Continuous Representation for Spin 1/2, Quantum Probability Theory and Bell Paradox.

摘要

Quantum mechanics of spin 1/2 is translated into a classical language namely into a continuous representation (''coherent state representation''). This permits us to compare the quantum probability theory with the classical one. The Bell paradox is analysed. It is shown that the quantum correlator of two spins 1/2 in the singlet state turns out to be equal 9 times a classical one, and therefore it is illegitimate to put it into the Bell inequality. The true quantum inequality is absolutely unrestrictive. In the continuous representation, equations of motion take a classical form similar to the Liouville equation in classical mechanics. Their solutions can be expressed via characteristics, subjected to equations relative to the Hamiltonian ones. However quantum theory still differs from classical one in choice of probability densities and in construction of correlators, of other quantities, of an analog of the Markov property, etc. These quantities and relations can be converted into their classical form in the framework of the quantum mechanics as well, but only in terms of modified ''probability densities'', which cannot be possible definite. 32 refs. (Atomindex citation 19:101787)