Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Abstract

Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single-valuedness of wave functions.

An Entropic Dynamics Approach to Geometrodynamics

“…which involves the introduction of a "drift" potential φ[χ] whose complete justification is still a subject of future investigation. 5 Maximizing (1) subject to (3) and normalization, we obtain a Gaussian transition probability distribution,…”

“…ED is a scheme for generating dynamical theories that are consistent with the entropic and Bayesian rules for processing information. 1 Among the successes of the ED framework are principled derivations of several aspects of the quantum formalism (For a review of current work, see e.g., [5]) that are also sensitive to, and indeed, help to clarify many conceptual issues that plague QT [6]. The standout feature of ED that makes this possible is that a clear delineation is maintained between the ontological, or physical, aspects of the theory and those that are of epistemological significance.…”

“…This prior can itself be derived from the ME method, and in that case, the αx appear as Lagrange multipliers 4. Note that since χx and ∆χx are scalars, in order that (3) be invariant under coordinate transformations of the surface the derivative δ/δχx must transform as a scalar density 5. There is strong reason to believe more compelling answers will come from the ED of Fermions.…”

Quantum Trajectories in Entropic Dynamics

“…Their unknown values are quantified by a probability density ρ(x). We also make another assumption, that the particles follow continuous trajectories; the particles move in short steps [1]. The inference framework allows us to find a large change by iterating over many small steps, and thus we only need to find the transition probability for a short step.…”

The Information Geometry of Space-Time

“…The subject of information geometry was introduced in statistics by Fisher[8] and Rao[9] with important later contributions by other authors[10]-[13]. Important aspects were also independently discovered in thermodynamics[14][15] 3. It is possible that there is some connection with the ideas formulated in the language of spectral geometry proposed byKempf [24].…”