ROLE OF THE LIE-SANTILLI ISOTHEORY FOR THE PROOF OF THE EPR ARGUMENT.

In 1935, A. Einstein stated, in a historical paper with-B. Podolsky and N. Rosen [1] that " quantum mechanics is not a complete theory" and that determinism could be recovered at least under limit conditions (EPR argument). In 1964, J. S. Bell [2] proved a theorem according to which a system of quantum mechanical particles with spin 1/2 with SU(2) Lie algebra [σ_i, σ_j] = 2ϵ_i,j,kσ_k, where the σs are the Pauli matrices, cannot admit a classical counterpart, thus appearing to disprove the EPR argument. In 1978, R. M. Santilli [3] discovered the axiom-preserving generalization-" completion" of the various branches of Lie's theory (universal enveloping algebras, Lie algebras, and Lie groups) based on the isoassociative product X_i*X_j = X_i...X_j,... > 0, with Lie-Santilli isoalgebras [X_iX_j]* = X_i*X_j - X_j*X_i = C_i,j,k,X_k classified into regular (irregular) when the C-quantities are constant (functions). In 1998 [4] Santilli proved that Bell's theorem is valid for point-particles, but it is inapplicable for systems of extended particles with spin 1/2 under deep mutual entanglement, and that said systems do admit classical counterparts when represented with the isotopic SU(2) Lie-Santilli isoalgebars [Σ_i, Σ_j]* = 2ϵ_i,j,kΣ_k, where Σ_k are the new Pauli-Santilli isomatrices, with realization of the isotopic element ... = Diag. (1/λ, λ), det ... = 1 providing a concrete and explicit realization of "hidden variables" under the full validity of quantum axioms. Subsequently, Santilli [5] proved that Einstein's determinism is progressively approached in the structure of hadrons, nuclei and stars and it is fully recovered at the limit of gravitational collapse (see Refs. [6] for a detailed presentation). In this lecture, by following our recent paper [7], we outline the aspects of the Lie-Santilli isotheory which are essential for Santilli's proofs of the EPR argument. [ABSTRACT FROM AUTHOR]