6 research outputs found
Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities
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.Comment: 1 figur
Entanglement of Conceptual Entities in Quantum Model Theory (QMod)
We have recently elaborated 'Quantum Model Theory' (QMod) to model situations
where the quantum effects of contextuality, interference, superposition,
entanglement and emergence, appear without the entities giving rise to these
situations having necessarily to be of microscopic nature. We have shown that
QMod models without introducing linearity for the set of the states. In this
paper we prove that QMod, although not using linearity for the state space,
provides a method of identification for entangled states and an intuitive
explanation for their occurrence. We illustrate this method for entanglement
identification with concrete examples
The Unreasonable Success of Quantum Probability I: Quantum Measurements as Uniform Fluctuations
We introduce a 'uniform tension-reduction' (UTR) model, which allows to
represent the probabilities associated with an arbitrary measurement situation
and use it to explain the emergence of quantum probabilities (the Born rule) as
'uniform' fluctuations on this measurement situation. The model exploits the
geometry of simplexes to represent the states, in a way that the measurement
probabilities can be derived as the 'Lebesgue measure' of suitably defined
convex subregions of the simplexes. We consider a very simple and evocative
physical realization of the abstract model, using a material point particle
which is acted upon by elastic membranes, which by breaking and collapsing
produce the different possible outcomes. This easy to visualize mechanical
realization allows one to gain considerable insight into the possible hidden
structure of an arbitrary measurement process. We also show that the UTR-model
can be further generalized into a 'general tension-reduction' (GTR) model,
describing conditions of lack of knowledge generated by 'non-uniform'
fluctuations. In this ampler framework, particularly suitable to describe
experiments in cognitive science, we define and motivate a notion of 'universal
measurement', describing the most general possible condition of lack of
knowledge in a measurement, emphasizing that the uniform fluctuations
characterizing quantum measurements can also be understood as an average over
all possible forms of non-uniform fluctuations which can be actualized in a
measurement context. This means that the Born rule of quantum mechanics can be
understood as a first order approximation of a more general non-uniform theory,
thus explaining part of the great success of quantum probability in the
description of different domains of reality. This is the first part of a
two-part article.Comment: 50 pages, 10 figure