A new “classical” formulation of conventional quantum mechanics is used to construct a description of quantum states with spin j =1/2 which uses only positive classical probabilities of observables instead of a complex density matrix. These probabilities are functions of points on a unit sphere which determine the directions relative to which the spin projections are measured. The proposed construction is a generalization of a system for tomography of the spin states of a single particle and may be used as a new method of measuring two-particle spin states. For pure spin states this method is exactly the same as the case of a single particle. Additional probabilities must be defined to describe mixed states.
A general quantum-mechanical description of relativistic spin 1/2 particles and nuclei channeled in bent crystals is presented using the cylindrical system of coordinates. The previously derived Dirac equation in this system is supplemented with terms characterizing anomalous magnetic and electric dipole moments. For the general case, transformation into the Foldy-Wouthhuysen representation is performed, quantum-mechanical equations of the motion of particles and their spins are obtained, and their classical limit is found. The physical nature of the main features of the description of particles and nuclei in the cylindrical system of coordinates is determined.
An argument, due originally to J. S. Bell, is somewhat simplified and made more specific. It deals primarily with a quantum mechanical system consisting of the spins of two spin-12 particles. It shows that a description of the quantum mechanical measurement of the spin components of these two particles by means of hidden parameters is impossible if we assume that the parameters determining the outcome of the measurement of the spin of each particle are independent of the direction in which we decide to measure the spin of the other particle. The mathematical reason for the impossibility is analyzed.