Studies on A. Einstein , B. Podolsky and N. Rosen argument that ”quantum mechanics is not a complete theory,” I: Basic methods

Abstract

In 1935, A. Einstein expressed his view, jointly with B. Podolsky and N. Rosen, that ”quantum mechanics is not a complete theory” (EPR argument). Following decades of preparatory studies, R. M. Santilli published in 1998 a paper showing that the objections against the EPR argument are valid for point-like particles in vacuum (exterior dynamical systems), but the same objections are inapplicable (rather than being violated) for extended particles within hyperdense physical media (interior dynamical systems) because the latter systems appear to admit an identical classical counterpart when treated with the isotopic branch of hadronic mathematics and mechanics. In a more recent paper, Santilli has shown that quantum uncertainties of extended particles appear to progressively tend to zero when in the interior of hadrons, nuclei and stars, and appear to be identically null at the limit of gravitational collapse, essentially along the EPR argument. In this first paper, we review, upgrade and specialize the basic mathematical, physical and chemical methods for the study of the EPR argument. In two subsequent papers, we review the above results and provide specific illustrations and applications.