Could quantum mechanics, and even gravity, be all about a correct resolution of the classical self-force problem?

TL;DR

This paper proposes extended charge dynamics (ECD), a classical theory resolving the self-force problem, which can reproduce quantum phenomena like interference and Bell violations through statistical effects of self-interacting charges.

Contribution

The paper introduces ECD, a classical, symmetry-preserving theory that addresses the self-force problem and can replicate quantum mechanics' statistical predictions.

Findings

ECD maintains classical symmetries and conservation laws with finite quantities.

Ensembles of ECD solutions can reproduce quantum interference and Bell inequality violations.

Quantum concepts emerge as statistical effects of classical self-interacting charges.

Abstract

The self-force problem of classical electrodynamics has two closely linked facets: The ill defined dynamics of a point charge due to the divergent self field at the position of the charge, and the divergence of formally conserved quantities, such as the energy, associated with symmetries of the corresponding Lagrangian. Fixing the self-force problem amounts to the construction of a \emph{new} theory, which is free of the above pathologies and yet "sufficiently close" to the immensely successful original. In a recent paper by the present author such a proposal, dubbed extended charge dynamics (ECD), was presented. The essential ingredients of classical electrodynamics preserved by ECD (and, among the plethora of solutions to the problem, only by ECD) are: - Ontology. The electromagnetic field is the same unquantized classical field, while charges are sufficiently localized conserved currents, accounting for the manifest corpuscular nature of elementary charges. - Symmetries. ECD enjoys the full symmetry group of classical electrodynamics, most importantly the hidden symmetry of scale covariance. - Conservation laws. All ECD conservation laws formally coincide with their classical counterparts, and yet lead to finite conserved quantities. Despite this seemingly classical setting, and the reduction of ECD to classical electrodynamics in the latter's domain of validity, it is shown in the present paper that ensembles of ECD solutions could, in principle, reproduce the statistical predictions of quantum mechanics. Exclusively quantum mechanical concepts, such as interference, violations of Bell's inequalities, spin and even photons (despite the use of a classical EM field), all emerge as mere statistical manifestations of the self interaction of ECD charges.