A discrete spacetime model for quantum mechanics

TL;DR

This paper introduces a discrete spacetime model using integer arithmetic and lattice structures to replicate quantum mechanics phenomena, such as self-interference, through probabilistic particle trajectories without wavefunctions.

Contribution

It proposes a novel discrete spacetime framework that reproduces key quantum effects using simple arithmetic and random walks, avoiding traditional wavefunction formalism.

Findings

Successfully reproduces quantum interference patterns

Uses only integer arithmetic and lattice structures

Models particle trajectories as random walks

Abstract

This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard QM picture, the proposed model only uses integer-valued quantities and arithmetic operations. In particular, it assumes a discrete spacetime under the form of an euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice sites they visit during the walk. Non-relativistic QM predictions, particularly selfinterference, are retrieved as probability distributions of similarly-prepared ensembles of particles. Extension to interacting particles is discussed but not detailed in this paper.