A Graph Model for the quantum mechanics of a moving cyclic disturbance interacting at a spatial position

TL;DR

This paper introduces a graph-based model for quantum mechanics of a moving cyclic disturbance, deriving uncertainty relations and enabling computer simulations, bridging classical graph theory with quantum phenomena.

Contribution

It presents a novel graph model for quantum mechanics that calculates position probabilities and uncertainty loci, compatible with computational simulation.

Findings

Derived a probability formulation for disturbance positions

Established a minimum uncertainty locus consistent with quantum mechanics

Developed a computer simulation tool for the model

Abstract

An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a freely moving entity interacting in a particular spatial position is calculated and a formulation is derived for the minimum locus of uncertainty in position and momentum. This is found to accord with calculations for quantum mechanics. The model has proven amenable to computer modelling; a copy of the "SimulTime" program is available on request.