Discretization and degeometrization: A new relational quantum physics and an alternate path to quantum gravity

Abstract

A novel quantum mechanical framework in discrete space and time leads to the derivation of the relativistic energy equation and a potential path toward quantum gravity. A unique approach to geometry is also derived where pregeometric points containing intrinsic compactified geometries generate a topologically 4D cosmos with a local dynamical 3D geometry. An interpretation of the quantum mechanics wavefunction is considered as longitudinal density waves traveling through dynamical pregeometric points. Similarly, general relativity can be described as density variations of the pregeometric points caused by matter-energy distribution. A primordial quantum (Higgs) field emerging at the big bang that generates all the other quantum fields is considered. A four-dimensional structure of black holes, and dark matter and energy are discussed.