Diederik Aerts

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Diederik Aerts (born April 17, 1953) is a Belgian theoretical physicist and a professor at Brussels Free University (Vrije Universiteit Brussel - VUB), where he directs the Center Leo Apostel for Interdisciplinary Studies (CLEA).[1]


Diederik Aerts was born in Heist-op-den-Berg, Belgium, on April 17, 1953. He attended secondary school at 'Koninklijk Atheneum' in Heist-op-den-Berg, in the section Latin-Mathematics. He received his MSc in Mathematical Physics in 1975 from Brussels Free University (Vrije Universiteit Brussel - VUB). For his doctorate he worked at the University of Geneva with Constantin Piron on the Foundations of Quantum Theory, obtaining his PhD in Theoretical Physics in 1981 from VUB with Jean Reignier.

In 1976 he started working as a researcher for the Belgian National Fund for Scientific Research (NFWO), where in 1985 he became a tenured researcher. Since 1995, he has been director of the VUB's Center Leo Apostel for Interdisciplinary Studies (CLEA) and in 2000 he was appointed professor at the VUB. From 1990, he has been a board member of the 'Worldviews group',[2] founded by the late philosopher Leo Apostel. In 1997 he became Editor-in-Chief of the international ISI and Springer journal 'Foundations of Science (FOS)'.[3] He was the scientific and artistic coordinator of the 'Einstein meets Magritte' conference,[4] where some of the world's leading scientists and artists gathered to reflect about science, nature, human action and society.


Diederik Aerts investigated for his PhD work with Constantin Piron the description of compound quantum entities within the realistic and axiomatic approach to quantum physics elaborated in Geneva by the group of quantum physicists headed by Josef-Maria Jauch.

Research in quantum theory[edit]

In the course of this investigation, he proved that two of the traditional axioms of quantum theory - more specifically 'weak modularity' and 'the covering law' - are not satisfied for two 'separated' quantum entities. This result is an axiomatic deepening and exploration of the type of situation that make quantum entities violate Bell's inequalities.[5][6][7] His original quantum axiomatic approach to exploring the way that quantum entities combine enabled Aerts to put forward a thoroughly new analysis of the Einstein–Podolsky–Rosen paradox, identifying explicitly the 'missing elements of reality'. Aerts's analysis is very different from the Einstein–Podolsky–Rosen one, since it arrives at a constructive proof of the incompleteness rather than a proof by reductio ad absurdum as in Einstein–Podolsky–Rosen.

As a consequence the incompleteness identified by Aerts is not due to missing hidden variables, but to the impossibility to model separated quantum entities using quantum theory.[8][9] Elaborating further on this analysis of separated quantum entities, Aerts explored a conceptual view on quantum reality substituting the notion of non locality by that of non spatiality, hence interpreting three-dimensional Euclidean space as a theatre for macroscopical material objects, but 'not' as the space containing all of reality. More concretely, quantum entities are considered to be not inside this three-dimensional space when in non local states.[10]

Macroscopic entities and the hidden-measurements approach[edit]

Another result of the above-mentioned findings was the identification of 'real experimentally realizable macroscopic systems violating Bell's inequalities'.[11][12] Around this time Luigi Accardi, proved that the violation of Bell's inequalities is equivalent to the non-existence of one Kolmogorovian probability model for the considered joint experiments.[13] An intriguing implication of Accardi's findings was that the macroscopic systems violating Bell's inequalities identified by Aerts should entail a non-Kolmogorovian probability structure, possibly even a quantum probability structure, which, at that time, was very much contrary to general belief.

It motivated Aerts to conduct an in-depth investigation, which yielded new concrete macroscopic models based on genuine quantum structure, as well as a new explanation, namely that quantum structure appears as a consequence of the presence of fluctuations on the interaction between the measurement apparatus and the entity under investigation.[14] In this period, several PhD students, including Bruno Van Bogaert, Thomas Durt and Bob Coecke, later Frank Valckenborgh, Bart D'Hooghe and Sven Aerts,[15] started to work with Diederik Aerts, exploring ideas related to several aspects of the above-mentioned findings. The investigation of the presence of quantum structure in macroscopic reality was continued,[16] also identifying entities whose structure was neither quantum nor classical but 'between quantum and classical', by varying the amount of fluctuations between the measurement apparatus and the entity considered.[17][18]

It was proven that the axioms that failed to describe separated quantum entities,[6][7] also failed when modeling the 'between quantum and classical' situations.[19] The 'origin of quantum structure due to fluctuations on the interactions between the measurements and the entity under consideration' was developed into a formulation of quantum mechanics called the hidden measurements approach.[20][21][22][23][24][25]

Interdisciplinary research, worldviews, and foundations of science[edit]

In the 1970s and 1980s, Aerts's focus of research was on the foundations of quantum theory, and the Geneva-Brussels realistic axiomatic and operational approach to quantum theory. In 1990, Leo Apostel founded the Worldviews group[2] and invited Aerts to be one of its members. The aim of the Worldviews group, viz. to construct global views integrating different fragmented parts of knowledge from different scientific disciplines, arose a deep interest in interdisciplinary research, and two books were the results of the monthly gatherings of the group.[26][27] Leo Apostel had founded in 1985 the center of interdisciplinary studies at VUB, but it had been dormant, which was one of the reasons why Leo Apostel created the Worldviews group.

In the early 1990s, the idea grew to try to revive the center, and Apostel asked Aerts to look into it. As a result, in the aftermath of a major international and interdisciplinary conference entitled 'Einstein meets Magritte',[4] in 1995, the Center Leo Apostel was re-founded, with Diederik Aerts as its director. Senior researcher Francis Heylighen, and his PhD student Johan Bollen, as well as Aerts's group of PhD students joined the center. Funding was obtained for new postdocs, Jan Broekaert and Alex Riegler, and for a new PhD student, Ernest Mathijs. At the same time, funding was secured for a FWO-research community entitled 'Research on the Construction of Integrating World Views', which still is one of the center's pillars.[28] Also Aerts's acceptance to become Editor-in-Chief of the journal 'Foundations of Science' was part of the broadening of his research interest and focus to cover a more interdisciplinary realm.[3] The Worldviews group continues gathering on a regular basis and its publications contain the fruits of the discussions during these meetings.[2]

Quantum structure in psychology[edit]

The Geneva-Brussels operational axiomatic approach to quantum theory is founded on very general notions, such as `yes-no experiment', 'property', 'state', 'measurement'. The generality of this approach aided very much in the identification and investigation of quantum structures in the non-microscopic realm.[11][12] The interdisciplinary interest, together with this generality of the Geneva-Brussels quantum theory, made it possible to put forward a modeling of a simple opinion poll and prove that quantum structure was involved in the dynamics of the decision processes of the human participants of the survey.[29] Two new PhD students, Sonja Smets and Liane Gabora, joined the center, and more signatures of the presence of quantum structure in the realm of cognitive science were investigated, a quantum model for the Liar paradox reasoning was elaborated,[30] and the presence of entanglement, i.e. the violation of Bell's inequalities, in the dynamics of concepts was identified.[31]

Investigations on quantum modeling focused on the dynamics of concepts and the role of context,[32] and an approach was worked out, influenced by quantum axiomatics and traditional theories of concept, where concepts are considered as entities in states, changing under the influence of context, making it possible to account for unsolved problems in the domain, such as the guppy effect,[32][33] for which and explicit representation in the complex Hilbert space of quantum theory was elaborated.[34] The identification of quantum probability in the dynamics of an opinion poll,[29] the quantum modeling of the liar paradox reasoning,[30] the identification of quantum entanglement in the dynamics of concepts[31] and the elaboration of a modeling scheme for concepts and their combinations that makes explicit use of the mathematical formalism of quantum theory,[32][33][34] have been pioneering results in the currently active domain of research referred to as quantum cognition.

Quantum cognition[edit]

As a consequence of the research on concepts and the guppy effect, Aerts became intrigued by the results of James Hampton's experiments on membership weights of exemplars with respect to conjunctions and disjunctions of concepts, more specifically the effects that indicated severe deviations from the supposedly underlying classical logic and that Hampton called overextension and underextension.[35][36][37] Aerts (i) proved that these effects could not be accounted for by a classical Kolmogorovian probability structure, and (ii) worked out a quantum modeling in Fock space for Hampton's experimental data, introducing interference and emergence as two quantum effects that did account for the deviations.[38][39][40]

An experiment was devised to provide direct evidence of the presence of entanglement when concepts are combined, and this experiment indeed delivered data violating Bell's inequality.[41] In parallel, and in collaboration with Marek Czachor, Aerts identified interesting connections between the quantum approach to concept modeling and semantic theories in computer science, such as Latent Semantic Analysis, and symbolic artificial intelligence.[42] It was investigated how geometric algebra could serve to model some of the quantum-like aspects and be used for an approach to holographic representations of memory.[43][44][45] The role of quantum structures in economics was investigated, and more specifically a quantum model was worked out for the situation of the Ellsberg paradox in economics accounting for the deviations from classical probability due to ambiguity aversion, and it was analyzed how this quantum model generalizes the classical expected utility hypothesis.[46][47]

The Geneva-Brussels approach[edit]

Parallel to his research on compound quantum entities,[5][6][7] Aerts also investigated aspects of quantum axiomatics per se. He dedicated himself to elaborating the operational realistic foundations of quantum theory started in Geneva by Jauch and Piron, and instigated an intense period of new developments, together with several doctoral students and postdocs at Brussels University, namely Bruno Van Bogaert, Thomas Durt, Bob Coecke, Frank Valckenborgh, Bart D'Hooghe, Sven Aerts, Sonja Smets, Bart Van Steirteghem, Isar Stubbe, Ann Van der Voorde and Didier Deses. As a result, the approach is now commonly referred to as the Geneva-Brussels approach to the foundations of quantum theory.[9][16][17][18][19][21][23][30][48] While earlier presentations of the operational realistic Geneva-Brussels formalism did not succeed in fully determining the mathematical structure underlying the physics-inspired axioms, this problem was definitively solved by the introduction of the mathematical notion of a State Property System.[49][50]

Another issue was the representation of the infinite dimensional irreducible components of a State Property System as the set of closed subspaces of one of three standard Hilbert spaces, real, complex or quaternionic. This was now concluded by introducing a new axiom called 'plane transitivity'.[51] An interesting mathematical result proven was the fact that the category of State Property Systems is categorically equivalent with the category of closure spaces.[50][52] The structure of State Property Systems was generalized to that of State Context Property Systems with the aim of providing a generalized quantum theoretic framework for the modeling of concepts and their dynamics.[33][34][53] The continued difficulty to incorporate the axiom of orthocomplementation operationally into the Geneva-Brussels approach, led to the study of the notion of orthogonality,[54] which yielded other more satisfying operational definitions, including the notion of 'weak modularity'.[55]

New explanatory framework for quantum theory[edit]

Around the turn of the millennium, inspired by the successful use of quantum structures to model aspects of human cognition, and more specifically for the quantum modeling of the dynamics of human concepts in human thought, Aerts started to work on an idea that, if true, would deliver a revolutionary explanatory framework for quantum theory. Although not complicated in itself, the idea has very far-reaching consequences for many aspects of our physical reality. His idea was the following: Quantum particles, as they appear to us by interacting with (macroscopic) measuring apparatuses, are not 'objects' but 'concepts' or 'conceptual entities'. In other words, quantum particles are not strangely behaving particle-like objects but they are conceptual entities or concepts, playing a semantic role in the conceptual interaction taking place between pieces of matter. This means that pieces of matter are the equivalent of memory structures for the conceptual entities that quantum particles are.

Initially, Aerts worked on this idea in silence, but when he found that promising results were obtained, including an explanation of the Heisenberg uncertainty principle within the theory, an understanding of the notion of and role played by identical particles, fermions and bosons, and an explanation of quantum entanglement, again within the theory, he decided to publish these first results of his quantum explanatory framework consisting in considering quantum particles as conceptual entities.[56][57][58]

Music Playing and Composing[edit]

In the magical music year 1968, together with five friends, Diederik Aerts started a rock band called Free Time Production. In 1970, the band won the Jazz Bilzen festival contest and as a reward was offered a one time record contract. Free Time Production stopped being active in the seventies as a consequence of the members going to different universities. Diederik Aerts remained active in music playing and composing and some of his work can be found on SoundCloud.


  1. ^ Diederik Aerts's homepage
  2. ^ a b c Homepage of the Worldview Group
  3. ^ a b Foundations of Science Journal
  4. ^ a b Homepage of the 'Einstein meets Magritte' conference
  5. ^ a b Aerts, D. (1981). The One and the Many: Towards a Unification of the Quantum and Classical Description of One and Many Physical Entities. Doctoral dissertation, Brussels Free University.
  6. ^ a b c Aerts, D. (1982). Description of many physical entities without the paradoxes encountered in quantum mechanics. Foundations of Physics, 12, pp. 1131-1170.
  7. ^ a b c See also Aerts's Theorem in the Stanford Encyclopedia of Philosophy.
  8. ^ Aerts, D. (1984). The missing elements of reality in the description of quantum mechanics of the EPR paradox situation. Helvetica Physica Acta, 57, pp. 421-428.
  9. ^ a b One of the 'failing quantum axioms, i.e. the covering law, is equivalent with the linearity of the state space of quantum mechanics. This aspect is analyzed in Aerts, D. and Valckenborgh, F. (2002). The linearity of quantum mechanics at stake: the description of separated quantum entities. In D. Aerts, M. Czachor and T. Durt (Eds.), Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics (pp. 20-46). Singapore: World Scientific.
  10. ^ Aerts, D. (1990). An attempt to imagine parts of the reality of the micro-world. In J. Mizerski, A. Posiewnik, J. Pykacz and M. Zukowski (Eds.), Problems in Quantum Physics (pp. 3-25). Singapore: World Scientific.
  11. ^ a b Aerts, D. (1982). Example of a macroscopical situation that violates Bell inequalities. Lettere al Nuovo Cimento, 34, pp. 107-111.
  12. ^ a b Aerts, D. (1991). A mechanistic classical laboratory situation violating the Bell inequalities with 2sqrt(2), exactly 'in the same way' as its violations by the EPR experiments. Helvetica Physica Acta, 64, pp. 1-23.
  13. ^ Accardi, L. (1984). The probabilistic roots of the quantum mechanical paradoxes. In S. Diner (Eds.), The Wave-Particle Dualism. Dordrecht: Springer.
  14. ^ Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics. Journal of Mathematical Physics, 27, pp. 202-210.
  15. ^ See the Mathematics Genealogy Project
  16. ^ a b Aerts, D., Durt, T., Grib, A., Van Bogaert, B. and Zapatrin, A. (1993). Quantum structures in macroscopical reality. International Journal of Theoretical Physics, 32, pp. 489-498.
  17. ^ a b Aerts, D., Durt, T. and Van Bogaert, B. (1993). Quantum probability, the classical limit and nonlocality. In K. V. Laurikainen and C. Montonen (Eds.), Symposium on the Foundations of Modern Physics 1992: The Copenhagen Interpretation and Wolfgang Pauli (pp. 35-56). Singapore: World Scientific.
  18. ^ a b 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.
  19. ^ a b Aerts, D. and Durt, T. (1994). Quantum, classical and intermediate, an illustrative example. Foundations of Physics, 24, pp. 1353-1369.
  20. ^ Aerts, D. (1994). Quantum structures, separated physical entities and probability. Foundations of Physics, 24, pp. 1227-1259.
  21. ^ a b Coecke, B. (1995). Generalization of the proof on the existence of hidden measurements to experiments with an infinite set of outcomes. Foundations of Physics Letters, 8, pp. 437-447.
  22. ^ Aerts, D. and Aerts, S. (1997). The hidden measurement formalism: quantum mechanics as a consequence of fluctuations on the measurement. In M. Ferrero and A. van der Merwe (Eds.), New Developments on Fundamental Problems in Quantum Physics (pp. 1-6). Dordrecht: Springer.
  23. ^ a b Aerts, D., Aerts, S., Coecke, B., D'Hooghe, B., Durt, T. and Valckenborgh, F. (1997). A model with varying fluctuations in the measurement context. In M. Ferrero and A. van der Merwe (Eds.), New Developments on Fundamental Problems in Quantum Physics (pp. 7-9). Dordrecht: Springer.
  24. ^ Aerts, S. (2002). Hidden measurements from contextual axiomatics. In D. Aerts, M. Czachor and T. Durt (Eds.), Probing the Structure of Quantum Mechanics (pp. 149-164). Singapore: World Scientific.
  25. ^ Aerts, S. (2005). The Born rule from a consistency requirement on hidden measurements in complex Hilbert space. International Journal of Theoretical Physics, 44, pp. 999-1009.
  26. ^ Aerts, D., Apostel, L., De Moor, B., Hellemans, S., Maex, E., Van Belle, H. and Van der Veken, J. (1994). Worldviews, from Fragmentation towards Integration. Brussels: VUBPress.
  27. ^ Aerts, D., Apostel, L., De Moor, B., Hellemans, S., Maex, E., Van Belle, H. and Van der Veken, J. (1995). Perspectives on the World, an Interdisciplinary Reflection. Brussels: VUBPress.
  28. ^ Homepage of Clea's research community.
  29. ^ a b Aerts, D. and Aerts, S. (1995). Applications of quantum statistics in psychological studies of decision processes. Foundations of Science, 1, pp. 85-97.
  30. ^ a b c Aerts, D., Broekaert, J. and Smets, S. (1999). A quantum structure description of the liar paradox. International Journal of Theoretical Physics, 38, pp. 3231-3239.
  31. ^ a b Aerts, D., Aerts, S., Broekaert, J. and Gabora, L. (2000). The violation of Bell inequalities in the macroworld. Foundations of Physics, 30, pp. 1387-1414.
  32. ^ a b c Gabora, L. and Aerts, D. (2002). Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence, 14, pp. 327-358.
  33. ^ a b c Aerts, D. and Gabora, L. (2005). A theory of concepts and their combinations I: The structure of the sets of contexts and properties. Kybernetes, 34, pp. 167-191.
  34. ^ a b c Aerts, D. and Gabora, L. (2005). A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes, 34, pp. 192-221.
  35. ^ Hampton, J. A. (1988). Overextension of conjunctive concepts: Evidence for a unitary model for concept typicality and class inclusion. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14, pp. 12-32.
  36. ^ Hampton, J. A. (1988). Disjunction of natural concepts. Memory & Cognition, 16, pp. 579-591.
  37. ^ Hampton, J. A. (1997). Conceptual combination: Conjunction and negation of natural concepts. Memory & Cognition, 25, pp. 888-909.
  38. ^ Aerts, D. (2007). Quantum interference and superposition in cognition: Development of a theory for the disjunction of concepts. Archive reference and link: http://uk.arxiv.org/abs/0705.0975. Printed in D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.), Worldviews, Science and Us: Bridging Knowledge and Its Implications for Our Perspectives of the World. Singapore: World Scientific (2011).
  39. ^ Aerts, D. (2007). General quantum modeling of combining concepts: A quantum field model in Fock space. Archive reference and link: http://uk.arxiv.org/abs/0705.1740.
  40. ^ Aerts, D. (2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53, pp. 314-348.
  41. ^ Aerts, D. and Sozzo, S. (2011). Quantum structure in cognition: Why and how concepts are entangled. Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27–29, 2011. Quantum Interaction. Lecture Notes in Computer Science, 7052, pp. 116-127.
  42. ^ Aerts, D. and Czachor, M. (2004). Quantum aspects of semantic analysis and symbolic artificial intelligence. Journal of Physics A: Mathematical and Theoretical, 37, pp. L123-L132.
  43. ^ Aerts, D. and Czachor, M. (2007). Cartoon computation: Quantum-like algorithms without quantum mechanics. Journal of Physics A: Mathematical and Theoretical, 40, F259-F266, Fast Track Communication.
  44. ^ Aerts, D. and Czachor, M. (2008). Tensor-product vs. geometric-product coding. Physical Review A, 77, 012316.
  45. ^ Aerts, D., Czachor, M. and De Moor, B. (2009). Geometric analogue of holographic reduced representation. Journal of Mathematical Psychology, 53, pp. 389-398.
  46. ^ Aerts, D., D'Hooghe, B. and Sozzo, S. (2011). A quantum cognition analysis of the Ellsberg paradox. Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27–29, 2011. Quantum Interaction. Lecture Notes in Computer Science, 7052, pp. 95-104.
  47. ^ Aerts, D., Sozzo, S. and Tapia, J. (2012). A quantum model for the Ellsberg and Machina paradoxes. Proceedings of the QI2012-Sixth International Symposium on Quantum Interaction, Paris, 27–29 June 2012. To appear in Lecture Notes in Computer Science.
  48. ^ Van Steirteghem, B. and Stubbe, I. (2007). Propositional systems, Hilbert lattices and generalized Hilbert spaces. D. Gabbay, D. Lehmann and K. Engesser, (Eds.), Handbook of Quantum Logic and Quantum Structures. Amsterdam: Elsevier.
  49. ^ Aerts, D. (1999). Foundations of quantum physics: a general realistic and operational approach. International Journal of Theoretical Physics, 38, pp. 289-358.
  50. ^ a b 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.
  51. ^ Aerts, D. and Van Steirteghem, B. (2000). Quantum axiomatics and a theorem of M.P. Soler. International Journal of Theoretical Physics, 39, pp. 497-502.
  52. ^ Aerts, D., Colebunders, E., Van der Voorde, A. and Van Steirteghem, B. (2002). On the amnestic modification of the category of state property systems. Applied Categorical Structures, 10, pp. 469-480.
  53. ^ Aerts, D. (2002). Being and change: foundations of a realistic operational formalism. In D. Aerts, M. Czachor and T. Durt (Eds.), Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics (pp. 71-110). Singapore: World Scientific.
  54. ^ Aerts, D. and Deses, D. (2005). State property systems and orthogonality. International Journal of Theoretical Physics, 44, pp. 919-929.
  55. ^ Aerts, D. (2009). Quantum axiomatics. In K. Engesser, D. Gabbay and D. Lehmann (Eds.), Handbook of Quantum Logic and Quantum Structures,. Amsterdam: Elsevier.
  56. ^ Aerts, D. (2009). Quantum particles as conceptual entities: A possible explanatory framework for quantum theory. Foundations of Science, 14, 361-411.
  57. ^ Aerts, D. (2010). Interpreting quantum particles as conceptual entities. International Journal of Theoretical Physics, 49, pp. 2950-2970.
  58. ^ Aerts, D. (2010). A potentiality and conceptuality interpretation of quantum physics. Philosophica, 83, pp. 15-52.

External links[edit]