Quantum dynamics and kinematics from a statistical model selected by the principle of Locality

Abstract

Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical interpretation of wave function and uncertainty relation can be derived from a statistical model of microscopic stochastic deviation from classical mechanics which is selected uniquely, up to a free parameter, by the principle of Local Causality. Quantization is thus argued to be physical and Planck constant acquires an interpretation as the average stochastic deviation from classical mechanics in a microscopic time scale. Unlike canonical quantization, the resulting quantum system always has a definite configuration all the time as in classical mechanics, fluctuating randomly along a continuous trajectory. The average of the relevant physical quantities over the distribution of the configuration are shown to be equal numerically to the quantum mechanical average of the corresponding Hermitian operators over a quantum state.