A Causal Net Approach to Relativistic Quantum Mechanics

TL;DR

This paper introduces a causal network model that reproduces key features of relativistic quantum mechanics, deriving the Dirac equation and quantum effects from a simple, structured causal net approach.

Contribution

It presents a novel causal net framework that derives the Dirac equation and models quantum phenomena, bridging relativistic quantum mechanics with causal network theory.

Findings

Derives the 1+1D Dirac equation from causal nets.

Models quantum effects like uncertainty and spin within the net.

Approximates Schrödinger and Pauli equations in low velocity limit.

Abstract

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.