The Galilean transformation is used to transform between the
coordinates of two reference frames which differ only by
constant relative motion within the constructs of Newtonian
physics. This is the passive transformation point of view. The
equations below, although apparently obvious, break down at
speeds that approach the speed of light on account of the
principles of relativity theory. Galileo formulated these
concepts in his description of uniform motion. The topic was
motivated by Galileo's description of the motion of a ball
rolling down a ramp, by which he measured the numerical value
for the acceleration of gravity near the surface of the Earth.
In essence, the Galilean transformations embody the intuitive
notion of addition and subtraction of velocities. The assumption
that time can be treated as absolute is at the heart of the
Galilean transformations. This assumption is abandoned in the
Lorentz transformations. These relativistic transformations are
applicable to all velocities, whilst the Galilean