Abstract
Orientability is an important global topological property of spacetime manifolds. It is often assumed that a test for spatial orientability requires a global journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is 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. Another theoretical argument also offered to support this choice comes from the impossibility of having globally defined spinor fields on non-orientable spacetime manifolds. In this paper, we argue that it is possible to locally access spatial orientability of Minkowski empty spacetime through physical effects involving quantum vacuum electromagnetic fluctuations. We study the motions of a charged particle and a point electric dipole subject to these electromagnetic fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive analytic expressions for a statistical orientability indicator for both of these point-like particles in two inequivalent spatially flat topologies. For the charged particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the time evolution of the orientability indicators. This result reveals that it is possible to access orientability through electromagnetic quantum vacuum fluctuations. However, the answer to the central question of the paper, namely how to locally probe the orientability of Minkowski 3-space intrinsically, comes about only in the study of the motions of an electric dipole. For this point-like particle, we find that a characteristic inversion pattern exhibited by the curves of the orientability statistical indicator is a signature of non-orientability. This result makes it clear that it is possible to locally unveil spatial non-orientability through the inversion pattern of curves of our orientability indicator for a point electric dipole under quantum vacuum electromagnetic fluctuations. Our findings might open the way to a conceivable experiment involving quantum vacuum electromagnetic fluctuations to locally probe the spatial orientability of Minkowski empty spacetime.
Highlights
The Universe is modeled as a four-dimensional differentiable manifold, which is a topological space with an additional differential structure that permits to locally define connections, metric and curvature with which the gravitation theories are formulated
Having set the stage for our investigation, we proceed to inquire whether the topological non-orientability property of the spatial section of Minkowski spacetime manifold is amenable to be locally probed through the study of the motions of a charged test particle or a point electric dipole under quantum vacuum fluctuations of the electromagnetic field
In general relativity and quantum field theory spacetime is modeled as a differentiable manifold, which is a topological space equipped with an additional differential structure
Summary
The Universe is modeled as a four-dimensional differentiable manifold, which is a topological space with an additional differential structure that permits to locally define connections, metric and curvature with which the gravitation theories are formulated. Since quantum vacuum fluctuations of the electromagnetic field can be used to disclose a putative nontrivial 3space topology of Minkowski spacetime through stochastic motions of test charged particles [37], and given that 8 out of the possible 17 quotient flat 3-manifolds are non-orientable [19], a question that naturally arises is whether these quantum vacuum fluctuations could be used to reveal locally specific topological properties such as orientability of 3-space.. 3 we present the physical systems along with the background geometry and topology, introduce the orientability statistical indicator and derive its expressions for both a charged particle and an electric dipole under quantum vacuum electromagnetic fluctuations in Minkowski spacetime with E16 and E17 flat 3-space topologies.
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