  Whether the space where we live is a globally orientable manifold $M_3$, and
whether the local laws of physics require that $M_3$ be equipped with a
canonical orientation, are among the unsettled questions in cosmology and
quantum field theory. It is often assumed that a test for spatial orientability
requires a global journey across the whole $3-$space. Since such a global
expedition is not feasible, theoretical arguments are usually offered to
support the choice of time orientation for the spacetime manifold $M_4$, and
space orientation for $M_3$. Theoretical arguments can certainly be used, but
one would expect that the ultimate answer to the orientability question should
rely on observations or local experiments, or can come from a topological
fundamental theory in physics. In a recent paper we have argued that it is
potentially possible to locally access the $3-$space orientability of Minkowski
spacetime through effects involving 'point-like charged particles' under
quantum electromagnetic fluctuations. Specifically, we studied the stochastic
motions of a charged particle and an electric dipole subjected to these
fluctuations in Minkowski spacetime, with either an orientable or a
non-orientable $3-$space topology, and derived expressions for a statistical
orientability indicator in these two flat topologically inequivalent manifolds.
For the dipole we found that a characteristic inversion pattern exhibited by
the curves of the orientability indicator is a signature of non-orientability,
making it possible to locally probe the orientability of the $3-$space. Here,
to shed some additional light on the spatial orientability, we briefly review
these results, and also discuss some of its features and consequences. The
results might open the way to a conceivable experiment involving quantum
fluctuations to look into the spatial orientability of Minkowski empty
spacetime.
