Title: Quantum Mechanics From Principle of Least Observability

Abstract: We show that the basic non-relativistic quantum formulations can be derived from a principle of least observability. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical object needs to exhibit during its dynamics in order to be observable. This enables us to calculate the degree of observability from a classical trajectory. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced to define the information metrics to measure additional observability due to vacuum fluctuations. Applying the variation principle to minimize the total degree of observability allows us to elegantly recover the basic quantum formulations including the uncertainty relation and the Schr\"{o}dinger equation in both position and momentum representations. Adding the no preferred representation assumption, we obtain the transformation formulation between position and momentum representations. The least observability principle shows clearly how classical mechanics becomes quantum mechanics. Furthermore, it is a mathematical tool that can bring in new results. By defining the information metrics for vacuum fluctuations using more general definitions of relative entropy, we obtain a generalized Schr\"{o}dinger equation that depends on the order of relative entropy. The principle can be applied to derive more advance quantum formalism such as quantum scalar field theory.