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A Short Survey on a “Strange” Potential

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Quantum Potential: Physics, Geometry and Algebra

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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.

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References

  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. 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. de Broglie, L.: The reinterpretation of quantum mechanics. Found. Phys. 1, 5 (1970)

    Article  ADS  Google Scholar 

  4. Pauli, W.: Électrons et photons: Rapports et discussions du cinquieme conseil de physique, pp. 280–282. Gauthier-Villars, Paris (1928)

    Google Scholar 

  5. Bohm, D.: A new suggested interpretation of quantum theory in terms of hidden variables. Part I. Phys. Rev. 85, 166–179 (1952)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Bohm, D.: A new suggested interpretation of quantum theory in terms of hidden variables. Part II. Phys. Rev. 85, 180–193 (1952)

    Article  MathSciNet  ADS  Google Scholar 

  7. Bohm, D.: Proof that probability density approaches |Ψ|2 in causal interpretation of the quantum theory. Phys. Rev. 89, 458–466 (1953)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  9. Bohm, D., Hiley, B., Kaloyerou, P.N.: An ontological basis for quantum theory. Phys. Rep. 144, 321–375 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  10. Bohm, D., Hiley, B.: The Undivided Universe. Routledge, London (1993)

    Google Scholar 

  11. Philippidis, C., Dewdney, C., Hiley, B.: Quantum interference and the quantum potential. Nuovo Cimento B 52(1), 15–28 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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. 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. Dürr, D., Goldstein, S., Zanghi, N.: Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67, 843–907 (1992)

    Article  ADS  MATH  Google Scholar 

  16. Bohm, D.: Quantum Theory. Routledge, London (1951)

    Google Scholar 

  17. Goldstein, S., Berndl, S., Daumer, M., Dürr, D., Zanghì, N.: A survey of Bohmian mechanics. Il Nuovo Cimento 110B, 737–750 (1995)

    ADS  Google Scholar 

  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. Goldstein, S.: Bohmian mechanics and the quantum revolution. Synthese 107, 145–165 (1996)

    Article  MathSciNet  Google Scholar 

  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. 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. Allori, V., Zanghì, N.: What is Bohmian mechanics. Intern. J. Theor. Phys. 43, 1743–1755 (2004)

    Article  Google Scholar 

  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. 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. 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. 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. 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. Esfeld, M., Lazarovici, D., Hubert, M., Dürr, D.: The ontology of Bohmian mechanics. http://philsci-archive.pitt.edu/9381 (2013)

  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)

    MathSciNet  Google Scholar 

  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. 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. Grössing, G.: The vacuum fluctuation theorem: exact Schrödinger equation via nonequilibrium thermodynamics. Phys. Lett. A 372, 4556 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Grössing, G.: On the thermodynamic origin of the quantum potential. Physica A 388(6), 811–823 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  34. Fiscaletti, D.: The geometrodynamic nature of the quantum potential. Ukrainian J. Phys. 57(5), 560–572 (2012)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Sbitnev, V.I.: Bohmian trajectories and the path integral paradigm. Complexified Lagrangian mechanics. Int. J. Bifurcat. Chaos 19(7), 2335–2346 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. Brillouin, L.: Science and Information Theory, 2 Reprint edn. Dover Publications, New York (17 July 2013) (1962)

    Google Scholar 

  39. Bittner, E.R.: Quantum tunneling dynamics using hydrodynamic trajectories. J. Chem. Phys. 112, 9703 (2000)

    Article  ADS  Google Scholar 

  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. 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)

    Article  Google Scholar 

  42. Grosche, C.: Path integrals, hyperbolic spaces, and Selberg trace formulae. World Scientific, Singapore (1996)

    Book  MATH  Google Scholar 

  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. 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. 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)

    Article  ADS  Google Scholar 

  46. Bohm, D.: Wholeness and the Implicate Order. Routledge, London (1980)

    Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  49. Hiley, B.J.: Non-commutative geometry, the Bohm interpretation and the mind-matter relationship. AIP Conf. Proc. 573(1), 77 (2001)

    Article  ADS  Google Scholar 

  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)

    Chapter  Google Scholar 

  51. Hiley, B.J., Monk, N.: A unified algebraic approach to quantum theory. Found. Phys. Lett. 11(4), 371–377 (1998)

    Article  MathSciNet  Google Scholar 

  52. Brown, M.R., Hiley, B.J.: Schrödinger revisited: an algebraic approach. arXiv: quant-ph/0005026 (2000)

    Google Scholar 

  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. 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. De Gosson, M.: The Principles of Newtonian and Quantum Mechanics. Imperial College Press, London (2001)

    Book  MATH  Google Scholar 

  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. 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. 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. 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. Takabayashi, T.: Relativistic hydrodynamics of the Dirac matter. Progress Theor. Phys. Suppl. 4, 2–80 (1957)

    Article  ADS  Google Scholar 

  61. Hiley, B.J., Callaghan, R.E.: Clifford algebras and the Dirac-Bohm quantum Hamilton-Jacobi equation. Found. Phys. 42, 192–208 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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 

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  1. Institute for Scientific Methodology, Palermo, Italy

    Ignazio Licata & Davide Fiscaletti

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  1. Ignazio Licata
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  2. Davide Fiscaletti
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Licata, I., Fiscaletti, D. (2014). A Short Survey on a “Strange” Potential. In: Quantum Potential: Physics, Geometry and Algebra. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-00333-7_1

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