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I always thought of current as the time derivative of charge, $\frac{dq}{dt}$. However, I found out recently that it is the ampere that is the base unit and not the coulomb. Why is this? It seems to me that charge can exist without current, but current cannot exist without charge. So the logical choice for a base unit would be the coulomb. Right?

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Because it was defined by measurements (the force between two wire segments) that could be easily made in the laboratory at the time. The phrase is "operational definition", and it is the cause of many (most? all?) of the seemingly weird decision about fundamental units.

It is why we define the second and the speed of light but derive the meter these days.

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    $\begingroup$ To amplify further on this answer, we have instruments (ammeters) that can measure current very accurately. But it's extremely difficult to do high-precision experiments with static electricity, i.e., it's relatively hard to measure charge. $\endgroup$
    – user4552
    Commented Jul 11, 2013 at 3:10
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    $\begingroup$ Well, you can always measure charge by measuring current and measuring the time for which the current was flowing. So I don't buy the measurement argument. It is true that any set of 4 quantities can be made as 'fundamental' and others would be 'derived'. But we should ideally choose quantities which appeal to our notion of fundamental - something which is a basic property or a primitive notion. Charge is a basic property of all matter, unlike current which is defined only with respect to a surface hence I feel that charge needs to be chosen as a fundamental quantity rather than current. $\endgroup$
    – guru
    Commented Jul 11, 2013 at 9:57
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    $\begingroup$ Of course it is historical. That's what I mean about it depending on what was easy at the time. The time the decision was taken. And when you say*"you can always measure charge by measuring current and measuring the time"* you have explained why the decision was made to have charge a derived unit. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jul 11, 2013 at 11:44
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    $\begingroup$ @guru, you can always measure charge by measuring current and measuring the time So, basically, you are agreeing that current and time should be base units, and charge should be a derived unit. $\endgroup$
    – Solomon Slow
    Commented Jul 14, 2015 at 14:26
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    $\begingroup$ @jameslarge Quoting dmckee: It is why we define the second and the speed of light but derive the meter these days. But the meter is still a base unit. You can measure something through a derivation and still let it be a base unit. Of course you usually choose the most easy thing and way to measure something, but what you decide is "base" is purely a matter of choosing your definition. $\endgroup$
    – DrZ214
    Commented Feb 24, 2016 at 3:45
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Since this question was asked, the situation has changed: there is movement towards a redefinition of the SI system which eliminates arbitrary artifacts in terms of quantities which quantum mechanics tells us are really, fundamentally constant. Starting sometime in 2018, the defined constants will be

  • the difference in frequency $\Delta\nu$ between two particular electronic transitions in cesium atoms (unless a more stable technology is developed)

  • a constant $K_\mathrm{cd}$ defining the candela

  • the speed $c \approx 3.0\times10^8\,\rm m/s$ of light in a vacuum, relating distance to time

  • the quantum of electric charge $e \approx 1.60\times10^{-19}\rm \,C$

  • the Planck constant $h \approx 6.6\times10^{-34} \rm\,J\,s$ relating the charge quantum to the magnetic flux quantum, and also relating wavelength, momentum, and mass

  • the Avogadro constant $N_A \approx 6.0\times10^{23}\,\rm mol^{-1}$ relating the kilogram and the atomic mass unit

  • the Boltzmann constant $k \approx 1.38\times10^{-23} \rm\, J/K$ relating temperature and thermal energy.

In the present version of SI, the first of these three are exactly defined, while the other four are empirically measured based on the international prototype kilogram, the magnetic force measurement used to define the ampere, the mass of a mole of carbon-12, and the triple point of water. All of these are macroscopic phenomena. After the 2018 redefinition all seven of the constants I listed will be "exact" in the way that $c$ is exact at present.

There's more information about the SI overhaul at the BIPM, on Wikipedia, and at NIST. Here's also a Nature news story about the redefinition of the ampere.

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    $\begingroup$ How the hell are we going to get a good operational definition of the Coulomb? $\endgroup$
    – DanielSank
    Commented Aug 10, 2016 at 17:10
  • $\begingroup$ @DanielSank Without passing through a current, you mean? Yeah, that's a good question - but it's also true of the ampere. If you look at the proposed implementations, you have single-electron tunnelling at the very low end, but at higher currents it just dodges and goes into fancy quantum standards for the volt and the ohm, and then folds those into the ampere. The coulomb is hard to define operationally from those constants, but the ampere is equally hard. Why it's still called a base quantity is beyond me at the moment. $\endgroup$
    – Emilio Pisanty
    Commented Aug 10, 2016 at 19:45
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    $\begingroup$ @EmilioPisanty I just meant how does one measure charge accurately? You mention single electron tunneling, but I'd have to read about how that's going to turn into a standard before I say I understand what they're talking about. Due to the Josephson effect, voltage can be standardized rather well, as you alluded. $\endgroup$
    – DanielSank
    Commented Aug 10, 2016 at 20:08
  • $\begingroup$ @DanielSank That'd make a good follow-up question. $\endgroup$
    – rob ♦
    Commented Aug 11, 2016 at 0:47

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