Towards an Entropic Geometrodynamics of Quantum Particles: Mouths of Casimir Wormholes as Planckeons

Abstract

A conformal gravity approach is presented here to describe the emergence of a quantized spacetime at the Planck scale from a lattice-like network of mouths of traversable wormholes as planckeons. This differs from the earlier work of Licata et.al., which started with the assumption that ER=EPR conjecture is valid and used an entanglement entropy from the Ryu-Takayanagi formula. Here, we developed first a conformal gravity model that is postulated to apply at the Planck scale to describe the spacetime fluctuation via a second-order form of the Ricci Flow, i.e., a wave equation of the metric tensor. We then consider its black hole solution to suggest the possible formation of Planckian wormholes. By considering the role of the entropic force due to Casimir effect as the source of negative energy, we suggest that Planckian wormholes will be stable and may allow for the transfer of field through a series of Casimir wormholes with mouths that are open at a given period of time as dictated by a modified Uncertainty Principle. From this phenomena at Planck scale, we showed that it can be the basis from which "quantum dynamics" emerges and therefore ER=EPR conjencture can be realized. Lastly, we develop a new quantum interpretation that focuses on the nature of quantum dynamics, particularly with the effect of generating the famous interference pattern in a macroscopic double-slit experiment. We showed that the interference pattern's origin is entropic and chaotic in nature, where the dynamics of a quantum particle through a series of wormholes is not just considered to be probabilistic in nature but also requires a combinatorial optimization.