Conditions for Quantum Interference in Cognitive Sciences

We present a general classification of the conditions under which cognitive science, concerned, e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that quantum effects in cognition can arise only when decisions are made under uncertainty. Conditions for the appearance of quantum interference in cognitive sciences and the conditions when interference cannot arise are formulated.

[1]  Jerome R. Busemeyer,et al.  Quantum Models of Cognition and Decision , 2012 .

[2]  N. Bohr,et al.  Light and Life , 1933, Nature.

[3]  D Sornette,et al.  Algorithm for model validation: Theory and applications , 2007, Proceedings of the National Academy of Sciences.

[4]  André de Palma,et al.  Discrete Choice Theory of Product Differentiation , 1995 .

[5]  Didier Sornette,et al.  Role of Information in Decision Making of Social Agents , 2012 .

[6]  Didier Sornette,et al.  Processing Information in Quantum Decision Theory , 2008, Entropy.

[7]  Dale Riepe,et al.  Atomic Physics and Human Knowledge. , 1960 .

[8]  J. Wheeler,et al.  Quantum theory and measurement , 1983 .

[9]  Didier Sornette,et al.  Mathematical Structure of Quantum Decision Theory , 2008, Adv. Complex Syst..

[10]  Harald Atmanspacher,et al.  The Potential of Using Quantum Theory to Build Models of Cognition , 2013, Top. Cogn. Sci..

[11]  Alexander Wilce,et al.  Tensor products in generalized measure theory , 1992 .

[12]  John William Nicholson,et al.  The Constitution of Atoms and Molecules , 1914, Nature.

[13]  Niels Bohr.  I. On the constitution of atoms and molecules , 1913 .

[14]  Matteo Marsili,et al.  The Rise and Fall of Trust Networks , 2010 .

[15]  A. Holevo.  Statistical decision theory for quantum systems , 1973 .

[16]  M. Jacobs.  The structure of the metastable precipitates formed during ageing of an Al-Mg-Si alloy , 1972 .

[17]  David W. Moore.  Measuring New Types of Question-Order Effects: Additive and Subtractive , 2002 .

[18]  Jerome R. Busemeyer,et al.  A Quantum Question Order Model Supported by Empirical Tests of an A Priori and Precise Prediction , 2013, Top. Cogn. Sci..

[19]  W. Zurek.  Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

[20]  Didier Sornette,et al.  A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics , 2007, 0710.0317.

[21]  J. Neumann,et al.  The Logic of Quantum Mechanics , 1936 .

[22]  D. Sornette,et al.  Entanglement production in quantum decision making , 2010, 1003.3761.

[23]  Didier Sornette,et al.  Quantum Decision Theory as Quantum Theory of Measurement , 2008, ArXiv.

[24]  N. David Mermin,et al.  Commentary: Quantum mechanics: Fixing the shifty split , 2012 .

[25]  Mermin Nd.  Quantum mechanics: Fixing the shifty split , 2012 .

[26]  Gerd Niestegge,et al.  An Approach to Quantum Mechanics via Conditional Probabilities , 2008 .

[27]  I. Pitowsky.  Quantum Probability ― Quantum Logic , 1989 .

[28]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[29]  John Harding,et al.  A Link between Quantum Logic and Categorical Quantum Mechanics , 2009 .

[30]  Didier Sornette,et al.  Decision theory with prospect interference and entanglement , 2011, ArXiv.

[31]  Didier Sornette,et al.  Physics of risk and uncertainty in quantum decision making , 2008, ArXiv.

[32]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[33]  G. Niestegge.  Composite systems and the role of the complex numbers in quantum mechanics , 2004 .

[34]  D. Sornette,et al.  Quantum decision making by social agents , 2012, 1202.4918.

[35]  Mikhail I. Dyakonov,et al.  State of the Art and Prospects for Quantum Computing , 2013 .