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Graphics and Quantum Mechanics—The Necker Cube as a Quantum-like Two-Level System

  • Giorgio Benedek
  • Giuseppe Caglioti
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)

Abstract

A simulation of the dynamic perception of the Necker cube in terms of a two-level quantum system, e.g. that of the hydrogen tunneling states of the ammonia molecules associated with the 24 GHz maser frequency, indicates that the neuro-physiological transformation leading, through a symmetry reduction, to perceptual reversal is controlled by the principles of quantum mechanics. An elementary neuro-physiological action similar to the Planck constant at a mesoscopic level is introduced.

Keywords

Two-level quantum and quantum-like systems Ambiguous figures Principle of superposition Symmetry reduction Tunneling Chemical and graphic barriers Perception Mind The unconscious 

Notes

Acknowledgements

It is a pleasure to thank Prof. Luigi Cocchiarella (Politecnico di Milano) for many stimulating comments and advices.

References

  1. 1.
    Caglioti, G.: From perception to thought—a nonequilibrium dynamic instability implying a symmetry breaking, in Katachi ∪ Symmetry. In: Ogawa, T., Miura, K., Masunari, T., Nagy, D. (eds.), pp. 355–361. Springer, Tokyo (1996); and Caglioti, G.: Optical art: “illusions” and paradoxes of symmetry and quantum mechanics, in Symmetry 2000. In: Hargittai, I., Laurent, T.C. (eds.) Part 2, pp. 457–466. Portland Press, London (2002)Google Scholar
  2. 2.
    Bertolotti, M.: The history of the Laser. Taylor & Francis (2004). ISBN 978-0-7503-0911-0Google Scholar
  3. 3.
    Feynman, R., Leighton, R.B., Sands, M.: The Feynman Lectures of Physics, vol III, pp. 8–12. Addison–Wesley Publishing Company (1965). This well known textbook offers an over-simplified picture in which the N atom tunnels from one side to the other of the triangle made of the three H atoms. If so no isotopic effect would be observed. The tunneling motion is actually a coherent one of all atoms so as to keep the center of mass fixed. In this motion the light H atoms are mostly displaced, which yields the large isotopic effect observed on the replacement of the H atoms with one or more D atoms. Note that the transition between the two specular configurations can also be obtained with a rigid rotation of the molecule. Rotational excitation frequencies are however in the THz range, much above the 24 GHz tunneling oscillation and with a much smaller isotope effectGoogle Scholar
  4. 4.
    Herbauts, I.M., Dunstan, D.J.: Quantum molecular dynamics study of the pressure dependence of the ammonia inversion transition. Phys. Rev. A 76, 062506 (2007); for deuterated ammonia ND3 the microwave frequency is as low as 1.6 GHZ, as compared to 24 GHz for NH3. While the chemical barrier to tunneling is about the same for the two isotopes, the tunneling frequency is an exponentially decreasing function of the isotope massGoogle Scholar
  5. 5.
    Caglioti, G., Benedek, G., Cocchiarella, L.: The perception of ambiguous images as a quantum information process. Istituto Lombardo Accademia di Scienze e Lettere (Rend. Scienze) 148, 35–50 (2014)Google Scholar
  6. 6.
    Leibniz, G.W.: Epistolae ad Diversos. In: Kortholt, Ch. (ed.) (Breitkopf, Lipsiae 1734) p. 241: “Musica est exercitium arithmeticae occultum nescientis se numerare animi”. http://reader.digitale-sammlungen.de/de/fs1/object/display/bsb10403201_00279.html

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienza dei MaterialiUniversità di Milano-BicoccaMilanItaly
  2. 2.Donostia International Physics Center (DIPC)San SebastianSpain
  3. 3.Dipartimento di EnergiaPolitecnico di MilanoMilanItaly

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