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Interpretación modal de la mecánica cuántica

Jon Pérez Laraudogoitia

Published Apr 1, 1985• 0 citations
OpenAlex

Abstract

In this paper, we present a (propositional) modal-logic approximation to Quantum Mechanics from a reduced and characteristic number of crucial experi ments and so independently of the lattice of subspaces of Hilbert s'pace. Kripke's semantics, which determinates this system, allows to define, from a new point of view, the notions of process and virtual world and admits a natural interpretation which in turn can help us to understand the measurement problem. In this way, we can attempt a many-worlds interpretation of Quantum Mechanics, in the way of Everett.

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Birkhäuser Basel eBooks•Jan 1, 2001•0 citations
In this paper, we present a (propositional) modal-logic approximation to Quantum Mechanics from a reduced and characteristic number of crucial experi ments and so independently of the lattice of subspaces of Hilbert s'pace. Kripke's semantics, which determinates this system, allows to define, from a new point of view, the notions of process and virtual world and admits a natural interpretation which in turn can help us to understand the measurement problem. In this way, we can attempt a many-worlds interpretation of Quantum Mechanics, in the way of Everett.
Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.
This short paper proposes the project of a modal logical semantics that will represent not the classical modalities but the many-worlds interpretation for the physical theory of quantum mechanics. It also views some problematic methodological questions of the doctrine such as measurement and a role of an interpreter. Special attention is given to the famous paradoxes of the QM such as EPR Paradox and Schrodinger’s Cat. The paper will be interesting for logicians, physicists and philosophers of science.
The Many Worlds Interpretation of Quantum Mechanics has been faced since its conception with the problem of how to reconcile the probabilistic nature of quantum theory with a deterministic description of the Universe in which all possibilities are actualised. This paper seeks to present the status of the problem through the solutions proposed by Lev Vaidman and David Deutsch and to relate them, as well as to present probability as an epistemological postulate, in accordance with the subjectivistic interpretation.
Many world interpretations (MWIs) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MIs) which state that quantum mechanics does not provide an account of what “actually is the case,” but rather deals with what “might be the case,” i.e., with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why—even though both interpretations share the same formal structure—MI fall pray of Kochen–Specker-type contradictions while MWI escape them.
The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.