Entropic Dynamics Derives Electrodynamics, Preserving Geometry and Recovering Maxwell Equations

The fundamental laws governing light and matter remain a cornerstone of physics, and researchers continually seek deeper explanations for these established principles. Ariel Caticha from University at Albany, SUNY, advances this understanding by applying a novel framework called entropic dynamics to the complexities of quantum electrodynamics. This approach derives physical theories from principles of maximum entropy and information geometry, effectively reconstructing the laws of electromagnetism from statistical foundations. The team demonstrates that this method successfully recovers the Maxwell equations, suggesting a powerful new way to understand the behaviour of radiation fields and their interactions with charged particles, and offering a potentially unifying perspective on fundamental physical laws.

Maximum Entropy Drives Quantum Dynamics

Scientists have developed an innovative framework called Entropic Dynamics (ED) to reconstruct quantum theory, treating it as a natural consequence of maximizing entropy on a statistical manifold, thereby preserving both symplectic and information geometric structures. This approach explains the inherent linearity of mechanics and the emergence of complex numbers within the quantum realm. The study establishes a fundamental distinction between what is real, the ontic, and what is known, the epistemic, arguing that particles and fields represent objective reality, while wave functions and probabilities are tools for describing it. This framework offers a fundamentally probabilistic approach to understanding physical systems, where evolution maximizes entropy subject to constraints like conservation laws.

The research advocates for a realist interpretation of physics, where physical quantities represent objective properties of the world, independent of the observer, and challenges the conventional view of quantum concepts like wave functions and probabilities, arguing they are epistemic tools rather than ontic entities. This approach proposes a new foundation for quantum field theory, potentially resolving conceptual problems associated with the standard formulation, and even suggests photons are not fundamental particles but rather epistemic tools describing the dynamics of radiation. The work spans theoretical physics, quantum foundations, mathematical physics, and the philosophy of physics, with a particular focus on gauge theory and field theory. The framework possesses conceptual clarity, mathematical rigor, novelty, and a compelling realist interpretation, offering a compelling alternative to the standard formulation and potentially resolving long-standing conceptual problems. The key takeaway is the shift in perspective: deriving laws from entropy maximization and separating what is from what we know.

Entropic Dynamics Reconstructs Quantum Electrodynamics

Scientists developed an innovative framework called Entropic Dynamics (ED) to derive quantum theory, treating it as a Hamilton-Killing flow on a statistical manifold, thereby preserving both symplectic and information metric geometries. This approach explains the inherent linearity of mechanics and the emergence of complex numbers within the quantum realm. The study extends this ED framework to encompass local gauge symmetries, reconstructing the quantum electrodynamics of radiation fields interacting with charged particles using maximum entropy methods and information geometry. The work pioneers a novel approach to quantum gauge fields, bypassing the traditional formulation of classical gauge theory and subsequent quantization, instead proceeding directly to formulating the quantum theory itself.

Scientists defined microstates representing particles and gauge fields, recognizing a clear distinction between ontic variables, representing what is real and possessing definite values, and epistemic variables, representing probabilities and managing inherent uncertainties. The dynamics within this framework focuses entirely on the evolution of these probabilities, relegating all dynamics to the epistemic sector. By reconstructing the formalism of quantum electrodynamics, scientists aim to clarify fundamental questions regarding ontological and epistemic variables within the theory, offering a unique perspective on the interpretation of quantum mechanics.

Entropic Dynamics Derive Maxwell’s Equations

This work presents a novel framework called entropic dynamics, extending existing theory to incorporate local gauge symmetries and derive the laws of electrodynamics from fundamental principles. Scientists developed a method based on maximum entropy and information geometry to model the interaction of radiation fields with charged particles, ultimately deriving the Maxwell equations as a successful empirical test of the approach. The research establishes a foundation where the dynamics of physical systems are understood not through traditional particle trajectories, but through the evolution of probability distributions over possible states. The team represented the ontic microstates of particles by their positions, while the radiation field is described by vector potential distributions, establishing a full ontic configuration space.

A key assumption is that the representation of the radiation field is redundant, mirroring classical gauge field theory. This continuity of paths allows the system’s evolution to be studied as a sequence of infinitesimally short steps. To model this evolution, scientists defined an epistemic phase space, a statistical manifold of normalized, gauge-invariant probability distributions. This space is equipped with a symplectic structure, allowing them to define gradients and tensor components within the epistemic phase space, providing a foundation for understanding the dynamics of probabilities and predicting the positions of particles and values of fields based on incomplete information.

Entropic Dynamics Reconstructs Maxwell’s Equations

This research extends the framework of entropic dynamics to incorporate local gauge symmetries, successfully deriving the equations of electrodynamics and, specifically, Maxwell’s equations. By applying maximum entropy methods and information geometry, the team demonstrates a pathway to reconstruct established physics from a foundation based on ontic variables and constraints. The approach models both matter and radiation, representing particles with definite positions and continuous trajectories, while describing radiation through vector potential distributions, effectively treating fields as fundamental rather than composed of particle-like entities. The core achievement lies in constructing a dynamics that remains consistent despite the inherent redundancy in representing the radiation field, acknowledging that different field configurations can represent the same physical state due to gauge transformations. This is accomplished by focusing on probability distributions that are invariant under gauge shifts, allowing for the prediction of particle positions.