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- Aerts, D. (Ed.) (1999).
Einstein meets Magritte: An Interdisciplinary Reflection about Science, Nature, Art, Human Action and Society. Dordrecht: Kluwer Academic, series of eight volumes.- Aerts, D. (1999). Foundations of quantum physics: a general realistic and operational approach.
International Journal of Theoretical Physics,38,pp. 289-358. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0105109.

Abstract:We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it 'changes' under the influence of the rest of the universe. Therefore we base our formalism on the following basic notions: (1) the states of the entity; they describe the modes of being of the entity, (2) the experiments that can be performed on the entity; they describe how we act upon and collect knowledge about the entity, (3) the probabilities; they describe our repeated experiments and the statistics of these repeated experiments, (4) the symmetries; they describe the interactions of the entity with the external world without being experimented upon. Starting from these basic notions we formulate the necessary derived notions: mixed states, mixed experiments and events, an eigen closure structure describing the properties of the entity, an orthoclosure structure introducing an orthocomplementation, outcome determination, experiment determination, state determination and atomicity giving rise to some of the topological separation axioms for the closures. We define the notion of subentity in a general way and identify the morphisms of our structure. We study specific examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity described by the standard quantum mechanical formalism. We present a possible solution to the problem of the description of sub entities within the standard quantum mechanical procedure using the tensor product of the Hilbert spaces, by introducing a new completed quantum mechanics in Hilbert space, were new 'pure' states are introduced, not represented by rays of the Hilbert space.- Aerts, D. (1999). The general introduction of Einstein meets Magritte, an introduction to the series. In D. Aerts, D., J. Broekaert, and E. Mathijs (Eds.),
Einstein meets Magritte: An Interdisciplinary Reflection(pp. vii-xiii). Dordrecht: Kluwer Academic.- Aerts, D. (1999). The scholar, Terpsichore and the barfly. In D. Aerts, J. Broekaert and E. Mathijs (Eds.),
Einstein meets Magritte: An Interdisciplinary Reflection(pp. 1-11). Dordrecht: Kluwer Academic.- Aerts, D. (1999). The stuff the world is made of: physics and reality. In D. Aerts, J. Broekaert and E. Mathijs (Eds.),
Einstein meets Magritte: An Interdisciplinary Reflection(pp. 129-183). Dordrecht: Kluwer Academic. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0107044.

Abstract:Taking into account the results that we have been obtained during the last decade in the foundations of quantum mechanic we put forward a view on reality that we call the 'creation discovery view'. In this view it is made explicit that a measurement is an act of a macroscopic physical entity on a microphysical entity that entails the creation of new elements of reality as well as the detection of existing elements of reality. Within this view most of the quantum mechanical paradoxes are due to structural shortcomings of the standard quantum theory, which means that our analysis agrees with the claim made in the Einstein Podolsky Rosen paper, namely that standards quantum mechanics is an incomplete theory. This incompleteness is however not due to the absence of hidden variables but to the impossibility for standard quantum mechanics to describe separated quantum entities. Nonlocality appears as a genuine property of nature in our view and makes it necessary to reconsider the role of space in reality. Our proposal for a new interpretation for space makes it possible to put forward an new hypothesis for why it has not been possible to unify quantum mechanics and relativity theory.- Aerts, D. (1999). Participating in the world: research and education in a changing society. In D. Aerts, S. Gutwirth, S. Smets and L. Van Langenhove (Eds.),
Science, Technology and Social Change(pp. 1-34). Dordrecht: Kluwer Academic.- Aerts, D. (1999). The game of the biomousa: a view of discovery and creation. In D. Aerts, H. Van Belle and J. Van der Veken (Eds.),
Worldviews and the Problem of Synthesis(pp. 95-125). Dordecht: Kluwer Academic.- Aerts, D. (1999). From freedom to freedom of movement. In D. Aerts, J. Broekaert and W. Wijns (Eds.),
A World in Transition, Humankind and Nature(pp. 43-82). Dordecht: Kluwer Academic.- Aerts, D. (1999). Quantum mechanics: structures, axioms and paradoxes. In D. Aerts and J. Pykacz (Eds.),
Quantum Mechanics and the Nature of Reality(pp. 141-205). Dordrecht: Kluwer Academic. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0106132.

Abstract:We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of 'quantum structures research'. We concentrate mostly on the results of our group FUND at Brussels Free University. By means of a spin 1/2 model where the quantum probability is generated by the presence of fluctuations on the interactions between measuring apparatus and physical system, we show that the quantum structure can find its origin in the presence of these fluctuations. This appraoch, that we have called the 'hidden measurement approach', makes it possible to construct systems that are in between quantum and classical. We show that two of the traditional axioms of quantum axiomatics are not satisfied for these 'in between quantum and classical' situations, and how this structural shortcoming of standard quantum mechanics is at the origin of most of the quantum paradoxes. We show that in this approach the EPR paradox identifies a genuine incompleteness of standard quantum mechanics, however not an incompleteness that means the lacking of hidden variables, but an incompleteness pointing at the impossibility for standard quantum mechanics to describe separated quantum systems. We indicate in which way, by redefining the meaning of density states, standard quantum mechanics can be completed. We put forward in which way the axiomatic approach to quantum mechanics can be compared to the traditional axiomatic approach to relativity theory, and how this might lead to studying another road to unification of both theories.- Aerts, D. (1999). Creativity and science.
Foundations of Science,4,pp. 111-112.- Aerts, D., Aerts, S., Durt, T. and Leveque, O. (1999). Classical and quantum probability in the epsilon model.
International Journal of Theoretical Physics,38,pp. 407-429.- Aerts, D., Broekaert, J. and Gabora, L. (1999). Formal and informal representations of science.
Foundations of Science,4,1-2.- Aerts, D., Broekaert, J. and Gabora, L. (1999). Nonclassical contextuality in cognition: Borrowing from quantum mechanical approaches to indeterminism and observer dependence. In R. Campbell (Ed.), Dialogues in Psychology,
10, Proceedings of 'Mind IV', Dublin.- Aerts, D., Broekaert, J. and Mathijs, E. (Eds.) (1999).
Einstein meets Magritte: An Interdisciplinary Reflection. Dordrecht: Kluwer Academic.- Aerts, D., Broekaert, J. and Mathijs, E. (1999). Somewhere over the rainbow, an introduction to the book. In D. Aerts, J. Broekaert and E. Mathijs (Eds.),
Einstein meets Magritte: An Interdisciplinary Reflection(pp. xv-xix). Dordrecht: Kluwer Academic.- Aerts, D., Broekaert, J. and Smets, S. (1999). The liar paradox in a quantum mechanical perspective.
Foundations of Science,4,pp. 115-132. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0007047.

Abstract:We propose a method to model the truth behaviour of cognitive entities taking into account the possible influence of the cognitive person on the truth behaviour of the entity. Hereby we specifically apply the mathematical formalism of quantum mechanics because of the fact that this formalism allows the description of real contextual influences, i.e. the influence of the measuring apparatus on the physical entity. We concentrated on the typical situation of the liar paradox and have shown that (1) the truth-false state of this liar paradox can be represented by a quantum vector in a finite dimensional complex Hilbert space and the different interpretative interactions by the actions of the corresponding quantum projections, (2) the typical oscillations between false and truth - the paradox - is now quantum dynamically described by a Schrodinger equation. We analyse possible philosophical implications of this result.- Aerts, D., Broekaert, J., Smets, S. (1999). A quantum structure description of the liar paradox.
International Journal of Theoretical Physics,38,pp. 3231-3239. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0106131.

Abstract:In this article we propose an approach that models the truth behavior of cognitive entities (i.e. sets of connected propositions) by taking into account in a very explicit way the possible influence of the cognitive person (the one that interacts with the considered cognitive entity). Hereby we specifically apply the mathematical formalism of quantum mechanics because of the fact that this formalism allows the description of real contextual influences, i.e. the influence of the measuring apparatus on the physical entity. We concentrated on the typical situation of the liar paradox and have shown that (1) the truth-false state of this liar paradox can be represented by a quantum vector of the non-product type in a finite dimensional complex Hilbert space and the different cognitive interactions by the actions of the corresponding quantum projections, (2) the typical oscillations between false and truth - the paradox - is now quantum dynamically described by a Schrodinger equation. We analyse possible philosophical implications of this result.- Aerts, D., Broekaert, J., Weyns, W. (Eds.) (1999).
A World in Transition, Humankind and Nature. Dordrecht: Kluwer Academic.- Aerts, D., Castagnino, M., Durt, T., Gangui, A. and Gunzig, E. (1999). Cosmology and quantum mechanics in Peyresc.
International Journal of Theoretical Physics,38,pp. 3-8.- Aerts, D. and Coecke, B. (1999). The creation-discovery-view: towards a possible explanation of quantum reality. In M. L. Dalla Chiara, R. Giuntini and F. Laudisa (Eds.),
Language, Quantum, Music: Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995. Dordrecht: Kluwer Academic.

Abstract:We present a realistic interpretation for quantum mechanics that we have called the 'creation discovery view' and that is being developed in our group in Brussels. In this view the change of state of a quantum entity during an experiment is taken to be a 'real change' under influence of the experiment, and the quantum probability that corresponds to the experiment is explained as due to a lack of knowledge of a deeper deterministic reality of the measurement process. The technical mathematical theory underlying the creation discovery view that we are elaborating we have called the 'hidden measurement formalism'. We present a simple physical example: the 'quantum machine', where we can illustrate easily how the quantum structure arises as a consequence of the two mentioned effects, a real change of the state, and a lack of knowledge about a deeper reality of the measurement process. We analyze non-locality in the light of the creation discovery view, and show that we can understand it if we accept that also the basic concept of 'space' is partly due to a creation: when a detection of a quantum entity in a non-local state occurs, the physical act of detection itself 'creates' partly the 'place' of the quantum entity. In this way the creation discovery view introduces a new ontology for space: space is not the all embracing theater, where all 'real' objects have their place, but it is the structure that governs a special type of relations (the space-like relations) between macroscopic physical entities. We bring forward a number of elements that show the plausibility of the approach and also analyze the way in which the presence of Bell-type correlated events can be incorporated.- Aerts, D., Coecke, B and Smets, S (1999). On the origin of probabilities in quantum mechanics: creative and contextual aspects. In G. Cornelis, S. Smets and J. P. Van Bendegem (Eds.),
Metadebates on Science(pp. 291-302). Dordrecht: Kluwer Academic.- Aerts, D., Colebunders, E., Van der Voorde, A. and Van Steirteghem, B. (1999). State property systems and closure spaces: a study of categorical equivalence.
International Journal of Theoretical Physics,38,pp. 359-385. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0105108.

Abstract:We show that the natural mathematical structure to describe a physical entity by means of its states and its properties within the Geneva-Brussels approach is that of a state property system. We prove that the category of state property systems (and morphisms), SP, is equivalent to the category of closure spaces (and continuous maps), Cls. We show the equivalence of the 'state determination axiom' for state property systems with the 'T0 separation axiom' for closure spaces. We also prove that the category SP0 of state determined state property systems is equivalent to the category L0 of based complete lattices. In this sense the equivalence of SP and Cls generalizes the equivalence of Cls0 (T0 closure spaces) and L0, proven in (Erne 1984).- Aerts, D., Gutwirth, S., Smets, S. and Van Langehove, L. (Eds.) (1999).
Science, Technology and Social Change. Dordrecht: Kluwer Academic.- Aerts, D., Mathijs, E. and Mosselmans, B. (Eds.) (1999).
Science and Art. Dordrecht: Kluwer Academic.- Aerts, D., Pykacz, J., (Eds.) (1999).
Quantum Structures and the Nature of Reality.Dordrecht: Kluwer Academic.- Aerts, D. and Pykacz, J. (1999). Quantum structures and the nature of reality, an introduction to the book. In D. Aerts and J. Pykacz,
Quantum Structures and the Nature of Reality(pp. xv-xviii). Dordrecht: Kluwer Academic.- Aerts, D., Van Belle, H. and Van der Veken, J. (Eds.) (1999).
Worldviews and the Problem of Synthesis. Dordrecht: Kluwer Academic.

1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990,

1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,