Quantum Entanglement without nonlocal causation in (3,2)-dimensional spacetime

Abstract

This work aims at exploring whether the nonlocal correlations due to quantum entanglement could exist without nonlocal causation. This is done with the aid of a toy model to investigate whether the ability of two quantum entangled particles to "correlate" their behaviors even at very large distances and in the absence of any physical connection can be seen as due to an exchange of information through an extra-temporal dimension. Since superluminal information exchange is forbidden in our (3,1) spacetime, an extra-temporal dimension is needed to recover the physical picture of finite velocity information exchange between entangled entities. Assuming that the geometry of space-time of dimension (3,2) is described by a metric containing a warping factor, the confinement of the massive particles in the extra time dimension follows. Therefore, why we do not experience an infinitely large extra time dimension can be explained. The toy model proposed here is defined by borrowing Bohm-Bub's proposal to describe the wavefunction collapse using nonlinear (non-unitary) dynamical equations and then elaborating this approach for an entangled system. The model so obtained is just speculative without any claim of being robust against any criticism, nevertheless, it satisfies the purpose of giving the possibility to the hypotheses formulated above to be verified experimentally; in fact, it proposes an experiment potentially interesting which would otherwise be immediately dismissed as manifestly trivial. The proposed experiment would consist of checking the possible violation of Bell's inequality between two identical but independent systems under appropriate conditions. Beyond its theoretical interest, entanglement is a key topic in quantum computing and quantum technologies, so any attempt to gain a deeper understanding of it could be useful.