6,139 research outputs found
On the Foundations of the Brussels Operational-Realistic Approach to Cognition
The scientific community is becoming more and more interested in the research
that applies the mathematical formalism of quantum theory to model human
decision-making. In this paper, we provide the theoretical foundations of the
quantum approach to cognition that we developed in Brussels. These foundations
rest on the results of two decade studies on the axiomatic and
operational-realistic approaches to the foundations of quantum physics. The
deep analogies between the foundations of physics and cognition lead us to
investigate the validity of quantum theory as a general and unitary framework
for cognitive processes, and the empirical success of the Hilbert space models
derived by such investigation provides a strong theoretical confirmation of
this validity. However, two situations in the cognitive realm, 'question order
effects' and 'response replicability', indicate that even the Hilbert space
framework could be insufficient to reproduce the collected data. This does not
mean that the mentioned operational-realistic approach would be incorrect, but
simply that a larger class of measurements would be in force in human
cognition, so that an extended quantum formalism may be needed to deal with all
of them. As we will explain, the recently derived 'extended Bloch
representation' of quantum theory (and the associated 'general
tension-reduction' model) precisely provides such extended formalism, while
remaining within the same unitary interpretative framework.Comment: 21 page
Quantum Theory and Human Perception of the Macro-World
We investigate the question of 'why customary macroscopic entities appear to
us humans as they do, i.e. as bounded entities occupying space and persisting
through time', starting from our knowledge of quantum theory, how it affects
the behavior of such customary macroscopic entities, and how it influences our
perception of them. For this purpose, we approach the question from three
perspectives. Firstly, we look at the situation from the standard quantum
angle, more specifically the de Broglie wavelength analysis of the behavior of
macroscopic entities, indicate how a problem with spin and identity arises, and
illustrate how both play a fundamental role in well-established experimental
quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly,
we analyze how the question is influenced by our result in axiomatic quantum
theory, which proves that standard quantum theory is structurally incapable of
describing separated entities. Thirdly, we put forward our new 'conceptual
quantum interpretation', including a highly detailed reformulation of the
question to confront the new insights and views that arise with the foregoing
analysis. At the end of the final section, a nuanced answer is given that can
be summarized as follows. The specific and very classical perception of human
seeing -- light as a geometric theory -- and human touching -- only ruled by
Pauli's exclusion principle -- plays a role in our perception of macroscopic
entities as ontologically stable entities in space. To ascertain quantum
behavior in such macroscopic entities, we will need measuring apparatuses
capable of its detection. Future experimental research will have to show if
sharp quantum effects -- as they occur in smaller entities -- appear to be
ontological aspects of customary macroscopic entities.Comment: 28 page
Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach
We show that the Brussels operational-realistic approach to quantum physics
and quantum cognition offers a fundamental strategy for modeling the meaning
associated with collections of documental entities. To do so, we take the World
Wide Web as a paradigmatic example and emphasize the importance of
distinguishing the Web, made of printed documents, from a more abstract meaning
entity, which we call the Quantum Web, or QWeb, where the former is considered
to be the collection of traces that can be left by the latter, in specific
measurements, similarly to how a non-spatial quantum entity, like an electron,
can leave localized traces of impact on a detection screen. The double-slit
experiment is extensively used to illustrate the rationale of the modeling,
which is guided by how physicists constructed quantum theory to describe the
behavior of the microscopic entities. We also emphasize that the superposition
principle and the associated interference effects are not sufficient to model
all experimental probabilistic data, like those obtained by counting the
relative number of documents containing certain words and co-occurrences of
words. For this, additional effects, like context effects, must also be taken
into consideration.Comment: 27 pages, 6 figures, Late
A theory of concepts and their combinations I: The structure of the sets of contexts and properties
We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts
Quantum entanglement in physical and cognitive systems: a conceptual analysis and a general representation
We provide a general description of the phenomenon of entanglement in
bipartite systems, as it manifests in micro and macro physical systems, as well
as in human cognitive processes. We do so by observing that when genuine
coincidence measurements are considered, the violation of the 'marginal laws',
in addition to the Bell-CHSH inequality, is also to be expected. The situation
can be described in the quantum formalism by considering the presence of
entanglement not only at the level of the states, but also at the level of the
measurements. However, at the "local'" level of a specific joint measurement, a
description where entanglement is only incorporated in the state remains always
possible, by adopting a fine-tuned tensor product representation. But
contextual tensor product representations should only be considered when there
are good reasons to describe the outcome-states as (non-entangled) product
states. This will not in general be true, hence, the entangement resource will
have to generally be allocated both in the states and in the measurements. In
view of the numerous violations of the marginal laws observed in physics'
laboratories, it remains unclear to date if entanglement in micro-physical
systems is to be understood only as an 'entanglement of the states', or also as
an 'entanglement of the measurements'. But even if measurements would also be
entangled, the corresponding violation of the marginal laws (no-signaling
conditions) would not for this imply that a superluminal communication would be
possible
Quantum Theory and Conceptuality: Matter, Stories, Semantics and Space-Time
We elaborate the new interpretation of quantum theory that we recently
proposed, according to which quantum particles are considered conceptual
entities mediating between pieces of ordinary matter which are considered to
act as memory structures for them. Our aim is to identify what is the
equivalent for the human cognitive realm of what physical space-time is for the
realm of quantum particles and ordinary matter. For this purpose, we identify
the notion of 'story' as the equivalent within the human cognitive realm of
what ordinary matter is in the physical quantum realm, and analyze the role
played by the logical connectives of disjunction and conjunction with respect
to the notion of locality. Similarly to what we have done in earlier
investigations on this new quantum interpretation, we use the specific
cognitive environment of the World-Wide Web to elucidate the comparisons we
make between the human cognitive realm and the physical quantum realm.Comment: 14 page
Interpreting Quantum Particles as Conceptual Entities
We elaborate an interpretation of quantum physics founded on the hypothesis
that quantum particles are conceptual entities playing the role of
communication vehicles between material entities composed of ordinary matter
which function as memory structures for these quantum particles. We show in
which way this new interpretation gives rise to a natural explanation for the
quantum effects of interference and entanglement by analyzing how interference
and entanglement emerge for the case of human concepts. We put forward a scheme
to derive a metric based on similarity as a predecessor for the structure of
'space, time, momentum, energy' and 'quantum particles interacting with
ordinary matter' underlying standard quantum physics, within the new
interpretation, and making use of aspects of traditional quantum axiomatics.
More specifically, we analyze how the effect of non-locality arises as a
consequence of the confrontation of such an emerging metric type of structure
and the remaining presence of the basic conceptual structure on the fundamental
level, with the potential of being revealed in specific situations.Comment: 19 pages, 1 figur
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