Foundations of Science

, Volume 18, Issue 1, pp 11–41

The δ-Quantum Machine, the k-Model, and the Non-ordinary Spatiality of Quantum Entities

Article

Abstract

The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts’ creation-discovery view and hidden measurement approach: a fundamental explanatory framework whose importance, in this author’s view, has been seriously underappreciated by the physics community, despite its success in clarifying many conceptual challenges of quantum physics. Secondly, it aims to introduce a new quantum machine—that we call the δ quantum machine—which is able to reproduce the transmission and reflection probabilities of a one-dimensional quantum scattering process by a Dirac delta-function potential. The machine is used not only to demonstrate the pertinence of the above mentioned explanatory framework, in the general description of physical systems, but also to illustrate (in the spirit of Aerts’ ∊-model) the origin of classical and quantum structures, by revealing the existence of processes which are neither classical nor quantum, but irreducibly intermediate. We do this by explicitly introducing what we call the k-model and by proving that its processes cannot be modelized by a classical or quantum scattering system. The third purpose of this work is to exploit the powerful metaphor provided by our quantum machine, to investigate the intimate relation between the concept of potentiality and the notion of non-spatiality, that we characterize in precise terms, introducing for this the new concept of process-actuality.

Keywords

Quantum structures Creation-discovery view Hidden measurement approach One-dimensional scattering Delta-function potential Potentiality Non-spatiality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Accardi L. (1982) On the statistical meaning of the complex numbers in quantum mechanics. Nuovo Cimento 34: 161Google Scholar
  2. Aerts D. (1982) Description of many physical entities without the paradoxes encountered in quantum mechanics. Foundations of Physics 12: 1131–1170CrossRefGoogle Scholar
  3. Aerts D. (1984) The missing element of reality in the description of quantum mechanics of the EPR paradox situation. Helvetica physica Acta 57: 421–428Google Scholar
  4. Aerts D. (1992a) A possible explanation for the probabilities of quantum mechanics. Journal of Mathematical Physics 27: 202–210CrossRefGoogle Scholar
  5. Aerts D. (1992b) The construction of reality and its influence on the understanding of quantum structures. International Journal of Theoretical Physics 31: 1815–1837CrossRefGoogle Scholar
  6. Aerts D. (1995) Quantum structures: An attempt to explain the origin of their appearance in nature. International Journal of Theoretical Physics 34: 1165CrossRefGoogle Scholar
  7. Aerts D. (1996a) Relativity theory: What is reality?. Foundations of Physics 26: 1627–1644CrossRefGoogle Scholar
  8. Aerts D. (1996b) Towards a framework for possible unification of quantum and relativity theories. International Journal of Theoretical Physics 35: 2399–2416CrossRefGoogle Scholar
  9. Aerts D. (1998) The entity and modern physics: The creation-discovery view of reality. In: Castellani E. (Ed.). Interpreting bodies: Classical and quantum objects in modern physics. Princeton Unversity Press, PrincetonGoogle Scholar
  10. Aerts D. (1999a) The stuff the world is made of: Physics and reality, p. 129. In: Aerts D., Broekaert J., Mathijs E. (eds) The white book of ‘Einstein meets magritte’. Kluwer, Dordrecht, p 274Google Scholar
  11. Aerts D. (1999b) Quantum mechanics: Structures, axioms and paradoxes, p. 141. In: Aerts D., Broekaert J., Mathijs E. (eds) The indigo book of ‘Einstein meets magritte’. Kluwer, Dordrecht, p 239Google Scholar
  12. Aerts D. (2000) The description of joint quantum entities and the formulation of a paradox. International Journal of Theoretical Physics 39: 485–496Google Scholar
  13. Aerts D. (2009) Quantum particles as conceptual entities. A possible explanatory framework for quantum theory. Foundations of Science 14: 361–411CrossRefGoogle Scholar
  14. Aerts D. (2010) Interpreting quantum particles as conceptual entities. International Journal of Theoretical Physics 49: 2950–2970CrossRefGoogle Scholar
  15. Aerts, D., & Sozzo, S. (2011a). Contextual risk and its relevance in economics. Journal of Engineering Science and Technology Review. arXiv:1105.1812 [physics.soc-ph].Google Scholar
  16. Aerts, D., & Sozzo, S. (2011b). A contextual risk model for the Ellsberg paradox. Journal of Engineering Science and Technology Review. arXiv:1105.1814v1 [physics.soc-ph].Google Scholar
  17. Aerts D., Durt T. (1994) Quantum, classical and intermediate, an illustrative example. Foundations of Science 24: 1353Google Scholar
  18. Aerts D. et al (1987) The origin of the non-classical character of the quantum probability model. In: Blanquiere A. (Ed.), Information, complexity, and control in quantum physics. Springer, New YorkGoogle Scholar
  19. Aerts, D., et al. (1990). An attempt to imagine parts of the reality of the micro-world. In J. Mizerski (Ed.), Problems in quantum physics II; Gdansk ’89 (pp. 3–25). Singapore: World Scientific Publishing Company.Google Scholar
  20. Amrein W. O. (1981) Non-relativistic quantum dynamics. Riedel, DordrechtGoogle Scholar
  21. Birkhoff G., Von Neumann J. (1936) The logic of quantum mechanics. The Annals of Mathematics 37: 823CrossRefGoogle Scholar
  22. Born M. (1926) Quantenmechanik der Stoßvorgänge. zeitschrift für physik 38: 803–827CrossRefGoogle Scholar
  23. Coecke B. (1998) A representation for compound quantum systems as individual entities: Hard acts of creation and hidden correlations. Foundations of Physics 28: 1109–1135CrossRefGoogle Scholar
  24. Emch G. G. (1984) Mathematical and conceptual foundations of twentieth century physics. North-Holland, AmsterdamGoogle Scholar
  25. Feynman R. P. (1992) The character of physical law. Penguin Books, LondonGoogle Scholar
  26. Foulis D., Randall C. (1972) Operational statistics I–Basic concepts. Journal of Mathematical Physics 11: 1667–1675CrossRefGoogle Scholar
  27. Gudder S. P. (1988) Quantum probability. Academic Press, Inc. Harcourt Brave Jovanovich, New YorkGoogle Scholar
  28. Jauch J. M. (1968) Foundations of quantum mechanics. Addison-Wesley, Reading, MassGoogle Scholar
  29. Piron C. (1976) Foundations of quantum physics. W. A. Benjamin, MassachusettsGoogle Scholar
  30. Piron C. (1978) La Description d’un Système Physique et le Présupposé de la Théorie Classique. Annales de la Fondation Louis de Broglie 3: 131–152Google Scholar
  31. Piron, C. (1990). Mécanique quantique: Bases et applications. Presses polytechniques et universitaires romandes, Lausanne, Switzerland.Google Scholar
  32. Pitovski I. (1989) Quantum probability—quantum logic. Springer, BerlinGoogle Scholar
  33. Randall, C., & Foulis, D. (1983). A mathematical language for quantum physics, in Les Fondements de la Mecanique Quantique, ed. C. Gruber et al, A.V.C.P., case postale 101, 1015 Lausanne, Suisse.Google Scholar
  34. Rauch H. (1988) Neutron interferometric tests of quantum mechanics. Helvetica Physica Acta 61: 589Google Scholar
  35. Sassoli de Bianchi, M. (2011a). From permanence to total availability: A quantum conceptual upgrade. Foundations of Science. doi:10.1007/s10699-011-9233-z.
  36. Sassoli de Bianchi, M. (2011b). Time-delay of classical and quantum scattering processes: A conceptual overview and a general definition. Central European Journal of Physics. doi:10.2478/s11534-011-0105-5.
  37. Sassoli de Bianchi, M. (2011c). Ephemeral properties and the illusion of microscopic particles. Foundations of Science, 16(4), 393–409. doi:10.1007/s10699-011-9227-x. An Italian translation of the article is also available: Proprietá effimere e l’illusione delle particelle microscopiche. AutoRicerca, Volume 2, pp. 39–76 (2011).
  38. Segal I. E. (1947) Postulates for general quantum mechanics. Annals of Mathematics 48: 930–948CrossRefGoogle Scholar
  39. Smets S. (2005) The modes of physical properties in the logical foundations of physics Logic and Logical Philosophy 14:37–53Google Scholar
  40. Vassell M. O., Lee J., Lockwood H. F. et al (1983) Multibarrier tunneling in Ga1-xAlxAs/GaAs heterostructures. Journal of Applied Physics 54: 5206–5213CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Laboratorio di Autoricerca di BaseCaronaSwitzerland

Personalised recommendations