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

TL;DR

This paper proposes a method to test the spatial orientability of flat Friedmann--Robertson--Walker spacetime using local quantum vacuum electromagnetic fluctuations, potentially revealing non-orientability through particle motion analysis.

Contribution

It introduces a novel local physical effect-based approach to determine spatial orientability in cosmological models, challenging the reliance on global topological tests.

Findings

Quantum vacuum fluctuations influence charged particle motion.

Dipole motion can indicate non-orientability of space.

Local effects can test global topological properties.

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 non-orientable 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 non-orientability of the spatial sections of spatially flat FRW 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 non-orientability of $3-$space in itself.