No Drama Quantum Theory?

TL;DR

This paper presents a simplified, local realistic model of scalar electrodynamics that eliminates matter fields, uses Carleman linearization, and aligns with experimental data, challenging some interpretations of quantum nonlocality.

Contribution

It introduces a novel approach to scalar electrodynamics by removing matter fields and embedding the resulting equations into a linear Hilbert space framework, offering a simpler quantum theory.

Findings

Matter field eliminated in scalar electrodynamics

Carleman linearization produces a second-quantized-like linear system

Model aligns with experimental data but lacks spin description

Abstract

This work builds on the following result of a previous article (quant-ph/0509044): the matter field can be naturally eliminated from the equations of the scalar electrodynamics (the Klein-Gordon-Maxwell electrodynamics) in the unitary gauge. The resulting equations describe independent dynamics of the electromagnetic field (they form a closed system of partial differential equations). An improved derivation of this surprising result is offered in the current work. It is also shown that for this system of equations, a generalized Carleman linearization (Carleman embedding) procedure generates a system of linear equations in the Hilbert space, which looks like a second-quantized theory and is equivalent to the original nonlinear system on the set of solutions of the latter. Thus, the relevant local realistic model can be embedded into a quantum field theory. This model is equivalent to a well-established model - the scalar electrodynamics, so it correctly describes a large body of experimental data. Although it does not describe the electronic spin and possibly some other experimental facts, it may be of great interest as a "no drama quantum theory", as simple (in principle) as classical electrodynamics. Possible issues with the Bell theorem are discussed.