Why is the ampere a base unit and not the coulomb?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

Disclaimer: this is more about the etymology, semantics, and the psychology behind accepting conventions that underpin the decision between using charge per second (Ampere; accepted syntactic consensus) versus charge (Coulomb; fundamental physical property). These distinctions are important for communication to ensure the sharing of ideas maintains the highest fidelity we can muster.

Aside from the other answers, I wanted to point out that “fundamental property” (and elective, universal) and “base unit” (subjective, convention) is the fundamental cognitive dissonance here.

As was stated previous, the Ampere was more easily measured when “base units” were established as an adopted convention which was before fundamental properties were discovered/established. This is much like the argument between Imperial units versus “Metric” Units. Even that discussion is cluttered with ill-defined terms, like “metric” which based on the French word for meter and has nothing to do with base 10 numbering systems. It was just that Imperial was established using easily (but not nearly universal) measured quantities AT THE TIME (just like when Amperes was established) which resulted in a messy gradation system that didn’t even keep the same base numbering system from one magnitude to another. Furthermore, base 10 is an arbitrary numbering system when base 2 would be more fundamental and universal. So even the Metric system has many accepted conventions that are merely far easier for calculations because it maintains a standard base numbering system of 10 for all gradations.

Also, Imperial and Metric systems are typically based around on the every day life of humans which makes it easier to teach to young children and those not so inclined to math or science. Celsius is based upon water phases, atmospheric pressure, and a base numbering system which is why its absolute scale counterpart, Kelvin, is not a simple conversion using some power of 10. Scientifically speaking, using water, air pressure, and a gradation of 100 between water freezing and water evaporating as a base measurement makes less sense than using absolute zero and a scale based on the relationship between absolute zero (slowest molecular motion) and the speed of light (fastest molecular motion).

If we were to design a more fundamental measuring system using accepted (for now) universal constants, like Planck length, time, mass, charge, and speed of light; then we would have a far different measurement system than the metric one we currently use. This will likely not happen anytime soon since we have done so much work using the metric system that to convert current scientific thinking on such a large scale would be quite difficult. I would say it would be far less difficult to convince Imperial Unit users to Metric Units. It is interesting to me that pro-Metric zealots do not use the arguments they apply to the Imperial System to the Metric System as well. Personally, I think adaptability is more important than convention since science seems to be always evolving, and skepticism is the default stance of science; not consensus.