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

TL;DR

Quantum Model Theory (QMod) offers a generalized framework for modeling quantum effects like entanglement and interference, applicable to various entities beyond standard quantum mechanics, including concepts and macroscopic systems.

Contribution

QMod introduces a more general, locally applied quantum calculus framework that models quantum effects without requiring linearity of states, extending quantum mechanics to broader contexts.

Findings

QMod can model entities exhibiting quantum effects in diverse fields.

The theory is supported by a representation theorem.

Applications demonstrated in concept theory and macroscopic physics.

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.