The Entropic Dynamics approach to Quantum Mechanics. (arXiv:1908.04693v1 [quant-ph])

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived
as an application of entropic methods of inference. In ED the dynamics of the
probability distribution is driven by entropy subject to constraints that are
codified into a quantity later identified as the phase of the wave function.
The central challenge is to specify how those constraints are themselves
updated. In this paper we review and extend the ED framework in several
directions. A new version of ED is introduced in which particles follow smooth
differentiable Brownian trajectories (as opposed to non-differentiable Brownian
paths). To construct the ED we make use of the fact that the space of
probabilities and phases has a natural symplectic structure (i.e., it is a
phase space with Hamiltonian flows and Poisson brackets). Then, using an
argument based on information geometry, a metric structure is introduced. It is
shown that the ED that preserves the symplectic and metric structures -- which
is a Hamilton-Killing flow in phase space -- is the linear Schr\"odinger
equation. These developments allow us to discuss why wave functions are complex
and the connections between the superposition principle, the single-valuedness
of wave functions, and the quantization of electric charges. Finally, it is
observed that Hilbert spaces are not necessary ingredients in this
construction. They are a clever but merely optional trick that turns out to be
convenient for practical calculations.

Article web page: