A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime (Extended version)

TL;DR

This paper introduces a local, realistic, and discrete spacetime model that reproduces quantum mechanics results using integer operations and stochastic processes without relying on the standard mathematical formalism.

Contribution

It proposes a novel discrete spacetime model with integer-based probabilities that can replicate nonrelativistic quantum mechanics outcomes.

Findings

Successfully reproduces quantum predictions for various scenarios

Demonstrates quantization of energy levels and angular momentum

Uses simple probabilistic functions on a Euclidean lattice

Abstract

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described 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 nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum.