Abstract
It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.
Highlights
The General Theory of Relativity and Quantum Mechanics (in the present essay “Quantum Mechanics” refers to the standard formulation of quantum theory) (QM), the pillars of contemporary physics, are our most accurate answers to the questions concerning the inherent nature of spacetime and matter, respectively, changing the conception of the world provided by classical gravitational theories and Classical Mechanics (CM)
It is not my intention to claim that Quantum Logic (QL) is not needed to account for the physical content of standard non-relativistic QM, but rather, I will challenge that a new quantum logic is indispensable in order to model the propositions in the context of every conceivable quantum theory
We asked whether quantum physics necessarily implies a revision of the classical propositional calculus, or if it possible to restore a classical logical picture in the quantum domain
Summary
The General Theory of Relativity and Quantum Mechanics (in the present essay “Quantum Mechanics” refers to the standard (or textbook) formulation of quantum theory) (QM), the pillars of contemporary physics, are our most accurate answers to the questions concerning the inherent nature of spacetime and matter, respectively, changing the conception of the world provided by classical gravitational theories and Classical Mechanics (CM). The algebraic structure underlying classical mechanics is Boolean as well, being commutative, distributive, and associative; in this context, the logical operations of conjunction, disjunction, and negation are replaced respectively by multiplication, addition, and complementation among the variables of the theory This fact has an interesting physical significance, since the variables associated with the magnitudes of physical systems can be added and multiplied together—i.e., one can sum and multiply measurement results. It is not my intention to claim that QL is not needed (or it is useless) to account for the physical content of standard non-relativistic QM, but rather, I will challenge that a new quantum logic is indispensable in order to model the propositions in the context of every conceivable quantum theory In this paper, it will be shown, that taking into account BM, a theory implementing an ontology of particles in motion in three-dimensional physical space, it is possible to restore a classical interpretation of the logical connectives.
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