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Isomerism and decoherence

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Abstract

In the present paper we address the problem of optical isomerism embodied in the socalled “Hund’s paradox”, which points to the difficulty to account for chirality by means of quantum mechanics. In particular, we explain the answer to the problem proposed by the theory of decoherence. The purpose of this article is to challenge this answer on the basis of a conceptual analysis of the phenomenon of decoherence, that reveals the limitations of the theory of decoherence to solve the difficulties posed by optical isomerism and, in general, by quantum measurement.

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Notes

  1. Although, strictly speaking, in quantum mechanics there is no distance between particles because in general they do not possess a definite position, the difference \( \left| {\bar{r}_{i} - \bar{r}_{j} } \right| \) is usually called “distance between particles”, where \( \bar{r}_{i} \) and \( \bar{r}_{j} \) are the coordinates of each electron in the position representation.

  2. The theory of decoherence works with the representation of the quantum state in the von Neumann–Liouville space. The ket \( \left| \upvarphi \right\rangle \) is represented in this space by an operator \( \hat{\uprho } = \left| \upvarphi \right\rangle \left\langle \upvarphi \right| \). The advantage of this space is that more general states can be represented in it (see Landau and Lifshitz 1958).

  3. The quaternionic formulation of quantum mechanics is a formalism based on quaternion fields instead of complex fields (see Adler 1995).

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Acknowledgments

We are very grateful to Eric Scerri for our discussions about the problem of isomerism. This publication was made possible through the support of grant 57919 from the John Templeton Foundation.

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Authors and Affiliations

  1. CONICET –Universidad de Buenos Aires, Buenos Aires, Argentina

    Sebastian Fortin & Juan Camilo Martínez González

  2. CONICET –Universidad de Buenos Aires-Theiss Research, La Jolla, USA

    Olimpia Lombardi

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  1. Sebastian Fortin
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  2. Olimpia Lombardi
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  3. Juan Camilo Martínez González
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Correspondence to Olimpia Lombardi.

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This work is fully collaborative: the order of the names does not mean priority.

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Fortin, S., Lombardi, O. & Martínez González, J.C. Isomerism and decoherence. Found Chem 18, 225–240 (2016). https://doi.org/10.1007/s10698-016-9251-6

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