Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities

  • Diederik Aerts
  • Sandro Sozzo
Conference paper

DOI: 10.1007/978-3-642-35659-9_12

Volume 7620 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Aerts D., Sozzo S. (2012) Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities. In: Busemeyer J.R., Dubois F., Lambert-Mogiliansky A., Melucci M. (eds) Quantum Interaction. QI 2012. Lecture Notes in Computer Science, vol 7620. Springer, Berlin, Heidelberg

Abstract

In this paper we present Quantum Model Theory (QMod), a theory we developed to model entities that entail the typical quantum effects of contextuality, superposition, interference, entanglement and emergence. The aim of QMod is to put forward a theoretical framework that is more general than standard quantum mechanics, in the sense that, for its complex version it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement, and for its real version it does not need the property of ‘linearity of the set of states’ to model the quantum effect. In this sense, QMod is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity. We prove by means of a representation theorem that QMod can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic physics are also considered.

Keywords

Quantum modeling contextuality interference QMod 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Sandro Sozzo
    • 1
  1. 1.Center Leo Apostel (CLEA)Vrije Universiteit Brussel (VUB)BrusselsBelgium