HOW TO DESCRIBE MOTION
“La filosofia è scritta in questo grandissimo libro
che continuamente ci sta aperto innanzi agli
occhi (io dico l’universo) … Egli è scritto in
lingua matematica.* Galileo Galilei, Il saggiatore VI.”
Experiments show that the properties of Galilean time and space are extracted from the
environment by most higher animals and by young children. Among others, this has
been tested for cats, dogs, rats, mice, ants, fish and many other species.They all find the
First of all, motion is change of position with time. This description is illustrated by
rapidly flipping the lower left corners of this book, starting at page 195. Each page simulates
an instant of time, and the only change that takes place during motion is in the
position of the object, represented by the dark spot. The other variations from one picture
to the next, which are due to the imperfections of printing techniques, can be taken
to simulate the inevitable measurement errors.
Calling ‘motion’ the change of position with time is neither an explanation nor a definition,
since both the concepts of time and position are deduced from motion itself. It
is only a description of motion. Still, the description is useful, because it allows for high
precision, as we will find out by exploring gravitation and electrodynamics. After all, precision
is our guiding principle during this promenade.Therefore the detailed description
of changes in position has a special name: it is called kinematics.
The idea of change of positions implies that the object can be followed during its motion.
This is not obvious; in the section on quantum theory we will find examples where
this is impossible. But in everyday life, objects can always be tracked.The set of all positions
taken by an object over time forms its path or trajectory.The origin of this concept
Ref. 49 is evident when one watches fireworks or again the flip film in the lower left corners
starting at page 195.
In everyday life, animals and humans agree on the Euclidean properties of velocity,
space and time. In particular, this implies that a trajectory can be described by specifying
three numbers, three coordinates (x, y, z) – one for each dimension – as continuous
functions of time t. (Functions are defined in detail on page 201.) This is usually written
as x = x(t) = (x(t), y(t), z(t)). For example, already Galileo found, using stopwatch and