Sofia Feb 12 '15 at 20:59

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