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International Journal of Quantum Chemistry

EPR correlations in the molecular domain

Thomas Kr�ger

Published Jan 1, 1997• 2 citations
Publisher

Abstract

“Quantum mechanics is the first mathematically formulated scientific theory where in a nontrivial way the whole is more than the combination of its parts” (H. Primas, 1982). Nowadays most chemical observations and phenomena are understood on the basis of the molecular point of view. The three-dimensional molecules chemists speak about are micro-entities that as such are subject to a theoretical description in terms of quantum mechanics. Therefore one would expect that also in the molecular domain holistic effects appear which are caused by the well-known Einstein–Podolsky–Rosen (EPR) correlations. In the present study we demonstrate that—the unrestricted validity of quantum mechanics presupposed—such correlation phenomena play an important role in the description of a dissociation reaction A2⇒2A, where an intrinsic (structure establishing) degree of freedom fades into a mere translation of the fragments. Finally we will address the question, why in general EPR correlations are observed quite rarely in the domain of molecules—despite their fundamental importance for the notion of molecule itself. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 679–687, 1997

DOI
10.1002/(sici)1097-461x(1997)64:6<679::aid-qua5>3.0.co;2-t

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International Journal of Quantum Chemistry•Jan 1, 1999•0 citations
“Quantum mechanics is the first mathematically formulated scientific theory where in a nontrivial way the whole is more than the combination of its parts” (H. Primas, 1982). Nowadays most chemical observations and phenomena are understood on the basis of the molecular point of view. The three-dimensional molecules chemists speak about are micro-entities that as such are subject to a theoretical description in terms of quantum mechanics. Therefore one would expect that also in the molecular domain holistic effects appear which are caused by the well-known Einstein–Podolsky–Rosen (EPR) correlations. In the present study we demonstrate that—the unrestricted validity of quantum mechanics presupposed—such correlation phenomena play an important role in the description of a dissociation reaction A2⇒2A, where an intrinsic (structure establishing) degree of freedom fades into a mere translation of the fragments. Finally we will address the question, why in general EPR correlations are observed quite rarely in the domain of molecules—despite their fundamental importance for the notion of molecule itself. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 679–687, 1997
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.
Einstein-Podolsky-Rosen (EPR) correlations Explaining the correlations predicted by quantum mechanics in the case of joint quantum systems of the EPR type has proved to be a major challenge for the Common Cause Principle. The EPR correlations have been confirmed by a large number of sophisticated experiments carried out since the early 1980s, and, since quantum theory does not give us any hints as to where to look for possible common causes that could explain the correlations in question, the suspicion arose that common causes of EPR correlations might not exist at all. If this were indeed the case, then the EPR correlations would constitute strong empirical evidence against Reichenbach's Common Cause Principle. But how could this be possible in view of the results presented in the previous chapters? As we have seen (Chapter 3), every common cause incomplete probability space is common cause extendible (even strongly common cause extendible with respect to any finite set of correlations; Proposition 3.9); therefore every correlation can, in principle, be explained by a (possibly hidden) common cause, including the (finite number of) EPR correlations. Could the EPR correlations (not) be explained by referring to such hidden common causes? To answer this question, one has to realize first that it is not quite obvious how to link the Common Cause Principle to quantum mechanics because Reichenbach's notion of common cause was defined in terms of classical probability theory (Chapter 2), not in terms of quantum probability theory.
Two “thought experiments” are central to most discussions of the famous EPR paradox: Experiment 1, in which two electrons with spins initially coupled to total spin S are carried apart to a great distance (e.g., in a molecular dissociation process), and Experiment 2, which is similar but refers to two bare protons. The crucial question to be asked is whether the spin coupling will be conserved at all distances: if it is, then the system exhibits “nonlocality” (the two particles stay “correlated” in some way, even at infinite distance) and thus violates Einstein's principle of locality—which denies that possibility. A recent discussion of Experiment 1 shows that nonlocality is the rule only up to a point at which the singlet–triplet interval is small enough to be bridged by weak interaction with the “heat bath” in which the system is embedded: Beyond that point, the system is no longer described by a wave function but instead by a statistical ensemble. When ensemble averaging is admitted, the spin-correlation function Qc(r1, r2) decreases to zero at all points in space and the coupling is broken; the particles are then independent and neither can be influenced by its previous interaction with the other. In the present work, the same approach is used to discuss the two-proton system (Experiment 2). The conclusions are similar: The protons are described by appropriate wave packets, with an initial overlap sufficient to give a substantial singlet–triplet separation ΔE, and, again, the spin coupling is broken when the overlap (and, consequently, ΔE) decreases to a sufficiently small value. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 573–584, 1999
The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by
Two “thought experiments” are central to most discussions of the famous EPR paradox: Experiment 1, in which two electrons with spins initially coupled to total spin S are carried apart to a great distance (e.g., in a molecular dissociation process), and Experiment 2, which is similar but refers to two bare protons. The crucial question to be asked is whether the spin coupling will be conserved at all distances: if it is, then the system exhibits “nonlocality” (the two particles stay “correlated” in some way, even at infinite distance) and thus violates Einstein's principle of locality—which denies that possibility. A recent discussion of Experiment 1 shows that nonlocality is the rule only up to a point at which the singlet–triplet interval is small enough to be bridged by weak interaction with the “heat bath” in which the system is embedded: Beyond that point, the system is no longer described by a wave function but instead by a statistical ensemble. When ensemble averaging is admitted, the spin-correlation function Qc(r1, r2) decreases to zero at all points in space and the coupling is broken; the particles are then independent and neither can be influenced by its previous interaction with the other. In the present work, the same approach is used to discuss the two-proton system (Experiment 2). The conclusions are similar: The protons are described by appropriate wave packets, with an initial overlap sufficient to give a substantial singlet–triplet separation ΔE, and, again, the spin coupling is broken when the overlap (and, consequently, ΔE) decreases to a sufficiently small value. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 573–584, 1999