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A Short Survey on a “Strange” Potential

  • Ignazio LicataEmail author
  • Davide Fiscaletti
Chapter
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Abstract

The David Bohm work on quantum mechanics starts from de Broglie pilot wave theory, which can be considered as the most significant hidden variables theory equivalent to quantum mechanics as for predictability and able to restore a causal completion to quantum mechanics. Such approach was originally proposed by Louis de Broglie at Solvay Conference in 1926.

Keywords

Wave Function Clifford Algebra Quantum Potential Bohmian Mechanic Quantum Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    De Broglie, L.: Solvay Congress (1927), Electrons and photons: rapports et discussions du Cinquime Conseil de Physique tenu Bruxelles du 24 au Octobre 1927 sous les auspices de l’Istitut International de Physique Solvay. Gauthier-Villars, Paris (1928)Google Scholar
  2. 2.
    de Broglie, L.: Une interpretation causale et non linéaire de la mécanique ondulatoire: la théorie de la doble solution. Gauthier-Villars, Paris (1956)Google Scholar
  3. 3.
    de Broglie, L.: The reinterpretation of quantum mechanics. Found. Phys. 1, 5 (1970)CrossRefADSGoogle Scholar
  4. 4.
    Pauli, W.: Électrons et photons: Rapports et discussions du cinquieme conseil de physique, pp. 280–282. Gauthier-Villars, Paris (1928)Google Scholar
  5. 5.
    Bohm, D.: A new suggested interpretation of quantum theory in terms of hidden variables. Part I. Phys. Rev. 85, 166–179 (1952)MathSciNetCrossRefADSzbMATHGoogle Scholar
  6. 6.
    Bohm, D.: A new suggested interpretation of quantum theory in terms of hidden variables. Part II. Phys. Rev. 85, 180–193 (1952)MathSciNetCrossRefADSGoogle Scholar
  7. 7.
    Bohm, D.: Proof that probability density approaches |Ψ|2 in causal interpretation of the quantum theory. Phys. Rev. 89, 458–466 (1953)MathSciNetCrossRefADSzbMATHGoogle Scholar
  8. 8.
    Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, Cambridge (1993)CrossRefGoogle Scholar
  9. 9.
    Bohm, D., Hiley, B., Kaloyerou, P.N.: An ontological basis for quantum theory. Phys. Rep. 144, 321–375 (1987)MathSciNetCrossRefADSGoogle Scholar
  10. 10.
    Bohm, D., Hiley, B.: The Undivided Universe. Routledge, London (1993)Google Scholar
  11. 11.
    Philippidis, C., Dewdney, C., Hiley, B.: Quantum interference and the quantum potential. Nuovo Cimento B 52(1), 15–28 (1979)MathSciNetCrossRefADSGoogle Scholar
  12. 12.
    Dewdney, C., Hiley, B.: A quantum potential description of one-dimensional time-dependent scattering from square barriers and square wells. Found. Phys. 12, 27–48 (1982)CrossRefADSGoogle Scholar
  13. 13.
    Honig, W.M., Kraft, D.W., Panarella, E. (eds.): Quantum Uncertainties: Recent and Future Experiments and Interpretations. Nato ASI Series, Plenum Press, New York (1987)Google Scholar
  14. 14.
    Hiley, B.: Some remarks on the evolution of Bohm’ proposals for an alternative to standard quantum mechanics. http://www.bbk.ac.uk/tpru/RecentPublications.html (2010)
  15. 15.
    Dürr, D., Goldstein, S., Zanghi, N.: Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67, 843–907 (1992)CrossRefADSzbMATHGoogle Scholar
  16. 16.
    Bohm, D.: Quantum Theory. Routledge, London (1951)Google Scholar
  17. 17.
    Goldstein, S., Berndl, S., Daumer, M., Dürr, D., Zanghì, N.: A survey of Bohmian mechanics. Il Nuovo Cimento 110B, 737–750 (1995)ADSGoogle Scholar
  18. 18.
    Goldstein, S., Dürr, D., Zanghì, N.: Bohmian mechanics and quantum equilibrium. In: Albeverio, S., Cattaneo, U., Merlini, D. (eds.) Stochastic Processes, Physics and Geometry II, pp. 221–232. World Scientific, Singapore (1995)Google Scholar
  19. 19.
    Goldstein, S.: Bohmian mechanics and the quantum revolution. Synthese 107, 145–165 (1996)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Goldstein, S., Dürr, D., Zanghì, N.: Bohmian mechanics as the foundation of quantum mechanics. In: Cushing, J.T., Fine, A., Goldstein, S. (ed.) Bohmian Mechanics and Quantum Theory: An Appraisal. Boston Studies in the Philosophy of Science, vol. 184, pp. 21–44. Kluwer, Dordrecht (1996)Google Scholar
  21. 21.
    Dürr, D., Goldstein, S., Zanghì, N.: Bohmian mechanics and meaning of the wave function. In: Cohen, R. S., Horne, M., Stachel, J. (eds.) Experimental Metaphysics. Quantum Mechanical Studies for Abner Shimony, vol. 1, pp. 25–38. Kluwer, Dordrecht (1997)Google Scholar
  22. 22.
    Allori, V., Zanghì, N.: What is Bohmian mechanics. Intern. J. Theor. Phys. 43, 1743–1755 (2004)CrossRefGoogle Scholar
  23. 23.
    Goldstein, G., Dürr, D., Tumulka, R., Zanghì, N.: Bohmian mechanics. In: Borchert, D.M. (ed.) The Encyclopedia of Philosophy, 2nd edn. Macmillan Reference, London (2006)Google Scholar
  24. 24.
    Goldstein, S., Dürr, D., Tumulka, R., Zanghì, N.: Bohmian mechanics. In: Weinert, F., Hentschel, K., Greenberger, D. (eds.) Compendium of Quantum Physics. Springer, Berlin (2009)Google Scholar
  25. 25.
    Goldstein, S., Tumulka, R., Zanghì, N.: Bohmian trajectories as the foundation of quantum mechanics. In: Chattaraj P. (ed.) Quantum Trajectories, pp. 1–15. Taylor & Francis, Boca Raton (2010)Google Scholar
  26. 26.
    Goldstein S., Teufel, S.: Quantum spacetime without observers: ontological clarity and the conceptual foundations of quantum gravity. In: Callender, C., Huggett, N. (eds.) Physics Meets Philosophy at the Planck Scale, pp. 275–289. Cambridge University Press, Cambridge (reprinted in Dürr, D., Goldstein, S., Zanghì, N.: Quantum Physics Without Quantum Philosophy. Springer, Berlin (2012)) (2001)Google Scholar
  27. 27.
    Goldstein, S., Zanghì, N.: Reality and the role of the wave function. In: Dürr, D., Goldstein, S., Zanghì, N. (eds.) Quantum Physics Without Quantum Philosophy. Springer, Berlin (2012)Google Scholar
  28. 28.
    Esfeld, M., Lazarovici, D., Hubert, M., Dürr, D.: The ontology of Bohmian mechanics. http://philsci-archive.pitt.edu/9381 (2013)
  29. 29.
    Atiq, M., Karamian, M., Golshani, M.: A quasi-Newtonian approach to Bohmian quantum mechanics. Annales de la Fondation Louis de Broglie 34(1), 67–81 (2009)MathSciNetGoogle Scholar
  30. 30.
    Schrödinger, E.: Quantizierung als Eigenwertproblem (Erste Mitteilung) (Quantization as a Problem of Proper Values. Part I). Annalen der Physik., 79, 361 (reprinted in Collected Papers on Wave Mechanics, American Mathematical Society, 3rd Revised edn. (Nov 12 2003) (1926)Google Scholar
  31. 31.
    Abolhasani M., Golshani, M.: The path integral approach in the frame work of causal interpretation. Annales de la Fondation Louis de Broglie, 28(1), 1–8 (2003)Google Scholar
  32. 32.
    Grössing, G.: The vacuum fluctuation theorem: exact Schrödinger equation via nonequilibrium thermodynamics. Phys. Lett. A 372, 4556 (2008)MathSciNetCrossRefADSzbMATHGoogle Scholar
  33. 33.
    Grössing, G.: On the thermodynamic origin of the quantum potential. Physica A 388(6), 811–823 (2009)MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    Fiscaletti, D.: The geometrodynamic nature of the quantum potential. Ukrainian J. Phys. 57(5), 560–572 (2012)Google Scholar
  35. 35.
    Novello, M., Salim, J.M., Falciano, F.T.: On a geometrical description of quantum mechanics. Int. J. Geom. Meth. Mod. Phys. 8(1), 87–98 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Sbitnev, V. I.: Bohmian split of the Schrödinger equation onto two equations describing evolution of real functions. Kvantovaya Magiya, 5(1), 1101–1111. http://quantmagic.narod.ru/volumes/VOL512008/p1101.html (2008)
  37. 37.
    Sbitnev, V.I.: Bohmian trajectories and the path integral paradigm. Complexified Lagrangian mechanics. Int. J. Bifurcat. Chaos 19(7), 2335–2346 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Brillouin, L.: Science and Information Theory, 2 Reprint edn. Dover Publications, New York (17 July 2013) (1962)Google Scholar
  39. 39.
    Bittner, E.R.: Quantum tunneling dynamics using hydrodynamic trajectories. J. Chem. Phys. 112, 9703 (2000)CrossRefADSGoogle Scholar
  40. 40.
    Fiscaletti, D.: The quantum entropy as an ultimate visiting card of the de Broglie-Bohm theory. Ukrainian J. Phys. 57(9), 946–963 (2012)Google Scholar
  41. 41.
    Fiscaletti, D.: A geometrodynamic entropic approach to Bohm’s quantum potential and the link with Feynman’s path integrals formalism. Quantum Matter 2(2), 122–131 (2013)CrossRefGoogle Scholar
  42. 42.
    Grosche, C.: Path integrals, hyperbolic spaces, and Selberg trace formulae. World Scientific, Singapore (1996)CrossRefzbMATHGoogle Scholar
  43. 43.
    Bohm, D.: Space, time and quantum theory understood in terms of a discrete structure process. In: Proceedings of the International Conference on Elementary Particles, Kyoto, pp. 252–287 (1965)Google Scholar
  44. 44.
    Bohm, D.: Quantum theory as an indication of a new order in physics part A: the development of new orders as shown through the history of physics. Found. Phys. 1(4), 359–371 (1971)Google Scholar
  45. 45.
    Bohm, D.: Quantum theory as a new order in physics, part B: implicate and explicate order in physical law. Found. Phys. 3(2), 139–155 (1973)CrossRefADSGoogle Scholar
  46. 46.
    Bohm, D.: Wholeness and the Implicate Order. Routledge, London (1980)Google Scholar
  47. 47.
    Wheeler, John A.: Information, physics, quantum: the search for links. In: Zurek, W. (ed.) Complexity, Entropy, and the Physics of Information. Addison-Wesley, Redwood City (1990)Google Scholar
  48. 48.
    Cartier, C.: A mad day’s work: from Grothendieck to Connes and Kontsevich: the evolution of concepts of space and symmetry. Bull. Am. Math. Soc. 38, 389–408 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Hiley, B.J.: Non-commutative geometry, the Bohm interpretation and the mind-matter relationship. AIP Conf. Proc. 573(1), 77 (2001)CrossRefADSGoogle Scholar
  50. 50.
    Hiley, B.J., Fernandes, M.: Process and time. In: Atmanspacher, H., Ruhnau, E. (eds.) Time, Temporality, and Now, pp. 365–382. Springer, Berlin (1997)CrossRefGoogle Scholar
  51. 51.
    Hiley, B.J., Monk, N.: A unified algebraic approach to quantum theory. Found. Phys. Lett. 11(4), 371–377 (1998)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Brown, M.R., Hiley, B.J.: Schrödinger revisited: an algebraic approach. arXiv: quant-ph/0005026 (2000)Google Scholar
  53. 53.
    Hiley, B. J.: From the Heisenberg picture to Bohm: a new perspective on active information and its relation to Shannon information. In: Khrennikov, A. (ed.) Proceedings of Conference Quantum Theory: Reconsideration of Foundations, pp. 141–162. Växjo University Press, Växjo (2002)Google Scholar
  54. 54.
    Hiley, B.J.: Algebraic quantum mechanics, algebraic spinors and Hilbert space. In: Bowden K.G. (ed.) Boundaries, pp. 149–186. Scientific Aspects of ANPA 24, ANPA, London (2003)Google Scholar
  55. 55.
    De Gosson, M.: The Principles of Newtonian and Quantum Mechanics. Imperial College Press, London (2001)CrossRefzbMATHGoogle Scholar
  56. 56.
    Hiley, B.J.: Non-commutative quantum geometry: a reappraisal of the Bohm approach to quantum theory. In: Elitzur, A., Dolev, S., Kolenda, N. (eds.) Quo Vadis Quantum Mechanics?, pp. 306–324. Springer, Berlin (2005)Google Scholar
  57. 57.
    Licata, I.: Emergence and computation at the edge of classical and quantum systems. In: Licata, I., Sakaji A. (Eds.) Physics of Emergence and Organization. World Scientific, Singapore, (2008)Google Scholar
  58. 58.
    Hiley, B. J.: Process, distinction, groupoids and Clifford algebras: an alternative view of the quantum formalism. In: Coecke B. (ed.) New Structures for Physics. Springer Lecture Notes in Physics, Berlin (2009)Google Scholar
  59. 59.
    Hiley, B.J.: The Clifford algebra approach to quantum mechanics A: the Schrödinger and Pauli particles. arXiv:1011.4031 [math-ph] (2010)Google Scholar
  60. 60.
    Takabayashi, T.: Relativistic hydrodynamics of the Dirac matter. Progress Theor. Phys. Suppl. 4, 2–80 (1957)CrossRefADSGoogle Scholar
  61. 61.
    Hiley, B.J., Callaghan, R.E.: Clifford algebras and the Dirac-Bohm quantum Hamilton-Jacobi equation. Found. Phys. 42, 192–208 (2012)MathSciNetCrossRefADSzbMATHGoogle Scholar
  62. 62.
    Hiley, B.: On the relationship between the Moyal algebra and the quantum operator algebra of von Neumann. arXiv:1211.2098 [quant-ph] (2012)Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute for Scientific MethodologyPalermoItaly

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