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Ratio mathematica

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

Ruggero María Santilli

Published Jun 1, 2020• 0 citations
Publisher

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.

DOI
10.23755/rm.v38i0.516

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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.
In the preceding Papers I and II of this series, we have presented a review and upgrade of basic mathematical, physical and chemical methods, and provided a confirmation of the apparent proof of the EPR argument [1] that extended particles within physical media (interior dynamical problems) admit classical counterparts [9], while Einstein’s determinism appears to be progressively verified with the increase of the density of the medium [10]. In this third and final paper of the series, we shown that the EPT argument in general, and Einstein’s determinism in particular, appear to be progressively verified in the structure of mesons, baryon, nuclei, and molecular bonds while being fully verified at the limit of gravitational collapse. We additionally show, apparently for the first time, the validity of the EPR final statement to the effect that the wavefunction [of quantum mechanics] does not provide a complete description of the physical reality” since the covering isowavefunctions of hadronic mechanics provide an otherwise impossible representation of all characteristics of various physical and chemical interior systems existing in nature.
From a phenomenological and experimental viewpoint, quantum mechanics is remarkably successful in explaining effects and processes in the microscopic world. Recently, however, a growing body of literature has revisited the theory's own formal foundations, specifically addressing issues of self-consistency and completeness. As a major historical example of these foundational challenges, the Einstein-Podolsky-Rosen (EPR) argument famously claimed that the theory is incomplete. While many valid criticisms and refutations of the EPR logic exist, they generally rely on a combination of technical results and conceptual objections to EPR's interpretive assumptions, thus transcending the plain quantum framework itself. Motivated by these trends of examining the theory's structural limits, here we revisit the EPR argument. Focusing on elements essential to the EPR reasoning, we first analyze general quantum correlations for EPR states: (i) the fact that their observables are always associated with non-commuting operators, and (ii) the nature of the correlated information obtained through measurement. From these two points alone, and relying strictly on the core rules of quantum mechanics, we demonstrate how to overturn the alleged EPR incompleteness without invoking any extraneous propositions. Consequently, we show that the standard formalism alone suffices to resolve such type of skepticism regarding the theory's physical reach. This offers, at least in a paradigmatic instance, a powerful indication of a structurally well-founded, self-consistent quantum theory.
In1935, A.Einsteinexpressedhishistoricalview, jointly with B.Podolsky and N. Rosen, that quantum mechanics could be “completed” into a form recovering classical determinism at least under limit conditions (EPR argument). In the preceding Paper I, we have outlined the basic methods underlying the “completion” of quantum mechanics into hadronic mechanics for the representation of extended particles within physical media. In this Paper II, we study the isosymmetries for interior dynamical systems; we confirm the 1998 apparent proof that interior dynamical systems admit a classical counterpart; we confirm the 2019 apparent proof that Einstein’s determinism is progressively approached for extended particles in the interior of hadrons, nuclei and stars, while being fully achieved in the interior of gravitational collapse; and we show for the first time that the recovering of Einstein’s determinism in interior systems implies the removal of quantum mechanical divergencies. In the subsequent Paper III, we present a number of illustrative examples and novel applications in mathematics, physics and chemistry.
The Einstein–Podolsky–Rosen (EPR) argument was originally posed as a challenge to the completeness of quantum mechanics, rather than its empirical adequacy. While subsequent developments—most notably Bell’s theorem and experimental tests of nonlocal correlations— have constrained classes of hidden-variable theories, they have not resolved the underlying on- tological question raised by EPR: whether the quantum state exhausts physical reality. In this paper, we revisit the EPR criterion of completeness from the perspective of a temporally grounded physical framework, the Temporal Inertia Framework (TIF). We argue that the orig- inal EPR dilemma rests on an implicit assumption that physical reality must be specified on spacelike hypersurfaces, an assumption shared by both EPR and Bohr. By relaxing this assump- tion and allowing physical correlations to arise from shared temporal structure rather than local spatial variables or superluminal influence, one may satisfy the EPR realism criterion without violating relativistic causality or Bell-type constraints. Quantum mechanics is thus interpreted as operationally complete but ontologically incomplete, with quantum indeterminacy emerging from dynamical interactions with a proposed underlying temporal structure.
In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.
In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.