The metre is the length of the path travelled by light in vacuum during a time interval of 1 ⁄ 299792458 of a second. – 17th CGPM (1983, Resolution 1, CR, 97), source
The meter (or metre) is considered one of the seven base units in SI, but since it depends on what is “a second”, shouldn’t it be a derived unit? Why is the meter considered a base SI unit, even though it depends on the definition of a second?
I am aware that other base units such as the ampere also depend on other base units (namely meter, kilogram and second), and this just increases my confusion even more. Perhaps my question boils down to: What property must a unit have so that it is called a base SI unit?
Answer
OP here.
Instead of choosing an answer to accept, I decided to post my own, collecting what I learned from the great answers by @Wrzlprmft, @Steeven and @MassimoOrtolano (all upvoted!), and organized in such a way that answers my own questions more directly. Thank you all, I learned a lot.
At a first glance, because although it does depend on the second, it is still arithmetically independent from the second (and the other five base units). But looking deeper, all this boils down to historical reasons.
First of all, the SI base units were chosen: they are not imposed by nature. Therefore, although quite disappointing, the correct answer to the question above would be "it must be one of meter, kilogram, second, ampere, kelvin, mole or candela". This answer is not fulfilling, though.
They are called "base" units because all units can be derived from them (similarly to the basis of a vector space, for example). Therefore, they are supposed to have these properties:
All units can be written as a combination of the base units and dimensionless constants.
All base units are arithmetically independent. This means that no base unit can be written as a combination of the other base units and dimensionless constants.
The set "meter, kilogram, second, ampere, kelvin, mole and candela" happen to satify these properties. But many other sets also do.
So this begs the question: Why this specific choice, why not other choices? The answer to this, to me, is quite disappointing as well: it all boils down to measurement convenience and historical reasons. Let's look further into this.
Consider the known "ampere versus coulomb" story. The ampere was chosen as a base SI unit, and coulomb is just a derived unit, obtained as $C = A \cdot s$. Instead, it would be fine to choose the coulomb as the base unit, and the ampere as the derived unit, obtained as $A = C \cdot s^{-1}$. Why the ampere and not the coulomb? Basically, the ampere was chosen for measurement convenience (see linked question to know more). So far so good, since a choice has to be made anyway.
But there is a major caveat in the second bullet above!! It might be surprising at the first, but whether or not two units are arithmetically independent is also historically grown!!
Consider the Magnetic Flux Density (B-field) and the Magnetic Field Intensity (H-field). The first is measured in tesla and the second in ampere per meter. They are arithmetically independent (because tesla cannot be written solely from ampere per meter). We have the relation $B = \mu H$, where $\mu$ is measured in $T \cdot m \cdot A^{-1}$. Well, instead, we could have $T = A \cdot m^{-1}$ and have $\mu$ dimensionless, had science developed in another way.
Consider the Electric Charge and the Electric Current. The first is measured in coulomb and the second in ampere. They are arithmetically dependent: $C = A \cdot s$. We have the relation $i = \frac{dq}{dt}$, or for the sake of the argument, $i = \alpha \frac{dq}{dt}$ where $\alpha = 1$ is dimensionless. Well, instead, we could have $C$ and $A$ arithmetically independent, and have $\alpha$ be measured in $A \cdot s \cdot C^{-1}$ had science developed in another way.
While writing this answer, I realized that this question has actually two interpretations. The unintended interpretation would be: Couldn't other unit be used in its place? The answer is, yes, definitely another unit could have been used, such as the newton. This would be the same story of using the coulomb in place of the ampere, no problem.
Now, to the correct interpretation: Why is the meter considered a base SI unit, even though it depends on the definition of a second? Shouldn't the meter be a derived unit, leaving only the other six units as the base units?
Short answer: It is indeed a base unit. It shouldn't be a derived unit. And this is all due to historical reasons.
First of all, although the meter does depend on the definition of a second, that is not the only thing it depends on. It also depends on this thing called "light" (more precisely, on how fast light moves). Just the fact that it depends on the second is by no means enough evidence that it is a derived unit. We have to look further into it.
Consider the other six base units, from the SI the way it is:
$$\{\text{kg}, \text{s}, \text{A}, \text{K}, \text{mol}, \text{cd}\}$$
Is it possible to write the meter as a combination of the above units and dimensionless constants? Think twice before answering!! You might have said "no!" in your head, but it's not that simple. In fact, this is also a choice. But not a choice that we make easily. Instead, it's a choice that history already made for us. History chose that meter can't be expressed this way. But, quoting @Wrzlprmft:
Had the finite speed of light been a pervasive phenomenon to mankind since the dawn of time, we might have incorporated this strict relationship in our thinking and unit system, always equating a length with the time it takes light to travel that length and never using separate units for length and time.
Therefore, had mankind evolved in a different way, it might be very natural to just write
$$1\text{ m} = \dfrac{1}{299\text{ }792\text{ }458}\text{ s}$$
and have the SI with only six base units.
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