Entropic Dynamics: from Information Geometry to Quantum Geometry

Entropic Dynamics (ED) is a framework in which dynamical laws are derived as an application of entropic methods of inference. The dynamics of the probability distribution is driven by entropy subject to constraints that are eventually codified into the phase of a wave function. The central challenge is to identify the relevant physical constraints and, in particular, to specify how those constraints are themselves updated.

In this talk I describe how the information geometry of the space of probabilities is extended to the ensemble-phase space of probabilities and phases. The result is a highly symmetric Riemannian geometry that incorporates the symplectic and complex structures that characterize the geometry of quantum mechanics. The ED that preserves these structures is a Hamiltonian flow and the simplest Hamiltonian suggested by the extended metric leads to quantum mechanics. Thus, in the entropic dynamics framework, Hamiltonians and complex wave functions arise as the natural consequence of information geometry.