Complex Systems

Emergent Properties of Discretized Wave Equations Download PDF

Paul Budnik
Mountain Math Software
555 Cresci Road
Los Gatos, CA 95033
paul@mtnmath.com

Abstract

A computational theory of everything (TOE) requires a universe with discrete (as opposed to continuous) space, time, and state. Any discrete model for the universe must approximate the continuous wave equation to extremely high accuracy. The wave equation plays a central role in physical theory. It is the solution to Maxwell's equations and the Klein Gordon (or relativistic Schrödinger) equation for a particle with zero rest mass.

No discrete equation can model the continuous wave equation exactly. Discretization must introduce nonlinearities at something like the Planck time and distance scales, making detailed predictions on an observable scale difficult. However, there are emergent properties and some of them mimic aspects of quantum mechanics. An additional emergent property is the possibility of local but superluminal effects that might help explain apparent experimental violations of Bell's inequality.