According to a textbook I have begun to read, there are seven base SI units:
What I do not understand is, why have these been chosen as the fundamental units? It seems to me that mass, amount, current and luminous intensity could all be expressed with energy. Instead energy is for some reason a derived unit. Why is this?
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.
eV and mass is just a rest energy.
$\endgroup$
why have these been chosen as the fundamental units?
Courtesy of the National Institute of Standards and Technology (NIST), we have some historical context. It basically boils down to wanting to have absolute measurements with respect to units of mass, length, and time.
These few were originally chosen because these form a set of mutually independent dimensions. That is to say, it is from these three that many common (at the time, though still often today) terms could be derived (velocity, acceleration, momentum, energy, etc)--though a few other units require other fundamental units (e.g., temperature).
Instead energy is for some reason a derived unit. Why is this?
Because energy is derived from other more primitive variables. From Wikipedia's article on Fundamental units
Many of these quantities are related to each other by various physical laws, and as a result the units of some of the quantities can be expressed as products (or ratios) of powers of other units (for example, momentum is mass multiplied velocity while velocity is measured in distance divided by time). These relationships are discussed in dimensional analysis. Those that cannot be so expressed can be regarded as "fundamental" in this sense)
So, since energy is the product of a few variables (e.g., $E=\frac12mv^2$ or $E=mg\Delta h$ or what have you), it cannot be a fundamental unit.
One Joule (the unit of energy) equals one $ \ $ kg m$^2$/s$^2$. So, you see, a unit of energy can be expressed in terms of units of mass, distance, and time. The people who chose the SI units could have made, for example, the Joule an SI basic-unit and could have defined the unit of mass in terms of distance, time, and energy (kg = Js$^2$/m$^2$). But then we would still have the same number of fundamental units. So the choice of which SI units to define as basic units is somewhat arbitrary. Though, I think that energy was not chosen as an SI basic-unit because it just doesn't seem as fundamental as time, mass, or distance.
Purely historical and convenience reasons, people standardized measures that were more obvious from real life (remember, quantum mechanics and relativity didn't exist when SI was drafted).
It's actually arbitrary how many quantities you define as fundamental (and associate them with base units), and it doesn't matter which ones are they.
In quantum mechanics energy is actually used as a base quantity (measured in $eV$). They say you effectively set $c=\hbar=1$ and then mass, energy, momentum, frequency and temperature are all measured in eV. Time and distance are also sometimes measured in $eV^{-1}$ instead of seconds & meters if that's more convenient. Velocities are nondimensional (fractions of the speed of light).
Each unit you define as a base unit comes with an associated "natural constant" that wouldn't be needed, if you unified two units of measurement. If you measure temperature in units of energy, the need for Boltzmann constant (the conversion factor) disappears. Similarly, space and time can be measured in the same units if you standardize the conversion velocity (usually the speed of light) to be equal to $1$. Then, you have $\hbar$ that converts between units of frequency and energy (and other related pairs). The unit electric charge connects amperes with the mechanical units.
In the purest form, there would be only one physical unit, and the only natural constants would be the dimensionless strengths of the elementary forces, and relative rest masses of elementary particles - these are the only things that must be given, not derived (so far - hopefully we'll get to the grand unification theory someday).
The whole notion of "fundamental units" is bogus, physics can be formulated in a purely dimensionless way. Given any set of equations, you are free to define new variables by e.g. introducing arbitrary scaling constants. This then allows you to study certain scaling limits of the theory. E.g. starting from special relativity (formulated in natural units), you can introduce a dimensionless parameter c to zoom in into the low velocity limit of the theory (you scale all the velocities but such that in terms of the new variables the values the velocities take remain constant as you scale the real velocities down to zero).
Exactly at the scaling limit, certain equations relating physical variables will become singular. Unable to relate these quantities to each other, stupid physicists living at approximately that scaling limit may think that they are fundamentally incompatible and need to be measured in units with incompatible dimensions.
Dimensional analysis as taught in most textbooks is wrong in the sense of "not even wrong". While formally correct, the argument made is not correct, because in natural units you can always relate any physical quantity to another. So, why are the results then still correct? The way the period of a pendulum depends on its length L and the local gravitational acceleration can only be found if you assume that hbar, G and c will not appear in the equations in SI units. But, from what I pointed out above, this must follow from an appropriate scaling argument. So, it's that scaling argument that is the only physically correct argument, not the given "dimensional calculus" argument.
