Central European Journal of Physics

, Volume 11, Issue 2, pp 147–161 | Cite as

Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts’ machine-models

Review Article

Abstract

From the beginning of his research, the Belgian physicist Diederik Aerts has shown great creativity in inventing a number of concrete machine-models that have played an important role in the development of general mathematical and conceptual formalisms for the description of the physical reality. These models can also be used to demystify much of the strangeness in the behavior of quantum entities, by allowing to have a peek at what’s going on behind the “quantum scenes,” during a measurement. In this author’s view, the importance of these machine-models, and of the approaches they have originated, have been so far seriously underappreciated by the physics community, despite their success in clarifying many challenges of quantum physics. To fill this gap, and encourage a greater number of researchers to take cognizance of the important work of so-called Geneva-Brussels school, we describe and analyze in this paper two of Aerts’ historical machine-models, whose operations are based on simple breakable elastic bands. The first one, called the spin quantum-machine, is able to replicate the quantum probabilities associated with the spin measurement of a spin-1/2 entity. The second one, called the connected vessels of water model (of which we shall present here an alternative version based on elastics) is able to violate Bell’s inequality, as coincidence measurements on entangled states can do.

Keywords

quantum-machines quantum probabilities hidden measurements entanglement Bell’s inequalities 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. G. Cramer, Rev. Mod. Phys. 58, 647 (1986)MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    R. P. Feynman, The Character of Physical Law (Penguin Books, London, 1992)Google Scholar
  3. [3]
    W. Heisenberg, Philosophic Problems of Nuclear Science (Pantheon Books, New York, 1952)Google Scholar
  4. [4]
    M. Sassoli de Bianchi, Found. Sci. 16, 393 (2011)MathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Sassoli de Bianchi, Found. Sci. 17, 223 (2012)MathSciNetCrossRefGoogle Scholar
  6. [6]
    D. Aerts, In: D. Aerts, J. Broekaert, E. Mathijs (Eds.), The white book of “Einstein meets Magritte” (Kluwer Academic Publishers, Dordrecht, 1999) 129Google Scholar
  7. [7]
    D. Aerts, In: D. Aerts, J. Broekaert, E. Mathijs (Eds.), The Indigo Book of “Einstein Meets Magritte” (Kluwer Academic Publishers, Dordrecht, 1999) 141Google Scholar
  8. [8]
    D. Aerts, J. Math, Phys. 27, 202 (1986)MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    D. Aerts, Int. J. Theor. Phys. 34, 1165 (1995)MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    D. Aerts, In: Elena Castellani (Ed.), Interpreting bodies, classical and quantum objects in modern physics (Princeton University Press, Princeton, 1998) 223Google Scholar
  11. [11]
    D. Aerts, Int. J. Theor. Phys. 32, 2207 (1993)MathSciNetCrossRefGoogle Scholar
  12. [12]
    A. D. O’Connell et al., Nature 464, 697 (2010)ADSCrossRefGoogle Scholar
  13. [13]
    D. Aerts, In: J. Mizerski et al. (Eds.), Problems in Quantum Physics II; Gdansk’ 89 (World Scientific Publishing Company, Singapore, 1990) 3Google Scholar
  14. [14]
    D. Aerts, Helv. Phys. Acta 57, 421 (1984)MathSciNetGoogle Scholar
  15. [15]
    D. Aerts, In: P. Mittelstaedt, E. W. Stachow (Eds.), Recent Developments in Quantum Logic (Bibliographisches Institut, Mannheim, 1985) 235Google Scholar
  16. [16]
    M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974) 151Google Scholar
  17. [17]
    D. Aerts, In: A. Blanquiere, S. Diner, G. Lochak (Eds.), Information, Complexity, and Control in Quantum Physics (Springer-Verlag, Wien and New York, 1987) 77Google Scholar
  18. [18]
    D. Aerts, T. Durt, Found. Phys. 24, 1353 (1994)MathSciNetADSMATHCrossRefGoogle Scholar
  19. [19]
    D. Aerts, T. Durt, In: K. V. Laurikainen, C. Montonen, K. Sunnaborg (Eds.), Proceedings of the International Symposium on the Foundations of Modern Physics, Helsinki, Finland (Editions Frontieres, Gives Sur Yvettes, 1994) 3Google Scholar
  20. [20]
    A. M. Gleason, J. Math. Mech. 6, 885 (1957)MathSciNetMATHGoogle Scholar
  21. [21]
    S. Kochen, E. P. Specker, J. Math. Mech. 17, 59 (1967)MathSciNetMATHGoogle Scholar
  22. [22]
    D. Aerts, B. Coecke, B. D’Hooghe, F. Valckenborgh, Helv. Phys. Acta 70, 793 (1997)MathSciNetMATHGoogle Scholar
  23. [23]
    D. Aerts, S. Aerts, J. Broekaert, L. Gabora, Found. Phys. 30, 1387 (2000)MathSciNetCrossRefGoogle Scholar
  24. [24]
    D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, New York, 1951)Google Scholar
  25. [25]
    J. S. Bell, In: B. d’Espagnat (Ed.), Proceedings of the International School of Physics “Enrico Fermi,” Course XLIX (Academic Press, New York, 1971) 171Google Scholar
  26. [26]
    J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964)Google Scholar
  27. [27]
    A. Aspect et al., Phys. Rev. Lett. 49, 91 (1982)MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    A. Aspect, Nature 398, 189 (1999)ADSCrossRefGoogle Scholar
  29. [29]
    S. Aerts, arXiv:quant-ph/0504171Google Scholar
  30. [30]
    E. Schroedinger, Naturwissenschaftern 23, 807 (1935)ADSCrossRefGoogle Scholar
  31. [31]
    D. Aerts, Helv. Phys. Acta 64, 1 (1991)MathSciNetGoogle Scholar
  32. [32]
    D. Aerts, Int. J. Theor. Phys. 39, 485 (2000)MathSciNetMATHGoogle Scholar
  33. [33]
    M. Sassoli de Bianchi, Found. Sci., DOI: 10.1007/s10699-011-9284-1Google Scholar
  34. [34]
    M. Sassoli de Bianchi, Found. Sci. 16, 393 (2011)MathSciNetCrossRefGoogle Scholar
  35. [35]
    M. Sassoli de Bianchi, Found. Sci. 17, 223 (2012)MathSciNetCrossRefGoogle Scholar
  36. [36]
    D. Aerts, Found. Sci. 14, 361 (2009)MathSciNetMATHCrossRefGoogle Scholar
  37. [37]
    D. Aerts, Int. J. Theor. Phys. 49, 2950 (2010)MathSciNetMATHCrossRefGoogle Scholar
  38. [38]
    G. Auletta, M. Fortunato, G. Parisi, Quantum Mechanics (Cambridge University Press, Cambridge, 2009)MATHCrossRefGoogle Scholar
  39. [39]
    A. N. Kolmogorov, Foundations of the Theory of Probability (Chelsea Publishing Company, New York, 1956)MATHGoogle Scholar
  40. [40]
    D. Salart et. al., Nature 454, 861 (2008)ADSCrossRefGoogle Scholar
  41. [41]
    H. P. Hberhard, Nuovo Cimento B 46, 392 (1978)ADSCrossRefGoogle Scholar

Copyright information

© Versita Warsaw and Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Laboratorio di Autoricerca di BaseCaronaSwitzerland

Personalised recommendations