Classical-mechanical models without observable trajectories and the Dirac electron

TL;DR

This paper develops a classical model for the Dirac electron that does not rely on observable trajectories, addressing quantum interpretation issues through a pseudo-classical approach.

Contribution

It introduces a non-Grassmann spinning-particle model that parallels quantum mechanics without requiring trajectory observability, resolving certain quantum inconsistencies.

Findings

Model avoids trajectory observability in classical analogy

Addresses quantum interpretation issues of the Dirac equation

Provides a consistent pseudo-classical framework for spin

Abstract

We construct a non-Grassmann spinning-particle model which, by analogy with quantum mechanics, does not admit the notion of a trajectory within the position space. The pseudo-classical character of the model allows us to avoid the inconsistencies arising in the quantum-mechanical interpretation of a one-particle sector of the Dirac equation.