Jan Broekaert

The Violation of Bell Inequalities in the Macroworld

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohms example of two entangled spin 1/2 quantum particles. We show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation.

A Quantum Structure Description of the Liar Paradox

In this article we propose an approach thatmodels the truth behavior of cognitive entities (i.e.,sets of connected propositions) by taking into accountin a very explicit way the possible influence of the cognitive person (the one that interactswith the considered cognitive entity). Hereby wespecifically apply the mathematical formalism of quantummechanics because of the fact that this formalism allows the description of real contextual influences,i.e., the influence of the measuring apparatus on thephysical entity. We concentrated on the typicalsituation of the liar paradox and have shown that (1) the true-false state of this liar paradox canbe represented by a quantum vector of the nonproducttype in a finite-dimensional complex Hilbert space andthe different cognitive interactions by the actions of the corresponding quantum projections, (2)the typical oscillations between false and true —the paradox — is now quantum dynamically describedby a Schrodinger equation. We analyze possiblephilosophical implications of this result.

The Liar-paradox in a Quantum Mechanical Perspective

In this paper we concentrate on the nature of the liar paradox asa cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model (Aerts, Broekaert and Smets, 1999) that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.

Contextual Random Boolean Networks

We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [1] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global properties of the same networks, namely the average number of attractors and the average percentage of states in attractors. We introduce the situation where we lack knowledge on the context as a more realistic model for contextual dynamical systems. We notice that this makes the network non-deterministic in a specific way, namely introducing a non-Kolmogorovian quantum-like structure for the modelling of the network [2]. In this case, for example, a state of the network has the potentiality (probability) of collapsing into different attractors, depending on the specific form of lack of knowledge on the context.

The guppy effect as interference

People use conjunctions and disjunctions of concepts in ways that violate the rules of classical logic, such as the law of compositionality. Specifically, they overextend conjunctions of concepts, a phenomenon referred to as the Guppy Effect. We build on previous efforts to develop a quantum model [1,2,3], that explains the Guppy Effect in terms of interference. Using a well-studied data set with 16 exemplars that exhibit the Guppy Effect, we developed a 17-dimensional complex Hilbert space

A spatially-VSL gravity model with 1-PN limit of GRT

{\cal H}

The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (spinless case)

that models the data and demonstrates the relationship between overextension and interference. We view the interference effect as, not a logical fallacy on the conjunction, but a signal that out of the two constituent concepts, a new concept has emerged.

The two-body plus potential problem between quantum field theory and relativistic quantum mechanics (two-fermion and fermion-boson cases)

In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré’s Principle of Relativity, i.e. the unobservability of ‘preferred’ frame movement. Poincaré’s principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the ‘vector potential’ ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, [1972]), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test particles. In conclusion the model’s merits in terms of a simpler space, time and gravitation ontology—in terms of a Lorentz-Poincaré-type interpretation—are explained (e.g. for ‘frame dragging’, ‘harmonic coordinate condition’).

Quantum structure in competing lizard communities

SummaryStarting with a pair of integrodifferential Bethe-Salpeter equations for two spinless particles interacting mutually and with an external static potential, we obtain a pair of compatible and separable coupled Klein-Gordon equations, between which the unwanted relative time variable can be easily eliminated. The method we use is a generalization of that proposed by Sazdijan for the two-particle problem, and the resulting equations are a generalization of the well-known Droz-Vincent-Todorov-Komar equations of relativistic quantum mechanics. We examine the instantaneous approximation and we test our methods in a simple case (Bethe-Salpeter kernel given by a single scalar particle exchange graph).

The generalised liar paradox: A quantum model and interpretation

SummaryStarting with a pair of integrodifferential Bethe-Salpeter equations for two fermions interacting mutually and with an external static potential, we obtain a pair of compatible and separable coupled Dirac equations, between which the unwanted relative time variable can be easily eliminated. We use two different adaptations of the method proposed by Sazdjian for the two-particle (without external potential) problem, leading to two different (although equivalent) systems of coupled Dirac equations. We examine the instantaneous approximation and we test our methods in the helium atom problem. The last section is devoted to the fermion-boson plus external potential problem.