Entropic Dynamics: from Entropy and Information Geometry to Quantum Mechanics

Abstract

Our subject is Entropic Dynamics, a framework that emphasizes the deep connections between the laws of physics and information. In attempting to understand quantum theory it is quite natural to assume that it reflects laws of physics that operate at some deeper level and the goal is to discover what these underlying laws might be. In contrast, in the entropic view no fundamental underlying dynamics is invoked. Quantum theory is an application of entropic methods of inference and the goal is to make the best possible predictions on the basis of some limited information represented by appropriate constraints. It is through the choice of microstates and of these constraints that the “physics” is introduced. In Entropic Dynamics a relational notion of entropic time is introduced as a book-keeping device to keep track of changes. We show that a non-dissipative entropic dynamics naturally leads to generic forms of Hamiltonian dynamics, and notions of information geometry naturally lead to those specific Hamiltonians (that is, those that include the correct quantum potential) that describes quantum mechanics.