International Journal of Theoretical Physics

, Volume 58, Issue 12, pp 4208–4234 | Cite as

Category-Theoretic Interpretative Framework of the Complementarity Principle in Quantum Mechanics

  • Elias ZafirisEmail author
  • Vassilios Karakostas


This study aims to provide an analysis of the complementarity principle in quantum theory through the establishment of partial structural congruence relations between the quantum and Boolean kinds of event structure. Specifically, on the basis of the existence of a categorical adjunction between the category of quantum event algebras and the category of presheaves of variable Boolean event algebras, we establish a twofold complementarity scheme consisting of a generalized/global and a restricted/local conceptual dimension, where the latter conception is subordinate to and constrained by the former. In this respect, complementarity is not only understood as a relation between mutually exclusive experimental arrangements or contexts of comeasurable observables, as envisaged by the original conception, but it is primarily comprehended as a reciprocal relation concerning information transfer between two hierarchically different structural kinds of event structure that can be brought into partial congruence by means of the established adjunction. It is further argued that the proposed category-theoretic framework of complementarity naturally advances a contextual realist conceptual stance towards our deeper understanding of the microphysical nature of reality.


Quantum event structures Complementarity Adjoint functors Kochen-Specker theorem Boolean frames Local-global relation Realist account 



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Authors and Affiliations

  1. 1.Parmenides FoundationCenter for the Conceptual Foundations of ScienceMunichGermany
  2. 2.Department of MathematicsUniversity of AthensAthensGreece
  3. 3.Department of Philosophy and History of Science, Faculty of ScienceUniversity of AthensAthensGreece

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