Аннотация:It is shown for the first time that description of an unpolarized neutron beam by density matrix can be contradictory. Density matrix is invariant with respect to choice of a quantization axis, while experimental devices can discriminate between different quantization axes. An experiment is proposed to discriminate a direction of a quantization axis of a specially prepared nonpolarized beam. The discrimination can be seen by observation of oscillations in statistical uncertainties. The success of the experiment will mean that an entanglement, following from the EPR paradox permits communication with a superluminal speed. A criticism of the EPR paradox and of some experiments on proof of Bell’s inequalities violation is presented.