Non-relativistic quantum theory consistent with principle of locality

Abstract

Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or multi-particle non-relativistic quantum system is initially in a stationary state, and its wave function field is locally perturbed, then perturbed and non-perturbed sub-regions appear in the region. According to Schr\"odinger equation, borders of the perturbed sub-region propagate with infinite speed, and the perturbation instantaneously affects all infinite region. It means that Schr\"odinger equation predicts infinite speed of the wave function perturbations propagation. This feature of classical Schr\"odinger equation is traditionally interpreted as non-locality of quantum mechanics. From physical point of view, such mathematical behavior of Schr\"odinger equation solutions is questionable because it is difficult to accept that in real world infinite physical objects can instantaneously appear. We introduce a hypothesis that in reality speed of propagation of the perturbed sub-region borders is equal speed of light. On this basis we develop and analyze a finite propagation speed concept for non-relativistic quantum equations. It leads to local interpretation of non-relativistic quantum mechanics consistent with principle of locality and free of local hidden variables. The theory is applied to analysis of Einstein-Podolsky-Rosen (EPR) paradox, entanglement and properties of perturbed matter waves. We proved that formulated theory agrees with results of classical experiments on electron matter waves diffraction.