  The present work shows that through a suitable change of variables
relativistic dynamics can be mapped to light propagation in a non-homogeneous
medium. A particle's trajectory through the modified space-time is thus
formally equivalent to a light ray and can be derived from a mechanical
equivalent of Fermat's principle. The similarities between light propagation
and mechanics are then extended to quantum mechanics, showing that relativistic
quantum mechanics can be derived from a wave equation in modified space-time.
Non-relativistic results, such as de Broglie's wavelength, Schroedinger
equation and uncertainty principle are shown to be direct consequences of the
theory and it is argued that relativistic conclusions are also possible.
