Statistical violation of Hamilton’s principle: quantization, quantum-classical correspondence and measurement problem

Institute for the Physical and Chemical Research, RIKEN,
2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan

We propose a method of quantization by assuming statistical violation of Hamilton’s principle of stationary action leading to a statistical and dynamical modification of classical ensemble of trajectories in configuration space. The quantum-classical correspondence is explicit in the quantization process, thus there is no conceptual jump from a quantum theory which has no place for trajectory to a classical mechanics which is founded based on the notion of trajectory. We apply the method to system of particle showing that it gives Hermitian quantum observable with specific operator ordering. We then apply the method to solve the measurement problem á la pilot-wave theory without wave function collapse. Some predictions beyond quantum mechanics are discussed.