  The theory of physical dimensions and units in physics is outlined. This
includes a discussion of the universal applicability and superiority of
quantity equations. The International System of Units (SI) is one example
thereof. By analyzing mechanics and electrodynamics, we are naturally led,
besides the dimensions of length and time, to the fundamental units of action
$\mathfrak h$, electric charge $q$, and magnetic flux $\phi$. We have $q\times
\phi=\text{action}$ and $q/\phi=1/\text{resistance}$. These results of
\emph{classical physics} suggests to look into the corresponding quantum
aspects of $q$ and $\phi$ (and also of $\mathfrak h$): The electric charge
occurs exclusively in elementary charges $e$, whereas the magnetic flux can
have any value; in specific situations, however, in superconductors of type II
at very low temperatures, $\phi$ appears quantized in the form of fluxons
(Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck
quantum $h$. Thus, we are directed to superconductivity and, because of the
resistance, to the quantum Hall effect. In this way, the Josephson and the
quantum Hall effects come into focus quite naturally. One goal is to determine
the behavior of the fundamental constants in special and in general relativity,
that is, if gravity is thought to be switched off versus the case in the
gravitational field.
