Frequency is a derived SI unit but its unit is 1/s. It uses only time once and no other fundamental quantities. So why is not included in SI base unit?
[Physics] Why frequency is a SI-derived unit
dimensional analysisfrequencymetrologysi-unitsterminology
Related Solutions
- Temperature
- Amount of a substance
- Luminous intensity
are pretty much bogus fundamental units. The unit temperature is just an expression of the Boltzmann constant (or you could say the converse, that the Boltzmann constant is not fundamental as it is merely an expression of the anthropocentric and arbitrary unit temperature).
The unit energy will be whatever is the unit of force times the unit of length. AJoule is the same as a Newton-Meter, which are already defined in the SI system.
You should read the NIST page on units to get the low-down on it.
In my opinion, electric charge is a more fundamental physical quantity than electric current, but NIST (or more accurately, BIPM) defined the unit current first and then, using the unit current and unit time, they defined the unit charge. I would have sorta defined charge first and then current.
Just like the unit charge (or current) is just another way to express the vacuum permittivity or, alternatively the Coulomb constant and the unit temperature is just another way to express the Boltzmann constant, the unit time, unit length, and unit mass, all three taken together could be just another way to express the speed of light, the Planck constant, and the gravitational constant. But because $G$ is not easy to measure (given independent units of measure) and can never be measured as accurately as we can measure the frequency of "radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom", we will never have $G$ as a defined constant as we do for $c$ and as we will soon for $\hbar$ and perhaps for $\epsilon_0$ and $k_\text{B}$.
But once we define length, time, and mass independently, we cannot define energy independently. The Joule is a "derived unit".
EDIT: so i will try to explain why the candela is bogus. (i had already for the mol.) so there is a sorta arbitrary specification of frequency, then what is the difference between 1 Candela and $\frac{4 \pi}{683} \approx$ 0.0184 watts? bogus base unit.
So, here's the thing. The chemistry that underlies molar mass ratios dates back at least to 1805. We've known that if you divide by a certain "relative mass" number you can get whole-number ratios for atoms in a pile of stuff, for that long. It took us about 60 more years to get a handle on how large atoms were with the estimations of Loschmidt, who worked out that atoms are much smaller than the wavelengths of visible light -- too small to ever "see". This gave a rough count of how many atoms there were in a confined space, too -- but we weren't able to connect these two different quantities (atomic relative masses, count of atoms) together to figure out the mass of a single atom until some work done by Einstein on diffusion in Brownian motion (1905) and some concrete numbers could finally be rolled in with Millikan's oil-drop experiment (1910).
So due to history and convenience, the chemists are basically at the level of saying, "okay, we have N grams of this stuff, our mass spectrometer says that it's M grams per mole, so we've got N/M moles, that includes N/M moles of nitrogen and 15 N/M moles of hydrogen due to the known atomic composition, ..." and so on. You never have to add the uncertainty in Avogadro's number to these calculations; the "size" of a mole isn't important. It's only important when you start to want to know things that are "beyond" historical chemistry approaches, like counting actual numbers of atoms.
With all that said, you'll be heart-warmed to know that there is a unit revision being considered by the SI organization, and one of the proposals is to fix the number of atoms in 1 mole. But of course they will still use as a guideline that "1 mole of carbon-12 has exactly 12 grams of mass"; it will just transition from what is now "exactly" to what will be "almost exactly."
Best Answer
They try to keep the base units to as few as possible. If it can be expressed wholly in terms of other base units, it is derived. Of course, they could have chosen Hz to be the base unit, and then s would have been derived.