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A Bridge Between Q-Worlds

Eva, Benjamin and Ozawa, Masanao and Doering, Andreas (2018) A Bridge Between Q-Worlds. [Preprint]

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Abstract

Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches attempt to resolve some of the conceptual difficulties surrounding quantum mechanics by reformulating parts of the theory inside of non-classical mathematical universes, albeit with very different internal logics. We call such mathematical universes, together with those mathematical and logical structures within them that are pertinent to the physical interpretation, `Q-worlds'. Here, we provide a unifying framework that allows us to (i) better understand the relationship between different Q-worlds, and (ii) define a general method for transferring concepts and results between TQT and QST, thereby significantly increasing the expressive power of both approaches. Along the way, we develop a novel connection to paraconsistent logic and introduce a new class of structures that have significant implications for recent work on paraconsistent set theory.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Eva, Benjaminbenedgareva@icloud.com
Ozawa, Masanaoozawa@is.nagoya-u.ac.jp
Doering, Andreasandreas.doering@posteo.de
Keywords: Quantum Logic, Topos Theory, Paraconsistent Set Theory
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Dr Benjamin Eva
Date Deposited: 13 Dec 2018 18:13
Last Modified: 13 Dec 2018 18:13
Item ID: 15427
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Physics > Quantum Mechanics
Date: 10 December 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15427

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