Krause, Decio and Arenhart, Jonas R. B. (2015) A logical account of superpositions. [Preprint]

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Abstract

In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this schema the claim that superpositions may involve contradictions, as in the case of the Schrödinger's cat, which (it is usually said) is both alive and dead. We argue that this claim is a misreading of the quantum case. Finally, we sketch a new form of quantum logic that involves three kinds of negations and present the relationships among them. The paper is a first approach to the subject, introducing some main guidelines to be developed by a `syntactical' logical approach to quantum superpositions.

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Item Type:	Preprint
Creators:	Creators Email ORCID Krause, Decio deciokrause@gmail.com Arenhart, Jonas R. B. jonas.becker2@gmail.com
Keywords:	Superpositions, quantum logic, modal logic, Schrödinger's cat, contradictions, collapse, quantum deduction.
Subjects:	Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories
Depositing User:	Prof. Décio Krause
Date Deposited:	16 Apr 2015 20:30
Last Modified:	16 Apr 2015 20:30
Item ID:	11422
Subjects:	Specific Sciences > Physics > Quantum Mechanics General Issues > Structure of Theories
Date:	14 April 2015
URI:	https://philsci-archive.pitt.edu/id/eprint/11422

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