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Perhaps it's that I've grown up with the SI system of units, but there's something about other unit systems that doesn't sit well with me. For example, Coulomb's law in Gaussian units can be written as $$F = \frac{q_1 q_2}{r^2}$$ without any reference to the permittivity or permeability of free space. How is it that something that doesn't have units of charge (in the SI system) is a unit of charge? Also, how do we know that after setting fundamental constants like $c$ or $\hbar$ (or is it $h$?) to $1$ we can recover the SI versions of formulas if we'd like to?

These ideas trouble me and it's my hope that someone can guide my intuition so that I'm no longer perplexed.

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  • $\begingroup$ I learned physics using beautiful Gaussian units, so the idea that people would think space has “permittivity” and “permeability” perplexes me! $\endgroup$ – G. Smith Feb 25 at 8:15
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    $\begingroup$ The unit of charge in Gassian units (the statcoulomb) is simply a derived unit. Most physical quantities in any system have derived units, so why should charge not be one of them? One statcoulomb of charge separated from one statcoulomb of charge by one centimeter of distance produces one dyne of force. To me this is a perfectly natural way to define the unit of charge. $\endgroup$ – G. Smith Feb 25 at 8:26

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