  One of the foremost goals of research in physics is to find the most basic
and universal theories that describe our universe. Many theories assume the
presence of an absolute space and time in which the physical objects are
located and physical processes take place. However, it is more fundamental to
understand time as relative to the motion of another object, e.g. the number of
swings of a pendulum, and the position of an object primarily as relative to
other objects. The goals of this paper is to explain, how using the principle
of relationalism (to be introduced below), classical mechanics can be
formulated on a most elementary space, which is freed from absolute entities:
shape space. On shape space only the relative orientation and length of
subsystems are taken into account. In order to find out how the shape of a
classical system evolves in time, the method of "symplectic reduction of
Hamiltonian systems" is extended to include scale transformations, and in this
way the reduction of a classical system with respect to the full similarity
group is achieved. A necessary requirement for the validity of the principle of
relationalism is that changing the length scale of a system, all parameters of
the theory that depend on the length, get changed accordingly. In particular,
the principle of relationalism requires a proper transformation of the coupling
constants of the interaction potentials in Classical Physics. This leads
consequently to a transformation in Planck's measuring units, which enables us
to derive a metric on shape space in a unique way. Later in this paper, we will
explain the derivation of the reduced Hamiltonian and symplectic form on shape
space.
