Foundations of Physics

, Volume 30, Issue 9, pp 1387–1414 | Cite as

The Violation of Bell Inequalities in the Macroworld

  • Diederik Aerts
  • Sven Aerts
  • Jan Broekaert
  • Liane Gabora
Article

Abstract

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via Bell's theorem,” Phys. Rev. Lett. 47, 460 (1981).Google Scholar
  2. A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-sPodolsky-Rosen-Bohm gedankenexperiment: A new violation of Bell's inequalities,” Phys. Rev. Lett. 48, 91 (1982).Google Scholar
  3. D. Aerts, “The one and the many,” Doctoral dissertation (Brussels Free University, 1981).Google Scholar
  4. D. Aerts, “Example of a macroscopical situation that violates Bell inequalities,” Lett. Nuovo Cim. 34, 107 (1982).Google Scholar
  5. D. Aerts, “The missing elements of reality in the description of quantum mechanics of the EPR paradox situation,” Helv. Phys. Acta. 57, 421 (1984).Google Scholar
  6. D. Aerts, “The physical origin of the EPR paradox and how to violate Bell inequalities by macroscopical systems,” in On the Foundations of modern Physics, P. Lathi and P. Mittelstaedt, eds. (World Scientific, Singapore, 305, 1985a).Google Scholar
  7. D. Aerts, “A possible explanation for the probabilities of quantum mechanics and a macro-scopical situation that violates Bell inequalities,” in Recent Developments in Quantum Logic, P. Mittelstaedt et al., eds. (Bibliographisches Institut, Mannheim, 235, 1985b).Google Scholar
  8. D. Aerts, “A mechanistic classical laboratory situation violating the Bell inequalities with 2/2, exactly ‘in the same way’ as its violations by the EPR experiments,” Helv. Phys. Acta 64, 1–24 (1991).Google Scholar
  9. D. Aerts, “The construction of reality and its influence on the understanding of quantum structures,” Int. J. Theor. Phys. 31, 1815–1837 (1992).Google Scholar
  10. D. Aerts, “The description of joint quantum entities and the formulation of a paradox,” Int. J. Theor. Phys. 39, 483 (2000).Google Scholar
  11. D. Aerts, S. Aerts, B. Coecke, and F. Valckenborgh, “The meaning of the violation of Bell Inequalities: nonlocal correlation or quantum behavior?,” preprint (Free University of Brussels, 1995).Google Scholar
  12. D. Aerts and T. Durt, “Quantum, classical and intermediate, an illustrative example,” Found. Phys. 24, 1353–1368 (1994).Google Scholar
  13. D. Aerts and L. Gabora, “Quantum mind web course, lecture week 10,” part of “Conscious-ness at the Millennium: Quantum Approaches to Understanding the Mind,” an online course offered by consciousness studies (The University of Arizona, September 27, 1999 through January 14, 2000).Google Scholar
  14. D. Aerts and L. Szabo, “Is quantum mechanics really a non-Kolmogorovian probability theory,” preprint, CLEA (Brussels Free University, 1993).Google Scholar
  15. J. S. Bell, “On the Einstein_Podolsky–Rosen paradox,” Physics 1, 195 (1964).Google Scholar
  16. D. Bohm, Quantum Theory (Prentice–Hall, Englewood Cliffs, New York, 1951).Google Scholar
  17. J. F. Clauser, Phys. Rev. Lett. 36, 1223 (1976).Google Scholar
  18. J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1976).Google Scholar
  19. A. Einstein, B. Podolskyi, and N. Rosen, “Can quantum mechanical description of physical reality be considered complete,” Phys. Rev. 47, 777 (1935). Faraci et al., Lett. Nuovo Cim. 9, 607 (1974).Google Scholar
  20. S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972).Google Scholar
  21. L. Gabora, “Autocatalytic closure in a cognitive system: A tentative scenario for the origin of culture,” Psycoloquy 9, (67), (1998).Google Scholar
  22. L. Gabora, “Weaving, bending, patching, mending the fabric of reality: A cognitive science perspective on worldview inconsistency,” Foundations of Science 3(2), 395–428 (1999).Google Scholar
  23. L. Gabora, “Conceptual closure: Weaving memories into an interconnected worldview,” in Closure: Emergent Organizations and their Dynamics, G. Van de Vijver and J. Chandler, eds., Ann. New York Acad. Sci. (2000).Google Scholar
  24. P. J. B. Hancock, L. S. Smith, and W. A. Phillips, “A biologically supported error-correcting learning rule,” Neural Computation 3(2), 201–212 (1991).Google Scholar
  25. S. B. Holden and M. Niranjan, “Average-case learning curves for radial basis function networks,” Neural Computation 9(2), 441–460 (1997).Google Scholar
  26. R. A. Holt and F. M. Pipkin, preprint Harvard University (1973).Google Scholar
  27. S. A. Kauffman, Origins of Order (Oxford University Press, Oxford, 1993).Google Scholar
  28. Kasday, Ullmann and Wu, Bull. Am. Phys. Soc. 15, 586 (1970).Google Scholar
  29. Y. W. Lu, N. Sundararajan, and P. Saratchandran, “A sequential learning scheme for function approximation using minimal radial basis function neural networks,” Neural Computation 9(2), 461–478 (1997).Google Scholar
  30. I. Pitowsky, Quantum Probability-Quantum Logic (Springer, Berlin, New York, 1989).Google Scholar
  31. D. Willshaw and P. Dayan, “Optimal plasticity from matrix memories: What goes up must come down,” Neural Computation 2(1), 85–93 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Sven Aerts
    • 2
  • Jan Broekaert
    • 3
  • Liane Gabora
    • 4
  1. 1.Center Leo ApostelBrussels Free UniversityBrusselsBelgium;
  2. 2.Center Leo ApostelBrussels Free UniversityBrusselsBelgium;
  3. 3.Center Leo ApostelBrussels Free UniversityBrusselsBelgium;
  4. 4.Center Leo ApostelBrussels Free UniversityBrusselsBelgium;

Personalised recommendations