Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable

Abstract

A quantization method based on replacement of c-number by c-number parameterized by an unbiased hidden random variable is developed. In contrast to canonical quantization, the replacement has straightforward physical interpretation as statistical modification of classical dynamics of ensemble of trajectories, and implies a unique operator ordering. We then apply the method to develop quantum measurement without wave function collapse \'a la pilot-wave theory.