About the causality principle in quantum theory

Various approaches to understanding causality in quantum theory are considered, since the violation of the causality principle has long been the subject of active research. Four experimental situations are considered from the causality point of view: instantaneous collapse of the quantum state vector of a system of entangled particles, quantum eraser, quantum Zeno paradox and the operation of the nonlinear light beam splitter. The last one is a flat interface between two transparent dielectrics, at least one of which exhibits Kerr nonlinearity, i.e., its refractive index depends on the transmitted radiation intensity. It is shown, that in the first two cases, the causality principle can be violated only in terms of the speed of the consequences, not limited by the light cone. For the nonlinear beam splitter, besides the fact that the quantum and classical descriptions give opposite predictions of the behavior of the phase, the causality principle is violated in the most general sense: the effect of subsequent events on the previous one. The quantum paradox of Zeno occupies, as it were, an intermediate position of equal participation of cause and consequence in the total cascade of two successive events, i.e. as the first can prevent the second, so the second - the first.