A classically stochastic non-differentiable mechanics with emergent quantum behavior

Abstract

A classical stochastic mechanics for randomly-perturbed particles is provided that in the limit of small mass recovers quantum-like behavior. Although, the theory does maintain traditional classical mechanics as an approximation, the present theory differs from traditional classical physics in that particle trajectories are inherently non-differentiable in a manner that depends on the resolution of observation. The theory is founded upon a path integral formulation of Jaynes' maximum entropy (MaxEnt) principle. A classical analog of Heisenberg's uncertainty principle, which arises from the random perturbations of the particles, is used as a constraining factor on the entropy maximization. Based upon the closed form probability distribution that results from the entropy maximization, an analytical solution is derived for a perturbed particle in free flight.