Entropic Dynamics approach to Quantum Electrodynamics

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.

• The paper develops a framework deriving QED from entropic inference using Hamilton-Killing flows on statistical manifolds.
• It employs information geometry to reconcile symplectic and metric structures, yielding the natural emergence of complex numbers.
• The approach reinterprets gauge symmetries in probabilistic terms, successfully deriving Maxwell’s equations and establishing charge conservation.

Entropic Dynamics Approach to Quantum Electrodynamics

Introduction

The paper "Entropic Dynamics approach to Quantum Electrodynamics" (2511.19238) extends the framework of Entropic Dynamics (ED) to embody the principles of Quantum Electrodynamics (QED) without recourse to classical dynamics. The author, Ariel Caticha, proposes that QED can be derived as a Hamilton-Killing flow on the cotangent bundle of a statistical manifold, preserving both symplectic and metric geometries. This reformulation emphasizes the distinction between ontic and epistemic variables and utilizes entropic methods and information geometry to facilitate a fresh interpretation of gauge symmetries in quantum mechanics. The paper concludes with the successful derivation of Maxwell’s equations, demonstrating the theoretical and empirical robustness of the approach.

Ontic and Epistemic Variables

A central tenet of the paper is the distinction between ontic variables, which embody reality, and epistemic variables, which are probabilistic and uncertain. In this context, particles have definite, albeit unknown, positions in continuum with classical nature. Conversely, radiation is described entirely by probabilistic wave functions with no associated ontic dynamics. The novel interpretation asserts the absence of ontic momenta, which are traditionally a staple of classical physics, thus emphasizing a move away from classical interpretations towards a purely probabilistic approach in quantum dynamics.

The Role of Information Geometry and Symplectic Structure

The mathematical underpinnings of ED in quantum theory involve the use of a complex structure within the epistemic phase space. This structure, which derives from the dual presence of symplectic and metric geometries, naturally leads to the introduction of complex numbers in quantum mechanics. The ensuing framework justifies the linear formalism of quantum mechanics and the superposition of states by adopting a metric consistent with information geometry, further illuminating the fundamental structure of quantum states in phase space.

Quantum Electrodynamics Within the ED Framework

ED circumvents traditional field quantization by directly formulating quantum field theories. In QED, correlations between fields and particles are captured through probabilistically inferred charge densities rather than through intrinsic particle properties. The paper describes how the consistent application of gauge symmetries naturally gives rise to the Maxwell equations and demonstrates that charge conservation is a natural consequence rather than a postulated axiom. This approach highlights the conceptual shift from classical field theory by emphasizing probabilistic dynamics as opposed to deterministic evolution, typical in conventional approaches.

Implications and Future Directions

The reconciliation of entropic inference and quantum mechanics in the paper signifies a potential paradigm shift, suggesting that quantum fields and particles can be fully described in epistemic terms without ontic counterparts. Practically, this generates a framework wherein photons are merely probabilistic constructs without physical instantiation, challenging traditional interpretations. Future investigations are encouraged to extend the ED framework to relativistic quantum fields such as Yang-Mills theories and gravitational interactions, potentially paving new pathways in theoretical physics. Moreover, the entropic foundation promises innovative insights into quantum correlations, transition rates, and the very nature of quantum entities.

Conclusion

The entropic dynamics approach meticulously developed in this research offers a novel probabilistic perspective on QED, effectively integrating information geometry and entropic reasoning with the quantum mechanics formalism. This nuanced framework not only reinterprets gauge symmetries and quantum fields but also aims to redefine the epistemic and ontic roles in quantum physics. While significant inroads have been made, the paper invites further exploration into the entropic reconstruction of more complex quantum field theories.