  The starting point of this work is the principle that all movement of
particles and photons in the observable Universe must follow geodesics of a
4-dimensional space where time intervals are always a measure of geodesic arc
lengths, i.e. $c^2(\mathrm{d}t)^2 = g_{\alpha \beta} \mathrm{d} x^\alpha
\mathrm{d} x^\beta$, with $c$ is the speed of light in vacuum, $t$ time,
$g_{\alpha \beta}$ and the metric tensor; $x^\alpha$ represents any of 4 space
coordinates. The last 3 coordinates $(\alpha = 1,2,3)$ are immediately
associated with the usual physical space coordinates, while the first
coordinate $(\alpha=0)$ is later found to be related to \emph{proper time}. The
work shows that this principle is applicable in several important situations
and suggests that the underlying principle can, in fact, be used universally.
Starting with special relativity it is shown that there is perfect mapping
between the geodesics on Minkowski space-time and on this alternative space.
The discussion than follows through light propagation in a refractive medium,
and some cases of gravitation, including Schwartzschild's outer metric. The
last part of the presentation is dedicated to electromagnetic interaction and
Maxwell's equations, showing that there is a particular solution where one of
the space dimensions is eliminated and the geodesics become equivalent to light
rays in geometrical optics. A very brief discussion is made of the implications
for wave-particle duality and quantization.
