Some aspects of lightlike dimensional reduction in flat spacetime are studied
with emphasis to classical applications. Among them the Galilean transformation
of shadows induced by inertial frame changes is studied in detail by proving
that, (i) the shadow of an object has the same shape in every
orthogonal-to-light screen, (ii) if two shadows are simultaneous in an
orthogonal-to-light screen then they are simultaneous in any such screen. In
particular, the Galilean group in 2+1 dimensions is recognized as an exact
symmetry of Nature which acts on the shadows of the events instead that on the
events themselves. The group theoretical approach to lightlike dimensional
reduction is used to solve the reconstruction problem of a trajectory starting
from its acceleration history or from its projected (shadow) trajectory. The
possibility of obtaining a Galilean projected physics starting from a
Poincar\'e invariant physics is stressed through the example of relativistic
collisions. In particular, it is shown that the projection of a relativistic
collision between massless particles gives a non-relativistic collision in
which the kinetic energy is conserved.Comment: Latex2e, 28 pages, 3 figures, uses psfra
