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Around the notion of state and the superposition principle

Mauricio Rozo Clavijo, Diana Mendoza, Javier Alberto Olarte Torres

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

this article presents a reflection on the concepts of state and principle\nsuperposition within classical and quantum context. Are highlighted the strategies\nthat serve as the basis for the explanation of phenomena at the atomic level,\nexplanation than requires a formalization and an image as a support for their\nelaboration. In addition, the processes of formalization are characterized by the\nconstruction of relations than gives account of the phenomenon. In this sense, are\ngiven examples than allow conceptualize the notion of state and the superposition\nprinciple within the two contexts which play a key role in the formalism of every\nphysical theory. This analysis allows us to contribute elements for the teaching the\nquantum mechanics giving the possibility of develop a different pedagogical and\ndidactic practice than the usual.

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this article presents a reflection on the concepts of state and principle\nsuperposition within classical and quantum context. Are highlighted the strategies\nthat serve as the basis for the explanation of phenomena at the atomic level,\nexplanation than requires a formalization and an image as a support for their\nelaboration. In addition, the processes of formalization are characterized by the\nconstruction of relations than gives account of the phenomenon. In this sense, are\ngiven examples than allow conceptualize the notion of state and the superposition\nprinciple within the two contexts which play a key role in the formalism of every\nphysical theory. This analysis allows us to contribute elements for the teaching the\nquantum mechanics giving the possibility of develop a different pedagogical and\ndidactic practice than the usual.
Conceptual and formal problems Many of the problems surrounding the interpretation of quantum mechanics stem from the absence of a sufficiently general and physically transparent analysis of the connection with the domain in which classical concepts are assumed to apply. It is the purpose of this chapter to describe with the aid of a few examples how the quantum potential approach provides a context within which the conceptual and formal issues raised by this problem may be clarified. A key question is to explain how the state or context dependence which is so characteristic of the quantum domain turns into state independence at a certain level, characterized as ‘classical’. To illustrate one aspect of the conceptual problem we recall that in Bohr's interpretation the validity of classical concepts is already presupposed since, it is suggested, it is only in terms of these that one can unambiguously communicate the results of experiments in the quantum domain. Thus, classical physics must be considered as prior to quantum mechanics and the latter is a generalization of the former in that it provides a new set of laws governing the application of classical concepts. According to this view, any procedure by which classical mechanics is recovered from quantum mechanics as a mathematical limit can only be a demonstration of consistency with the already postulated epistemological relation between the two theories and not as a ‘derivation’ of classical mechanics from quantum mechanics (George, Prigogine & Rosenfeld, 1972).
The distinction between classical physics and quantum physics is traditionally analyzed based on concepts such as determinism, the continuous or discrete nature of variables, the non-commutativity of observables, and the superposition of states. This article proposes a more fundamental reinterpretation based on two complementary conceptual ingredients. The first is a minimal relational epistemology, developed from the author's previous work, in which space and time are not a priori frames but emerge from comparisons of movements between systems. The second is an analysis of the role played by the possibility—or impossibility—of defining independent events, a possibility that depends precisely on the prior construction of a spatio-temporal and causal structure. We show that the essential difference between classical physics and quantum physics lies in the rule of probability composition, and not in the features usually invoked. Quantum physics appears to be a coherent description of a physical regime prior to the establishment of the causal independence of events. The two conceptual ingredients are summarized in the form of axioms, broad enough to offer a new perspective on the usual notions of quantum physics, which we review here. Accompanying this text, another article presents more technical developments.
In this paper, I discuss two different formalisms of quantum mechanics, i.e. the orthodox and the de Broglie-Bohm formalisms, as explanations of the interference pattern observed in the doubleslit experiment. I evaluate the explanations provided by these two formalisms on the basis of Hempel's DN model of scientific explanation, showing that both formalisms can sufficiently explain the phenomenon. However, once the interpretations associated with the two formalisms come into play, the sufficiency of the DN model's evaluation of the explanations becomes questionable. Whereas the Copenhagen interpretation, associated with the orthodox quantum formalism, would evaluate the DN model as sufficient, Bohm's interpretation, associated with the de Broglie-Bohm formalism, would not. Bohm's interpretation would require descriptions containing relevant metaphysical relations to be included in the explanans. The DN model does not contain such a requirement. Then, Strevens's kairetic account of explanation will be introduced as an alternative model of scientific explanation. The kairetic account allows for descriptions of relevant metaphysical relations to be included in the explanans. I argue that the proponents of both interpretations will accept the evaluation provided by Strevens's kairetic account as sufficient. This highlights the role of quantum interpretations in modeling scientific explanation of quantum phenomena in two ways: (1) in determining the relevant explanans of the model of explanation, and (2) in evaluating models of explanation by virtue of evaluating the relevancy of their explanans or by evaluating whether the requirements of a model are fulfilled in the context of an interpretation.
The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."