Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2013, Article ID 296836, 8 pages
http://dx.doi.org/10.1155/2013/296836
Research Article

The Effects of Minimal Length in Entropic Force Approach

Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424, India

Received 17 August 2013; Accepted 3 October 2013

Academic Editor: George Siopsis

Copyright © 2013 Barun Majumder. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. D. Bekenstein, “Black holes and the second law,” Lettere Al Nuovo Cimento, vol. 4, no. 15, pp. 737–740, 1972. View at Google Scholar
  2. J. D. Bekenstein, “Generalized second law of thermodynamics in black-hole physics,” Physical Review D, vol. 9, no. 12, pp. 3292–3300, 1974. View at Publisher · View at Google Scholar
  3. J. D. Bekenstein, “Black holes and entropy,” Physical Review D, vol. 7, no. 8, pp. 2333–2346, 1973. View at Publisher · View at Google Scholar · View at Scopus
  4. S. W. Hawking, “Black hole explosions?” Nature, vol. 248, no. 5443, pp. 30–31, 1974. View at Publisher · View at Google Scholar · View at Scopus
  5. S. W. Hawking, “Particle creation by black holes,” Communications in Mathematical Physics, vol. 43, pp. 199–220, 1975. View at Publisher · View at Google Scholar
  6. A. D. Sakharov, “Vacuum quantum fluctuations in curved space and the theory of gravitation,” General Relativity and Gravitation, vol. 32, no. 2, pp. 365–367, 2000, Translated from Doklady Akademii Nauk SSSR, vol. 177, No. 1, pp. 7071, November 1967. View at Publisher · View at Google Scholar
  7. T. Jacobson, “Thermodynamics of spacetime: the Einstein equation of state,” Physical Review Letters, vol. 75, no. 7, pp. 1260–1263, 1995. View at Publisher · View at Google Scholar · View at Scopus
  8. T. Padmanabhan, “Classical and quantum thermodynamics of horizons in spherically symmetric spacetimes,” Classical and Quantum Gravity, vol. 19, no. 21, pp. 5387–5408, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. C. Eling, R. Guedens, and T. Jacobson, “Nonequilibrium thermodynamics of spacetime,” Physical Review Letters, vol. 96, no. 12, Article ID 121301, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. T. Padmanabhan, “Thermodynamical aspects of gravity: new insights,” Reports on Progress in Physics, vol. 73, no. 4, Article ID 046901, 2010. View at Publisher · View at Google Scholar
  11. M. Akbar and R. G. Cai, “Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe,” Physical Review D, vol. 75, no. 8, Article ID 084003, 9 pages, 2007. View at Publisher · View at Google Scholar
  12. R. G. Cai and S. P. Kim, “First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe,” Journal of High Energy Physics, vol. 02, p. 050, 2005. View at Publisher · View at Google Scholar
  13. A. Sheykhi, B. Wang, and R. G. Cai, “Thermodynamical properties of apparent horizon in warped DGP braneworld,” Nuclear Physics B, vol. 779, no. 1-2, pp. 1–12, 2007. View at Publisher · View at Google Scholar
  14. R. G. Cai and L. M. Cao, “Thermodynamics of apparent horizon in brane world scenario,” Nuclear Physics B, vol. 785, no. 1-2, pp. 135–148, 2007. View at Publisher · View at Google Scholar
  15. A. Sheykhi, B. Wang, and R. G. Cai, “Deep connection between thermodynamics and gravity in Gauss-Bonnet braneworlds,” Physical Review D, vol. 76, Article ID 023515, 5 pages, 2007. View at Publisher · View at Google Scholar
  16. A. Sheykhi and B. Wang, “Generalized second law of thermodynamics in Gauss-Bonnet braneworld,” Physics Letters B, vol. 678, no. 5, pp. 434–737, 2009. View at Publisher · View at Google Scholar
  17. E. P. Verlinde, “On the origin of gravity and the laws of Newton,” Journal of High Energy Physics, vol. 2011, article 29, 2011. View at Publisher · View at Google Scholar
  18. T. Padmanabhan, “Equipartition of energy in the horizon degrees of freedom and the emergence of gravity,” Modern Physics Letters A, vol. 25, no. 14, pp. 1129–1136, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Smolin, “Newtonian gravity in loop quantum gravity,” http://arxiv.org/abs/1001.3668.
  20. R. G. Cai, L. M. Cao, and N. Ohta, “Friedmann equations from entropic force,” Physical Review D, vol. 81, no. 6, Article ID 061501(R), 4 pages, 2010. View at Publisher · View at Google Scholar
  21. A. Sheykhi, “Entropic corrections to Friedmann equations,” Physical Review D, vol. 81, no. 10, Article ID 104011, 4 pages, 2010. View at Publisher · View at Google Scholar
  22. A. Sheykhi and S. H. Hendi, “Power-law entropic corrections to Newton’s law and Friedmann equations,” Physical Review D, vol. 84, no. 4, Article ID 044023, 8 pages, 2011. View at Publisher · View at Google Scholar
  23. R. K. Kaul and P. Majumdar, “Logarithmic correction to the Bekenstein-Hawking entropy,” Physical Review Letters, vol. 84, no. 23, pp. 5255–5257, 2000. View at Google Scholar · View at Scopus
  24. A. J. M. Medved and E. C. Vagenas, “When conceptual worlds collide: the generalized uncertainty principle and the Bekenstein-Hawking entropy,” Physical Review D, vol. 70, no. 12, Article ID 124021, 5 pages, 2004. View at Publisher · View at Google Scholar
  25. S. Das, P. Majumdar, and R. K. Bhaduri, “General logarithmic corrections to black-hole entropy,” Classical and Quantum Gravity, vol. 19, no. 9, p. 2355, 2002. View at Publisher · View at Google Scholar
  26. M. Domagala and J. Lewandowski, “Black-hole entropy from quantum geometry,” Classical and Quantum Gravity, vol. 21, no. 22, p. 5233, 2004. View at Publisher · View at Google Scholar
  27. A. Chatterjee and P. Majumdar, “Universal canonical black hole entropy,” Physical Review Letters, vol. 92, no. 14, Article ID 141301, 2004. View at Publisher · View at Google Scholar · View at Scopus
  28. G. Amelino-Camelia, M. Arzano, and A. Procaccini, “Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law,” Physical Review D, vol. 70, no. 10, Article ID 107501, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. K. A. Meissner, “Black-hole entropy in loop quantum gravity,” Classical and Quantum Gravity, vol. 21, no. 22, pp. 5245–5251, 2004. View at Publisher · View at Google Scholar · View at Scopus
  30. C. A. Mead, “Possible connection between gravitation and fundamental length,” Physical Review, vol. 135, no. 3B, pp. B849–B862, 1964. View at Publisher · View at Google Scholar · View at Scopus
  31. D. Amati, M. Ciafaloni, and G. Veneziano, “Can spacetime be probed below the string size?” Physics Letters B, vol. 216, no. 1-2, pp. 41–47, 1989. View at Google Scholar · View at Scopus
  32. M. Maggiore, “The algebraic structure of the generalized uncertainty principle,” Physics Letters B, vol. 319, no. 1–3, pp. 83–86, 1993. View at Google Scholar · View at Scopus
  33. S. Hossenfelder, M. Bleicher, S. Hofmann, J. Ruppert, S. Scherer, and H. Stöcker, “Signatures in the Planck regime,” Physics Letters B, vol. 575, no. 1-2, pp. 85–99, 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. C. Bambi and F. R. Urban, “Natural extension of the generalized uncertainty principle,” Classical and Quantum Gravity, vol. 25, no. 9, Article ID 095006, 2008. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Kempf, G. Mangano, and R. B. Mann, “Hilbert space representation of the minimal length uncertainty relation,” Physical Review D, vol. 52, no. 2, pp. 1108–1118, 1995. View at Publisher · View at Google Scholar · View at Scopus
  36. F. Brau, “Minimal length uncertainty relation and the hydrogen atom,” Journal of Physics A, vol. 32, no. 44, pp. 7691–7696, 1999. View at Publisher · View at Google Scholar · View at Scopus
  37. J. Magueijo and L. Smolin, “Lorentz invariance with an invariant energy scale,” Physical Review Letters, vol. 88, no. 19, pp. 1904031–1904034, 2002. View at Google Scholar · View at Scopus
  38. M. Maggiore, “A generalized uncertainty principle in quantum gravity,” Physics Letters B, vol. 304, no. 1-2, pp. 65–69, 1993. View at Google Scholar · View at Scopus
  39. F. Scardigli, “Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment,” Physics Letters B, vol. 452, no. 1-2, pp. 39–44, 1999. View at Google Scholar · View at Scopus
  40. J. L. Cortes and J. Gamboa, “Quantum uncertainty in doubly special relativity,” Physical Review D, vol. 71, no. 6, Article ID 065015, 4 pages, 2005. View at Publisher · View at Google Scholar
  41. G. M. Hossain, V. Husain, and S. S. Seahra, “Background-independent quantization and the uncertainty principle,” Classical and Quantum Gravity, vol. 27, no. 16, Article ID 165013, 2010. View at Publisher · View at Google Scholar · View at Scopus
  42. A. F. Ali, S. Das, and E. C. Vagenas, “Discreteness of space from the generalized uncertainty principle,” Physics Letters B, vol. 678, no. 5, pp. 497–499, 2009. View at Publisher · View at Google Scholar · View at Scopus
  43. S. Das and E. C. Vagenas, “Universality of quantum gravity corrections,” Physical Review Letters, vol. 101, Article ID 221301, 4 pages, 2008. View at Publisher · View at Google Scholar
  44. G. Amelino-Camelia, M. Arzano, Y. Ling, and G. Mandanici, “Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles,” Classical and Quantum Gravity, vol. 23, no. 7, pp. 2585–2606, 2006. View at Publisher · View at Google Scholar · View at Scopus
  45. B. Majumder, “Black hole entropy and the modified uncertainty principle: a heuristic analysis,” Physics Letters B, vol. 703, no. 4, pp. 402–405, 2011. View at Publisher · View at Google Scholar · View at Scopus
  46. B. Majumder, “Black hole entropy with minimal length in tunneling formalism,” General Relativity and Gravitation, vol. 45, no. 11, pp. 2403–2414, 2013. View at Google Scholar
  47. I. Pikovski, M. R. Vanner, M. Aspelmeyer et al., “Probing Planck-scale physics with quantum optics,” Nature Physics, vol. 8, pp. 393–397, 2012. View at Publisher · View at Google Scholar
  48. I. Pikovski, M. R. . Vanner, M. Aspelmeyer, M. Kim, and C. Brukner, “Probing Planck-scale physics with quantum optics,” Nature Physics, vol. 8, p. 393, 2012. View at Publisher · View at Google Scholar
  49. A. F. Ali, S. Das, and E. C. Vagenas, “Proposal for testing quantum gravity in the lab,” Physical Review D, vol. 84, Article ID 044013, p. 10, 2011. View at Publisher · View at Google Scholar
  50. S. Das and E. C. Vagenas, “Universality of quantum gravity corrections,” Physical Review Letters, vol. 101, Article ID 221301, 4 pages, 2008. View at Publisher · View at Google Scholar
  51. J. D. Bekenstein, “Is a tabletop search for Planck scale signals feasible?” Physical Review D, vol. 86, Article ID 124040, 9 pages, 2012. View at Publisher · View at Google Scholar
  52. J. D. Bekenstein, “Can quantum gravity be exposed in the laboratory? A tabletop experiment to reveal the quantum foam,” http://arxiv.org/abs/1301.4322.
  53. L. Modesto and A. Randono, “Entropic corrections to Newton’s law,” http://arxiv.org/abs/1003.1998.
  54. S. H. Hendi and A. Sheykhi, “Entropic corrections to Einstein equations,” Physical Review D, vol. 83, no. 8, Article ID 084012, 2011. View at Publisher · View at Google Scholar · View at Scopus
  55. S. Das, S. Shankaranarayanan, and S. Sur, “Power-law corrections to entanglement entropy of horizons,” Physical Review D, vol. 77, no. 6, Article ID 064013, 2008. View at Publisher · View at Google Scholar · View at Scopus
  56. N. Radicella and D. Pavon, “The generalized second law in universes with quantum corrected entropy relations,” Physics Letters B, vol. 691, no. 3, p. 126, 2010. View at Publisher · View at Google Scholar
  57. K. Nozari, P. Pedram, and M. Molkara, “Minimal length, maximal momentum and the entropic force law,” International Journal of Theoretical Physics, vol. 51, no. 4, pp. 1268–1275, 2012. View at Publisher · View at Google Scholar · View at Scopus
  58. M. Milgrom, “A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis,” Astrophysical Journal, vol. 270, pp. 365–370, 1983. View at Google Scholar
  59. M. Milgrom, “A modification of the Newtonian dynamics—implications for galaxies,” Astrophysical Journal, vol. 270, pp. 371–389, 1983. View at Publisher · View at Google Scholar
  60. M. Milgrom, “A modification of the Newtonian dynamics—implications for galaxy systems,” Astrophysical Journal, vol. 270, pp. 384–389, 1983. View at Publisher · View at Google Scholar
  61. R. H. Sanders and S. S. McGaugh, “Modified Newtonian dynamics as an alternative to dark matter,” Annual Review of Astronomy and Astrophysics, vol. 40, pp. 263–317, 2002. View at Publisher · View at Google Scholar · View at Scopus
  62. C. Gao, “Modified entropic force,” Physical Review D, vol. 81, no. 8, Article ID 087306, 4 pages, 2010. View at Publisher · View at Google Scholar
  63. X. Li and Z. Chang, “Debye entropic force and modified Newtonian dynamics,” Communications in Theoretical Physics, vol. 55, no. 4, pp. 733–736, 2011. View at Publisher · View at Google Scholar · View at Scopus
  64. V. V. Kiselev and S. A. Timofeev, “The holographic screen at low temperatures,” Modern Physics Letters A, vol. 26, no. 2, pp. 109–118, 2011. View at Publisher · View at Google Scholar · View at Scopus
  65. J. A. Neto, “Nonhomogeneous cooling, entropic gravity and MOND theory,” International Journal of Theoretical Physics, vol. 50, no. 11, pp. 3552–3559, 2011. View at Publisher · View at Google Scholar · View at Scopus
  66. L. Randall and R. Sundrum, “An alternative to compactification,” Physical Review Letters, vol. 83, no. 23, pp. 4690–4693, 1999. View at Google Scholar · View at Scopus
  67. P. Callin and F. Ravndal, “Higher order corrections to the Newtonian potential in the Randall-Sundrum model,” Physical Review D, vol. 70, no. 10, Article ID 104009, pp. 1–104009, 2004. View at Publisher · View at Google Scholar · View at Scopus
  68. A. F. Ali and A. N. Tawfik, “Modified Newton’s law of gravitation due to minimal length in quantum gravity,” Advances in High Energy Physics, vol. 2013, Article ID 126528, 7 pages, 2013. View at Publisher · View at Google Scholar
  69. S.-Q. Yang, B.-F. Zhan, Q.-L. Wang et al., “Test of the gravitational inverse square law at millimeter ranges,” Physical Review Letters, vol. 108, no. 8, Article ID 081101, 5 pages, 2012. View at Publisher · View at Google Scholar
  70. C. D. Hoyle, D. J. Kapner, B. R. Heckel et al., “Submillimeter tests of the gravitational inverse-square law,” Physical Review D, vol. 70, no. 4, Article ID 042004, 31 pages, 2004. View at Publisher · View at Google Scholar
  71. D. J. Kapner, T. S. Cook, E. G. Adelberger et al., “Tests of the gravitational inverse-square law below the dark-energy length scale,” Physical Review Letters, vol. 98, no. 2, Article ID 021101, 2007. View at Publisher · View at Google Scholar · View at Scopus
  72. E. G. Adelberger, B. R. Heckel, S. Hoedl, C. D. Hoyle, D. J. Kapner, and A. Upadhye, “Particle-physics implications of a recent test of the gravitational inverse-square law,” Physical Review Letters, vol. 98, no. 13, Article ID 131104, 4 pages, 2007. View at Publisher · View at Google Scholar
  73. H. Grote, “The status of GEO 600,” Classical and Quantum Gravity, vol. 25, no. 11, Article ID 114043, 2008. View at Publisher · View at Google Scholar
  74. B. P. Abbott, R. Abbott, R. Adhikari et al., “LIGO: the laser interferometer gravitational-wave observatory,” Reports on Progress in Physics, vol. 72, no. 7, Article ID 076901, 2009. View at Publisher · View at Google Scholar
  75. G. A. Palma, “On Newton’s law in supersymmetric braneworld models,” Journal of High Energy Physics, vol. 2007, p. 091, 2007. View at Publisher · View at Google Scholar
  76. J. F. Donoghue, “General relativity as an effective field theory: the leading quantum corrections,” Physical Review D, vol. 50, p. 3874, 1994. View at Publisher · View at Google Scholar
  77. N. E. J. Bjerrum-Bohr, J. F. Donoghue, and B. R. Holstein, “Quantum gravitational corrections to the nonrelativistic scattering potential of two masses,” Physical Review D, vol. 67, Article ID 084033, 2003. View at Publisher · View at Google Scholar
  78. I. B. Khriplovich and G. G. Kirilin, “Quantum power correction to the Newton law,” Journal of Experimental and Theoretical Physics, vol. 95, pp. 981–986, 2002. View at Publisher · View at Google Scholar
  79. J. F. Donoghue, “The effective field theory treatment of quantum gravity,” http://arxiv.org/abs/1209.3511.
  80. J. F. Donoghue, “Leading quantum correction to the Newtonian potential,” Physical Review Letters, vol. 72, no. 19, pp. 2996–2999, 1994. View at Publisher · View at Google Scholar · View at Scopus
  81. R. M. Wald, General Relativity, Chicago University Press, Chicago, Ill, USA, 1984.