No Drama Quantum Electrodynamics?

TL;DR

This paper proposes a novel spinor electrodynamics model that reproduces quantum field theory evolution using a system of PDEs, aiming to clarify quantum theory interpretation and address Bell theorem issues.

Contribution

It introduces a new PDE-based model derived from spinor electrodynamics that reproduces quantum evolution without explicit spinor fields, offering a fresh perspective on quantum theory interpretation.

Findings

The model reproduces unitary quantum evolution in Fock space.

Electromagnetic field evolution is shown to be independent.

The theory addresses Bell theorem-related issues.

Abstract

This article builds on recent work (A. Akhmeteli, Int'l Journ. of Quantum Information, vol. 9, Suppl. (2011) p. 17, and A. Akhmeteli, Journ. Math. Phys., vol. 52 (2011) p. 082303), providing a theory that is based on spinor electrodynamics, is described by a system of partial differential equations in 3+1 dimensions, but reproduces unitary evolution of a quantum field theory in the Fock space. To this end, after introduction of a complex four-potential of electromagnetic field, which generates the same electromagnetic fields as the initial real four-potential, spinor field is algebraically eliminated from the equations of spinor electrodynamics. It is proven that the resulting equations for electromagnetic field describe independent evolution of the latter and can be embedded into a quantum field theory using a generalized Carleman linearization procedure. The theory provides a simple and at least reasonably realistic model, valuable for interpretation of quantum theory. The issues related to the Bell theorem are discussed.