Plausible "faster-than-light" displacements in a two-sheeted spacetime

In this paper, we explore the implications of a two-point discretization of an extra-dimension in a five-dimensional quantum setup. We adopt a pragmatic attitude by considering the dynamics of spin-half particles through the simplest possible extension of the existing Dirac and Pauli equations. It is shown that the benefit of this approach is to predict new physical phenomena while maintaining the number of constitutive hypothesis at minimum. As the most striking feature of the model, we demonstrate the possibility of fermionic matter oscillations between the two four-dimensional sections and hyper-fast displacements in case of asymmetric warping (without conflicting special relativity). This result, similar to previous reported ones in brane-world theories, is completely original as it is derived by using quantum mechanics only without recourse to general relativity and bulk geodesics calculation. The model allows causal contact between normally disconnected regions. If it proves to be physically founded, its practical aspects could have deep implications for the search of extra-dimensions.