A new model for the structure of spacetime: Physical applications

Abstract

From the properties of material beings, an infinite number of networks can be constructed, which are considered the arena where the elementary particles are emerging. For this arena we present three particular models described by simple graphs. These graphs are constructed by vertices and edges (interactions) which are nowhere in space and time. i) The n-dimensional hypercubic lattice, where each being is interacting with 2n different ones, giving rise to n-dimensional spacetime, where straight lines, orthogonal lines, orthogonal coordinates and metric distance can be defined intrinsically. ii) The n-simplicial lattice evolving with discrete time according to Pachner moves. iii) The planar graph with negative discrete curvature. Given a planar graph derived from hyperbolic tessellation by omitting the embedding space, we can define discrete curvature by combinatorial properties of the underlying discrete hyperboloid made up of vertices and edges. At the end some comparison will be made between our model and some current models on the structure of spacetime: spin networks (Penrose), spin foams (Rovelli et al.), causal sets (Sorkin et al.), quantum causal histories (Markopoulou).