Abstract
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent, response variables), and in quantum mechanics (QM), to deal with the EPR entanglement phenomena (deciding whether an EPR experiment allows for a “classical” account). The parallels between these problems are established by observing that any two noncommuting measurements in QM are mutually exclusive and can therefore be treated as analogs of different values of one and the same input. Both problems reduce to that of the existence of a jointly distributed system of random variables, one variable for every value of every input (in psychology) or every measurement on every particle involved (in an EPR experiment). We overview three classes of necessary conditions (some of them also sufficient under additional constraints) for the existence of such joint distributions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Basoalto, R.M., Percival, I.C.: BellTest and CHSH experiments with more than two settings. Journal of Physics A: Mathematical & General 36, 7411–7423 (2003)
Bell, J.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)
Bohm, D., Aharonov, Y.: Discussion of Experimental Proof for the Paradox of Einstein, Rosen and Podolski. Physical Review 108, 1070–1076 (1957)
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Physical Review Letters 23, 880–884 (1969)
Dzhafarov, E.N.: Conditionally selective dependence of random variables on external factors. Journal of Mathematical Psychology 43, 123–157 (1999)
Dzhafarov, E.N.: Unconditionally selective dependence of random variables on external factors. Journal of Mathematical Psychology 45, 421–451 (2001)
Dzhafarov, E.N.: Selective influence through conditional independence. Psychometrika 68, 7–26 (2003)
Dzhafarov, E.N.: Thurstonian-type representations for “same-different” discriminations: Probabilistic decisions and interdependent images. Journal of Mathematical Psychology 47, 229–243 (2003) see Dzhafarov, E.N.: Corrigendum to “Thurstonian-type representations for ‘same–different’ discriminations: Probabilistic decisions and interdependent images.” Journal of Mathematical Psychology 50, 511 (2006)
Dzhafarov, E.N., Gluhovsky, I.: Notes on selective influence, probabilistic causality, and probabilistic dimensionality. Journal of Mathematical Psychology 50, 390–401 (2006)
Dzhafarov, E.N., Kujala, J.V.: The Joint Distribution Criterion and the Distance Tests for Selective Probabilistic Causality. Frontiers in Quantitative Psychology and Measurement 1, 151 (2010), doi: 10.3389/fpsyg.2010.0015
Dzhafarov, E.N., Kujala, J.V.: Selectivity in probabilistic causality: Where psychology runs into quantum physics. Journal of Mathematical Psychology 56, 54–63 (2012)
Dzhafarov, E.N., Kujala, J.V.: Order-distance and other metric-like functions on jointly distributed random variables. Proceedings of the American Mathematical Society (2011) (in press)
Dzhafarov, E.N., Schweickert, R., Sung, K.: Mental architectures with selectively influenced but stochastically interdependent components. Journal of Mathematical Psychology 48, 51–64 (2004)
Einstein, A., Podolsky, B., Rosen, N.: Can Quantum-Mechanical Description of Physical Reality be Considered Complete? Physical Review 47, 777–780 (1935)
Fine, A.: Joint distributions, quantum correlations, and commuting observables. Journal of Mathematical Physics 23, 1306–1310 (1982)
Fine, A.: Hidden variables, joint probability, and the Bell inequalities. Physical Review Letters 48, 291–295 (1982)
Greenberger, D.M., Horne, M.A., Zeilinger, A.: Going beyond Bell’s theorem. In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory and Conceptions of the Universe, pp. 69–72. Kluwer, Dordrecht (1989)
Karmarkar, N.: A new polynomial-time algorithm for linear programming. Combinatorica 4, 373–395 (1984)
Kujala, J.V., Dzhafarov, E.N.: Testing for selectivity in the dependence of random variables on external factors. Journal of Mathematical Psychology 52, 128–144 (2008)
Kujala, J.V., Dzhafarov, E.N.: Regular Minimality and Thurstonian-type modeling. Journal of Mathematical Psychology 53, 486–501 (2009)
Pitowski, I.: Quantum Probability – Quantum Logic. Springer, Berlin (1989)
Sternberg, S.: The discovery of processing stages: Extensions of donders’ method. Acta Psychologica 30, 276–315 (1969)
Suppes, P., Zanotti, M.: When are probabilistic explanations possible? Synthese 48, 191–199 (1981)
Townsend, J.T.: Uncovering mental processes with factorial experiments. Journal of Mathematical Psychology 28, 363–400 (1984)
Townsend, J.T., Schweickert, R.: Toward the trichotomy method of reaction times: Laying the foundation of stochastic mental networks. Journal of Mathematical Psychology 33, 309–327 (1989)
Werner, R.F., Wolf, M.M.: All multipartite Bell correlation inequalities for two dichotomic observables per site. arXiv:quant-ph/0102024v1 (2001)
Werner, R.F., Wolf, M.M.: Bell inequalities and entanglement. arXiv:quant-ph/0107093 v2 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dzhafarov, E.N., Kujala, J.V. (2012). Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds) Quantum Interaction. QI 2012. Lecture Notes in Computer Science, vol 7620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35659-9_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-35659-9_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35658-2
Online ISBN: 978-3-642-35659-9
eBook Packages: Computer ScienceComputer Science (R0)