Inferences about Interactions: Fermions and the Dirac Equation

TL;DR

This paper develops a framework based on causal sets and interaction events to derive properties of Fermions, including the Dirac equation, using process calculus and connections to quantum mechanics.

Contribution

It introduces a novel approach linking causal set theory with quantum mechanics to derive Fermion properties and the Dirac equation from interaction events.

Findings

Derives Minkowski metric and Lorentz transformations from interaction events.

Reproduces Fermion properties such as Zitterbewegung.

Shows how the Feynman checkerboard model emerges in 1+1 dimensions.

Abstract

At a fundamental level every measurement process relies on an interaction where one entity influences another. The boundary of an interaction is given by a pair of events, which can be ordered by virtue of the interaction. This results in a partially ordered set (poset) of events often referred to as a causal set. In this framework, an observer can be represented by a chain of events. Quantification of events and pairs of events, referred to as intervals, can be performed by projecting them onto an observer chain, or even a pair of observer chains, which in specific situations leads to a Minkowski metric replete with Lorentz transformations. We illustrate how this framework of interaction events gives rise to some of the well-known properties of the Fermions, such as Zitterbewegung. We then take this further by making inferences about events, which is performed by employing the process calculus, which coincides with the Feynman path integral formulation of quantum mechanics. We show that in the 1+1 dimensional case this results in the Feynman checkerboard model of the Dirac equation describing a Fermion at rest.