  In general relativity, cosmology and quantum field theory, spacetime is
assumed to be an orientable manifold endowed with a Lorentz metric that makes
it spatially and temporally orientable. The question as to whether the laws of
physics require these orientability assumptions is ultimately of observational
or experimental nature, or the answer might come from a fundamental theory of
physics. The possibility that spacetime is time non-orientable lacks
investigation, and so should not be dismissed straightaway. In this paper, we
argue that it is possible to locally access a putative time non-orientability
of Minkowski empty spacetime by physical effects involving quantum vacuum
electromagnetic fluctuations. We set ourselves to study the influence of time
non-orientability on the stochastic motions of a charged particle subject to
these electromagnetic fluctuations in Minkowski spacetime equipped with a time
non-orientable topology and with its time orientable counterpart. To this end,
we introduce and derive analytic expressions for a statistical time
orientability indicator. Then we show that it is possible to pinpoint the time
non-orientable topology through an inversion pattern displayed by the
corresponding orientability indicator, which is absent when the underlying
manifold is time orientable.
