Advertisement

Nonlocal generalized uncertainty principle and its implications in gravity and entropic Verlinde holographic approach

  • Rami Ahmad El-NabulsiEmail author
Regular Paper

Abstract

Recently, a nonlocal generalized uncertainty principle was derived based on the new notion of quantum acceleratum operator within the framework of nonlocal-maximal quantum mechanics. In this study, we discuss some of its properties and some of its implications in Newtonian gravity theory and Verlinde’s entropic holographic approach. A number of features were revealed; in particular, the emergence of a logarithmic correction to the gravitational Newtonian potential, a minimum energy and a minimum mass which depend on the gravitational coupling constant. Based on the concept of holographic principle, Verlinde’s conjecture and equipartition rule, a quantized Newton’s force law of gravity for a particle of mass m gravitating around a Planck mass is derived.

Keywords

Nonlocal generalized uncertainty principle Gravity Verlinde’s entropic force 

Notes

Acknowledgements

The author is indebted to the anonymous referees for their useful comments and valuable suggestions.

References

  1. 1.
    Kempf, A., Mangano, G., Mann, R.B.: Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52, 1108 (1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Nozari, K., Pedram, P.: Minimal length and bouncing particle spectrum. Europhys. Lett. 92, 50013 (2010)CrossRefGoogle Scholar
  3. 3.
    Maggiore, M.: Quantum groups, gravity and the generalized uncertainty principle. Phys. Rev. D 49, 5182 (1994)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kragh, H.: Heisenberg’s lattice world: the 1930 theory sketch, American. J. Phys. 63(1995), 595–605 (1930)Google Scholar
  5. 5.
    Heisenberg, W., Pauli, W.: Zur Quantendynamik der Wellenfelder. Zeitsch. Phys. 56, 1–61 (1929)CrossRefzbMATHGoogle Scholar
  6. 6.
    Chang, L.N., Lewis, Z., Minic, D., Takeuchi, T.: On the minimal length uncertainty relation and the foundations of string theory. Adv. High Energy Phys. 2011, 30 (2011) (Article ID 493514)Google Scholar
  7. 7.
    Suykens, J.A.K.: Extending Newton’s law from nonlocal-in-time kinetic energy. Phys. Lett. A 373, 1201–1211 (2009)CrossRefzbMATHGoogle Scholar
  8. 8.
    Caianiello, E.R.: Is there a maximal acceleration. Lett. Nuovo Cimento 32, 65–70 (1981)CrossRefGoogle Scholar
  9. 9.
    Caianiello, E.R.: Geometry from quantum mechanics. Nuovo Cimento B 59, 350–366 (1980). 13MathSciNetCrossRefGoogle Scholar
  10. 10.
    Caianiello, E.R.: Quantum and other physics as systems theory. Riv. Nuovo Cimento 15, 1–65 (1992)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Caianiello, E.R.: Maximal acceleration as a consequence of Heisenberg’s uncertainty relations. Lett. Nuovo Cimento 41, 370–372 (1984)MathSciNetCrossRefGoogle Scholar
  12. 12.
    El-Nabulsi, R.A.: On maximal acceleration and quantum acceleratum operator in quantum mechanics. Quant. Stud. Math. Found. 5, 543–550 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    El-Nabulsi, R.A.: Nonlocal uncertainty and its implications in quantum mechanics at ultramicroscopic scales. Quant. Stud. Math. Found. (2018).  https://doi.org/10.1007/s40509-018-0170-1
  14. 14.
    Ali, A.F., Moussa, M.: Towards thermodynamics with generalized uncertainty relation. Adv. High Energy Phys. 2014, 7 (2014) (Article ID 629148)Google Scholar
  15. 15.
    Das, S., Vagenas, E.C.: Phenomenological implications of the generalized uncertainty principle. Can. J. Phys. 87, 233–240 (2009)CrossRefGoogle Scholar
  16. 16.
    Sprenger, M., Bleicher, M., Nicolini, P.: Neutrino oscillations as a novel probe for a minimal length. Class. Quantum Grav. 28, 235019 (2011)CrossRefzbMATHGoogle Scholar
  17. 17.
    Majumder, B., Sen, S.: Do the modified uncertainty principle and polymer quantization predict same physics? Phys. Lett. B 717, 291–294 (2012)CrossRefGoogle Scholar
  18. 18.
    Nozari, K., Saghafi, S.: Natural cutoffs and quantum tunneling from black hole horizon. J. High. Energ. Phys. 2012, 5 (2012)CrossRefGoogle Scholar
  19. 19.
    Nozari, K., Mehdipour, S.H.: Implications of minimal length scale on the statistical mechanics of ideal gas. Chaos, Solitons Fractals 32, 1637–1644 (2007)CrossRefGoogle Scholar
  20. 20.
    Nozari, K., Fazlpour, B.: Generalized uncertainty principle, modified dispersion relations and the early universe thermodynamics. Gen. Rel. Grav. 38, 1661–1679 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    McCulloch, M.C.: Gravity from the uncertainty relation. Astrophys. Space Sci. 349, 957–959 (2014)CrossRefGoogle Scholar
  22. 22.
    McCulloch, M.C.: Quantized inertia from relativity and the uncertainty principle. Europhys. Lett. 115, 69001 (2016)CrossRefGoogle Scholar
  23. 23.
    Cadoni, M.: An Einstein-like theory of gravity with a non-Newtonian weak-field limit. Gen. Rel. Grav. 36, 2681–2688 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Fabris, J.C., Campos, J.P.: Spiral galaxies rotation curves with a logarithmic corrected Newtonian gravitational potential. Gen. Rel. Grav. 41, 93–104 (2009)CrossRefzbMATHGoogle Scholar
  25. 25.
    Iorio, L.: The post-Newtonian mean anomaly advance as further post-Keplerian parameter in pulsar binary systems. Astrophys. Space Sci. 312, 331–335 (2007)CrossRefGoogle Scholar
  26. 26.
    Ragos, O., Haranas, I., Gkigkitzis, I.: Effects in the anomalistic period of celestial bodies to a logarithmic correction to the Newtonian gravitational constant. Astrophys. Space Sci. 345, 67–72 (2013)CrossRefGoogle Scholar
  27. 27.
    Quigg, C., Rosuer, J.L.: Quarkonium level spacing. Phys. Lett. B 71, 153–157 (1977)CrossRefGoogle Scholar
  28. 28.
    Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, San Francisco (1973)Google Scholar
  29. 29.
    Tucker, V.H.: Radiation Processes in Astrophysics. MIT Press, Cambridge (1975)Google Scholar
  30. 30.
    Hoyle, F., Burbidge, G., Narlikar, J.: A Different Approach to Cosmology. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  31. 31.
    Lake, M.J.: Which quantum theory must be reconciled with gravity? (and what does it mean for black holes?). Universe 2, 1–34 (2016)Google Scholar
  32. 32.
    He, X.-G., Ma, B.-Q.: Quantization of black holes. Mod. Phys. Lett. A 26, 2299–2304 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Verlinde, E.P.: On the origin of gravity and the laws of Newton. JHEP 1194, 029 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D 7, 2333 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Munkhammar, J.: Is holographic entropy and gravity the results of quantum mechanics? arXiv:1003.1262
  36. 36.
    Kamalov, T.F.: Model of extended mechanics and non-local hidden variables for quantum theory. J. Russ. Laser Res. 30, 466–471 (2009)CrossRefGoogle Scholar
  37. 37.
    Kamalov, T.F.: Axiomatization of mechanics. Quant. Comp. Comput. 11, 52–57 (2011)Google Scholar
  38. 38.
    Kamalov, T.F.: Classical and quantum-mechanical axioms with the higher time derivative formalism. J. Phys. Conf. Ser. 442, 012051 (2013). (4 pages)CrossRefGoogle Scholar
  39. 39.
    Kamalov, T.F.: Simulations the nuclear interaction. In: Proceed. of the 13th Lomonosov Conference on Elementary Particle Physics, 23–29 Aug 2007: Particle Physics on the Eve of LHC, pp. 439–442 (2009).  https://doi.org/10.1142/9789812837592_0076
  40. 40.
    Kamalov, T.F.: Physics of non-inertial reference frames. AIP Conf. Proc. 1316, 455–458 (2010)CrossRefGoogle Scholar

Copyright information

© Chapman University 2019

Authors and Affiliations

  1. 1.Mathematics and Physics Divisions, Athens Institute for Education and ResearchAthensGreece

Personalised recommendations