11,909 research outputs found
Quantum Entanglement in Concept Combinations
Research in the application of quantum structures to cognitive science
confirms that these structures quite systematically appear in the dynamics of
concepts and their combinations and quantum-based models faithfully represent
experimental data of situations where classical approaches are problematical.
In this paper, we analyze the data we collected in an experiment on a specific
conceptual combination, showing that Bell's inequalities are violated in the
experiment. We present a new refined entanglement scheme to model these data
within standard quantum theory rules, where 'entangled measurements and
entangled evolutions' occur, in addition to the expected 'entangled states',
and present a full quantum representation in complex Hilbert space of the data.
This stronger form of entanglement in measurements and evolutions might have
relevant applications in the foundations of quantum theory, as well as in the
interpretation of nonlocality tests. It could indeed explain some
non-negligible 'anomalies' identified in EPR-Bell experiments.Comment: 16 pages, no figure
Kochen-Specker theorem studied with neutron interferometer
The Kochen-Specker theorem theoretically shows evidence of the
incompatibility of noncontextual hidden variable theories with quantum
mechanics. Quantum contextuality is a more general concept than quantum
non-locality which is quite well tested in experiments by using Bell
inequalities. Within neutron interferometry we performed an experimental test
of the Kochen-Specker theorem with an inequality, which identifies quantum
contextuality, by using spin-path entanglement in a single neutron system. Here
entanglement is achieved not between different particles, but between degrees
of freedom, i.e., between spin and path degree of freedom. Appropriate
combinations of the spin analysis and the position of the phase shifter allow
an experimental verification of the violation of an inequality of the
Kochen-Specker theorem. The observed value of (2.291 +/- 0.008), which is above
the threshold of 1, clearly shows that quantum mechanical predictions cannot be
reproduced by noncontextual hidden variable theories.Comment: 5 pages, 3 figure
Quantum Structure in Cognition: Why and How Concepts are Entangled
One of us has recently elaborated a theory for modelling concepts that uses
the state context property (SCoP) formalism, i.e. a generalization of the
quantum formalism. This formalism incorporates context into the mathematical
structure used to represent a concept, and thereby models how context
influences the typicality of a single exemplar and the applicability of a
single property of a concept, which provides a solution of the 'Pet-Fish
problem' and other difficulties occurring in concept theory. Then, a quantum
model has been worked out which reproduces the membership weights of several
exemplars of concepts and their combinations. We show in this paper that a
further relevant effect appears in a natural way whenever two or more concepts
combine, namely, 'entanglement'. The presence of entanglement is explicitly
revealed by considering a specific example with two concepts, constructing some
Bell's inequalities for this example, testing them in a real experiment with
test subjects, and finally proving that Bell's inequalities are violated in
this case. We show that the intrinsic and unavoidable character of entanglement
can be explained in terms of the weights of the exemplars of the combined
concept with respect to the weights of the exemplars of the component concepts.Comment: 10 page
Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought
We analyze different aspects of our quantum modeling approach of human
concepts, and more specifically focus on the quantum effects of contextuality,
interference, entanglement and emergence, illustrating how each of them makes
its appearance in specific situations of the dynamics of human concepts and
their combinations. We point out the relation of our approach, which is based
on an ontology of a concept as an entity in a state changing under influence of
a context, with the main traditional concept theories, i.e. prototype theory,
exemplar theory and theory theory. We ponder about the question why quantum
theory performs so well in its modeling of human concepts, and shed light on
this question by analyzing the role of complex amplitudes, showing how they
allow to describe interference in the statistics of measurement outcomes, while
in the traditional theories statistics of outcomes originates in classical
probability weights, without the possibility of interference. The relevance of
complex numbers, the appearance of entanglement, and the role of Fock space in
explaining contextual emergence, all as unique features of the quantum
modeling, are explicitly revealed in this paper by analyzing human concepts and
their dynamics.Comment: 31 pages, 5 figure
Quantum Structure in Cognition, Origins, Developments, Successes and Expectations
We provide an overview of the results we have attained in the last decade on
the identification of quantum structures in cognition and, more specifically,
in the formalization and representation of natural concepts. We firstly discuss
the quantum foundational reasons that led us to investigate the mechanisms of
formation and combination of concepts in human reasoning, starting from the
empirically observed deviations from classical logical and probabilistic
structures. We then develop our quantum-theoretic perspective in Fock space
which allows successful modeling of various sets of cognitive experiments
collected by different scientists, including ourselves. In addition, we
formulate a unified explanatory hypothesis for the presence of quantum
structures in cognitive processes, and discuss our recent discovery of further
quantum aspects in concept combinations, namely, 'entanglement' and
'indistinguishability'. We finally illustrate perspectives for future research.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1412.870
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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