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Abstract
We discuss the problem of the generalization of Bell local hidden variable models for unstable particles as nucleons or decaying quantum bound states. We propose to extend the formalism of real deterministic hidden variables in the complex domain, in analogy with the quantum Gamow ket formalism, and we introduce a time dependent classical probability density distribution by which we implement hidden time dependence in the quantum expectation values. We suggest therefore a classical framework which may recover by asymptotic temporal limits the standard Bell stationary quantum statistical averages. Endly we discuss the possible relevance of our proposal for general non-isolated quantum systems in noninertial frames and the consequent dynamic effects of vacuum instabilities on E.P.R tests and Q.M. ensemble statistical averages.
Highlights
Since the pioneer work of Einstein, Podolsky and Rosen [1] against the standard Copenhagen interpretation of Quantum Mechanics on hidden variables have been debating the presumed incompleteness of quantum microscopic systems studying the dynamics of stable free particles like electrons
We propose to extend the formalism of real deterministic hidden variables in the complex domain, in analogy with the quantum Gamow ket formalism, and we introduce a time dependent classical probability density distribution by which we implement hidden time dependence in the quantum expectation values
We suggest a classical framework which may recover by asymptotic temporal limits the standard Bell stationary quantum statistical averages
Summary
Since the pioneer work of Einstein, Podolsky and Rosen [1] against the standard Copenhagen interpretation of Quantum Mechanics on hidden variables have been debating the presumed incompleteness of quantum microscopic systems studying the dynamics of stable free particles like electrons. Notwithstanding the formalism developed by Gamow for nuclear physics [7] described these particles states with wavefunctions which didn’t belong to HiIlbert space (and that were not eigenstates of hermitian operators) it was applied to them the Born probability interpretation and the wave function collapse postulate to make predictions that were successfully experimentally tested This contradictory approach, based on Gamow kets on the one hand and on the Schrodinger equation dynamics and Pauli spin operators on the other, was not strongly outlined by the famous opponents of the Copenhagen interpretation and it was not considered as a new theoretical and experimental context suitable to develop classical deterministic models of quantum accelerated systems as unstable nucleons or excited quasi bound states of atoms and ions. It is possible to implement this research program for every non-isolated quantum system exploiting some ideas developed in three previous papers of the author [8] [9] [10] introducing time dependent complex hidden variables (either scalars, vectors or matrices as moments of inertia) and generalizing the standard integral on the probability density distribution as a complex path dependent one
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