Probing spatial orientability of a Friedmann-Robertson-Walker spatially flat spacetime

Abstract

One important global topological property of a spacetime manifold is orientability. It is widely believed that spatial orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths. Since such global journeys are not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, $CP$ violation and $CPT$ invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. The nonexistence of globally defined spinor fields on a nonorientable spacetime is another theoretical argument for orientability. However, it is conceivable that orientability can be put to test by local physical effects. In this paper, we show that it is possible to locally access spatial orientability of a spatially flat Friedmann-Robertson-Walker spacetime through quantum vacuum electromagnestic fluctuations. We argue that a putative nonorientability of the spatial sections of spatially flat Friedmann-Robertson-Walker spacetime can be ascertained by the study of the stochastic motions of a charged particle or a point electric dipole under quantum vacuum electromagnetic fluctuations. In particular, the stochastic motions of a dipole permit the recognition of a presumed nonorientability of three space in itself.