Least Information Principle for Quantum Mechanics

Abstract

A least information principle is proposed here to derive the formulations of non-relativistic quantum mechanics, including the uncertainty relation and the Schrödinger equation in both position and momentum representations. The key element for this principle is the introduction of new metrics to measure the observable information due to vacuum fluctuations. In addition, the Planck constant is understood as the basic discrete action unit to uncover observable information of the dynamics behavior of a physical system. Besides recovering the quantum mechanics formulation, the principle also brings in new results on two fronts. Mathematically, defining the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. Conceptually, these information metrics are shown to be responsible for manifesting entanglement effects without underlying physical interactions, implying that entanglement effects are non-causal. The least information principle further demonstrates the information essence of quantum mechanics, and can be a mathematical tool to derive more advanced quantum theory.