Entropic Dynamics approach to Quantum Electrodynamics

TL;DR

The paper develops Entropic Dynamics (ED) as a probabilistic, information-geometric foundation for quantum theory and extends it to local gauge theories to derive non-relativistic quantum electrodynamics (QED). By constructing an epistemic phase space with a flat information metric and a compatible symplectic structure, it derives a bilinear Hamiltonian that generates Schrödinger evolution (via Hamilton-Killing flows) while enforcing gauge invariance and Gauss constraints, ultimately reproducing Maxwell’s equations and the QED Hamiltonian with Coulomb interactions. A key interpretation is that particles and fields are ontic, whereas probabilities, phases, and related quantities are epistemic tools; photons, in particular, are not ontic but arise as epistemic aspects of the radiation field. The framework thus provides a self-consistent, inference-based route to QED, with potential pathways to Yang–Mills theories and gravity, while clarifying the conceptual status of gauge fields and quantum states.

Abstract

Entropic dynamics (ED) is a framework that allows one to derive quantum theory as a Hamilton-Killing flow on the cotangent bundle of a statistical manifold. These flows are such that they preserve the symplectic and the (information) metric geometries; they explain the linearity of quantum mechanics and the appearance of complex numbers. In this paper the ED framework is extended to deal with local gauge symmetries. More specifically, on the basis of maximum entropy methods and information geometry, for an appropriate choice of ontic variables and constraints, we derive the quantum electrodynamics of radiation fields interacting with charged particles. As a test that despite its unorthodox foundation the ED approach is empirically successful we derive the Maxwell equations.