Inquiring electromagnetic quantum fluctuations about the orientability of space

Abstract

Orientability is an important topological property of spacetime manifolds. It is generally assumed that a test for spatial orientability requires a 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 offered to support the choosing of time- and space-orientable spacetime manifolds. We show that it is possible to access spatial orientability of Minkowski spacetime through local physical effects involving quantum electromagnetic fluctuations. To this end, we study the motions of a charged particle and an electric dipole under these fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive expressions for an orientability indicator for both point-like particles in two spatially flat topologies. For the particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the evolution of the indicators. This shows that it is possible to access orientability through electromagnetic quantum fluctuations.The answer to the question on how to locally probe the orientability of Minkowski 3-space intrinsically arises in the study of the dipole's motions. We find that a characteristic inversion pattern exhibited by the dipole indicator curves is a signature of non-orientability. This result makes it clear that it is possible to locally unveil spatial non-orientability by the inversion pattern of orientability indicator curves of an electric dipole under electromagnetic fluctuations. Our findings open the way to a conceivable experiment involving quantum electromagnetic fluctuations to locally probe the spatial orientability on the microscopic scale of Minkowski spacetime.

arXiv comment26 pages, 5 figures, 2 tables; V2: Negative values for the velocity dispersion is solved. Clarification of orientability indicator is added. New references are included. Misprints corrected; V3: Discussion on local and global definition of spinor fields in connection with non-orientability is added, new references included, version published in Eur.Phys.J.C (2021)

References in corpus (35)

• Cosmic Topology
• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Topology and the Cosmic Microwave Background
• Fluctuations and dissipation for a mirror in vacuum
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Vacuum fluctuations and Brownian motion of a charged test particle near a reflecting boundary
• Quantum simulation of non-trivial topology
• Constraints on the Topology of the Universe: Extension to General Geometries
• Casimir energy in multiply connected static hyperbolic Universes
• The Status of Cosmic Topology after Planck Data
• Detectability of Cosmic Topology in Almost Flat Universes
• Are Small Hyperbolic Universes Observationally Detectable?
• Brownian motion of a charged test particle in vacuum between two conducting plates
• A Topological Signature in Cosmic Topology
• Brownian motion of a charged test particle near a reflecting boundary at finite temperature
• Spikes in Cosmic Crystallography
• An improved cosmic crystallography method to detect holonomies in flat spaces
• Stochastic Spacetime and Brownian Motion of Test Particles
• Detecting topology in a nearly flat hyperbolic universe
• Casimir energy in a small volume multiply connected static hyperbolic pre-inflationary Universe
• Limits on the Detectability of Cosmic Topology in Hyperbolic Universes
• Brownian Motion in Robertson-Walker Space-Times from electromagnetic Vacuum Fluctuations
• Switching effect upon the quantum Brownian motion near a reflecting boundary
• A Model for Non-Cancellation of Quantum Electric Field Fluctuations
• Constraints on the Detectability of Cosmic Topology from Observational Uncertainties
• Probing quantum vacuum fluctuations over a charged particle near a reflecting wall
• The orientability of spacetime
• Remarks on the influence of quantum vacuum fluctuations over a charged test particle near a conducting wall
• Casimir Effect in $E^3$ closed spaces
• Distinguishing Marks of Simply-connected Universes
• Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle
• A brief introduction to cosmic topology
• Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes
• Vacuum Energy Density for Massless Scalar Fields in Flat Homogeneous Spacetime Manifolds with Nontrivial Topology
• Global Topology and Local Violation of Discrete Symmetries

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• Probing spatial orientability of Friedmann--Robertson--Walker spatially flat spacetime
• Quantum Brownian motion induced by an inhomogeneous tridimensional space and a $S^1\times R^3$ topological space-time
• Quantum Brownian motion induced by fluctuating boundaries and compactification
• Probing time orientability of spacetime