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Reconstructing Bohr’s Reply to EPR in Algebraic Quantum Theory

Masanao Ozawa, Yuichiro Kitajima

Published Aug 17, 2016• 6 citations
OpenAlex

Abstract

Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.

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Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.
After summarising a previously given analysis of Bohr's reply to Einstein, Podolsky and Rosen (EPR), this chapter endorses the claim made by Everett himself that Everettian quantum mechanics `in a certain sense bridges the positions of Einstein and Bohr'. On the one hand, it shows how Everett's theory provides a reconstruction of Bohr's viewpoint of complementarity as applied to the EPR case and a justi�cation of his criticism of EPR's `criterion of reality'. On the other hand, it includes a notion of physical reality that is independent of any observational context, and suggests a remaining shortcoming of Bohr's reply.
The article offers a rereading of Bohr’s reply to the argument of A. Einstein, B. Podolsky, and N. Rosen (EPR) concerning the incompleteness, or else nonlocality, of quantum mechanics. Bohr shows EPR’s argument to be deficient on their own terms, by virtue of an ambiguity found in their application of the criterion of reality they propose to the phenomena in question. He also offers an alternative interpretation of the EPR experiment itself, the thought experiment proposed by EPR, as part of his overall interpretation of quantum mechanics as complementarity.
This study posits that Bohr failed to defend the completeness of the quantum mechanical description of physical reality against Einstein–Podolsky–Rosen’s (EPR) paper. Although there are many papers in the literature that focus on Bohr’s argument in his reply to the EPR paper, the purpose of the current paper is not to clarify Bohr’s argument. Instead, I contend that regardless of which interpretation of Bohr’s argument is correct, his defense of the quantum mechanical description of physical reality remained incomplete. For example, a recent trend in studies of Bohr’s work is to suggest he considered the wave-function description to be epistemic. However, such an interpretation cannot be used to defend the completeness of the quantum mechanical description.
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.
In their celebrated paper titled Can quantum mechanical description of physical reality be considered complete?, Einstein, Podolsky and Rosen (EPR) showed for the first time the existence of `Spooky action-at-a-distance'. Though the result of their paper is unquestionable, but the conclusion of the same became sensational because of its challenge to quantum mechanical formalism whether it's complete or not in describing the physical reality of Nature. Bohr's physical and philosophical reply to that conclusion justified the completeness of quantum mechanics. Here, a simple algebraic way is presented for the results of these two classic papers in such a way that the actual reason behind why quantum world necessarily exhibits the action-at-a-distance and how Bohr defended against the incompleteness of the quantum formalism will become clear.This approach naturally reveals what physical assumption of EPR went wrong while considering the entangled quantum system and also provides the missing mathematical argument in Bohr's reply.