Quantum Mechanics From Principle of Least Observability

Abstract

We show that the formulations of non-relativistic quantum mechanics can be derived from the principle of least observability. Observability is a concept introduced here to measure the distinguishability (or traceability) that a physical object exhibits during its dynamics. To quantify observability, we assume that the Planck constant defines the discrete amount of action a physical object needs to exhibit in order to be observable. Then, observability is calculated by 1.) dividing the action variable along the classical path by the Planck constant, and 2.) adding information metrics on distinguishability due to vacuum fluctuations. The least observability principle not only recovers quantum formulations including the uncertainty relation and the Schr\"{o}dinger equation in both position and momentum representations, but also brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for manifesting entanglement effects without underlying physical interactions, implying that entanglement effects are non-causal. At the mathematical level, defining the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schr\"{o}dinger equation that depends on the order of relative entropy. The least observability principle is a new mathematical tool, and we expect other advanced quantum formulations can be obtained from it.Comment: 17 pages, 1 figure. Revised Section I and II to clarify the concept of observability; Further improved the mathematical notation