Sven Aerts

Applications of quantum statistics in psychological studies of decision processes

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us caapble of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach.

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.

Experimental Evidence for Quantum Structure in Cognition

We prove a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments from [26] to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights, as for example in [17] , can accomplish what classical membership weights cannot do.

A Model with Varying Fluctuations in the Measurement Context

In the “hidden measurement formalism,” we try to explain the emergence of the quantum probabilities from the presence of fluctuations in the measurement context. We use a model that was constructed by Aerts et al. as a metaphorical model to extend these ideas.

Two-Photon Franson-Type Experiments and Local Realism

The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a “Bell test of local realism.” However, it has been suggested that this i ...

Towards a General Operational and Realistic Framework for Quantum Mechanics and Relativity Theory

We propose a general operational and realistic framework that aims at a generalization of quantum mechanics and relativity theory, such that both appear as special cases of this new theory. Our framework is operational, in the sense that all aspects are introduced with specific reference to events to be experienced, and realistic, in the sense that the hypothesis of an independent existing reality is taken seriously. To come to this framework we present a detailed study of standard quantum mechanics within the axiomatic approach to quantum mechanics, more specifically the Geneva-Brussels approach, identifying two of the traditional 6 axioms as ‘failing axioms’. We prove that these two failing axioms are at the origin of the impossibility for standard quantum mechanics to describe a continuous change from quantum to classical and hence its inability to describe macroscopic physical reality. Moreover we show that the same two axioms are also at the origin of the impossibility for standard quantum mechanics to deliver a model for the compound entity of two ‘separated’ quantum entities. We put forward that it is necessary to replace these two axioms in order to proceed to the more general theory. Next we analyze the nature of the quantum probability model and show that it can be interpreted as the consequence of the presence of a lack of knowledge on the interaction between the measurement apparatus and the physical entity under consideration. These two insights, the failing axioms and the nature of quantum probability, give rise to a very specific view on the quantum phenomenon of nonlocality. Nonlocality should be interpreted as nonspatiality. This means that an entity in a nonlocal state, like for example the typical EPR state, is ‘not inside space’. As a consequence, space is no longer the all embracing theatre of reality, but a structure that has emerged together with the macroscopic material entities that have emerged from the microworld. This clarifies why general relativity theory cannot be used as a basis for the elaboration of the new generalized theory, since in general relativity theory the set of events is taken a priori to be the time-space continuum. Hence in general relativity theory time-space is a basic structure considered to capture all of reality. In our framework we introduce ‘happenings’ and the ‘set of happenings’ as constituting reality. A happening is however not identified with a point of time-space, as this is the case for an events of general relativity theory. We analyze different aspects of the new framework, and list the most important problems to be investigated for an elaboration of this framework into a workable and as complete as possible

The Hidden-Measurement Formalism: Quantum Mechanics as a Consequence of Fluctuations on the Measurement

We expose a formalism, that we have called the’ hidden measurement formalism’, where the quantum structure is due to the presence of ‘fluctuations’ on the interaction between the system and the measurement apparatus. In this formalism the quantum mechanical probabilities are not ontological but arrise as a consequence of ‘lack of knowledge’ about this interaction. We study the quantum classical limit and the EPR problem in the light of this explanation.

CLASSICAL AND QUANTUM PROBABILITY IN THE -MODEL

We describe the probabilistic study of a hiddenvariable model in which the origin of the quantumprobability is due to fluctuations of the internal stateof the measuring apparatus. By varying the intensity of these fluctuations from zero to a maximalvalue, we describe in a heuristic manner the transitionfrom classical behavior to quantum behavior. Wecharacterize this transition in terms of theAccardi–Fedullo inequalities. This is a review article in whichwe gather our recent contributions to the subject, mostof which have not been published in articleform.

Similarity metrics within a point of view

Vector space based approaches to natural language processing are contrasted with human similarity judgements to show the manner in which human subjects fail to produce data which satisfies all requirements for a metric space. This result would constrains the validity and applicability vector space based (and hence also quantum inspired) approaches to the modelling of cognitive processes. This paper proposes a resolution to this problem, by arguing that pairs of words imply a context which in turn induces a point of view, so allowing a subject to estimate semantic similarity. Context is here introduced as a point of view vector (POVV) and the expected similarity is derived as a measure over the POVVs. Different pairs of words will invoke different contexts and different POVVs. We illustrate the proposal on a few triples of words and outline further research.

Interactive Probability Models: Inverse Problems on the Sphere

We expose a class of probabilistic models withonly two outcomes that we call interactive probabilitymodels for the analysis of data that arise in situationswhere there is influence of the measurer on the measured. We reconstruct a Borel measurecorresponding to possible sets of probabilities that arerelated to outcomes of experiments. We give threeexamples: one that corresponds to the quantum mechanical case, one to a deterministic measurement, andone to a situation where the outcome of the measurementis determined by the measurement apparatusonly.