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International Journal of Theoretical Physics

, Volume 50, Issue 11, pp 3544–3551 | Cite as

The Klein-Gordon Equation in Machian Model

  • Bin Liu
  • Yun-Chuan Dai
  • Xian-Ru Hu
  • Jian-Bo Deng
Article

Abstract

The non-local Machian model is regarded as an alternative theory of gravitation which states that all particles in the Universe as a ‘gravitationally entangled’ statistical ensemble. It is shown that the Klein-Gordon equation can be derived within this Machian model of the universe. The crucial point of the derivation is the activity of the Machian energy background field which causing a fluctuation about the average momentum of a particle, the non-locality problem in quantum theory is addressed in this framework.

Keywords

Klein-Gordon equation Mach principle Quantum mechanics 

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References

  1. 1.
    Jacobson, T.: Phys. Rev. Lett. 75, 1260 (1995) MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Padmanabhan, T.: Class. Quantum Gravity 21, 4485 (2004) MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Padmanabhan, T.: Rep. Prog. Phys. 73, 046901 (2010) ADSCrossRefGoogle Scholar
  4. 4.
    Verlinde, E.P.: On the origin of gravity and the laws of Newton. arXiv:1001.0785 [hep-th]
  5. 5.
    Wang, T.: Phys. Rev. 81, 104045 (2010) Google Scholar
  6. 6.
    Banerjee, R., Majhi, B.R.: Phys. Rev. D 81, 124006 (2010) ADSCrossRefGoogle Scholar
  7. 7.
    Munkhammar, J.: Is holographic entropy and gravity the result of quantum mechanics? arXiv:1003.1262 [hep-th]
  8. 8.
    Liu, B., Dai, Y.C., Hu, X.R., Deng, J.B.: The modified wave function of test particle approaching holographic screen from entropy force. arXiv:1007.2941 [hep-th] (2010)
  9. 9.
    Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987) Google Scholar
  10. 10.
    Mashhoon, B.: Ann. Phys. (Leipz.) 17, 705 (2008) MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Mashhoon, B.: Ann. Phys. (Leipz.) 16, 57 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Deser, S., Woodard, R.P.: Phys. Rev. Lett. 663, 111301 (2007) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Capozziello, S., Elizalde, E., Nojiri, S., Odintsov, S.D.: Phys. Lett. B 671, 193 (2009) ADSCrossRefGoogle Scholar
  14. 14.
    Hehl, F.W., Mashhoon, B.: Phys. Rev. D 79, 064028 (2009) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Barbour, J., Pfister, H.: Mach’s Principle: From Newton’s Bucket to Quantum Gravity. Birkhäuser, Boston (1995). Einstein studies, Vol. 6 MATHGoogle Scholar
  16. 16.
    Gogberashvili, M.: Eur. Phys. J. C 54, 671 (2008) MathSciNetADSMATHCrossRefGoogle Scholar
  17. 17.
    Gogberashvili, M.: Eur. Phys. J. C 63, 317 (2009) MathSciNetADSMATHCrossRefGoogle Scholar
  18. 18.
    Gogberashvili, M.: arXiv:1008.2544 [gr-qc] (2010)
  19. 19.
    Nikolić, H.: Found. Phys. 37, 1563 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  20. 20.
    Grössing, G.: Physica A 388, 811 (2009) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Grössing, G.: Phys. Lett. A 372, 4556 (2008) MathSciNetADSMATHCrossRefGoogle Scholar
  22. 22.
    Grössing, G.: Found. Phys. Lett. 17, 343 (2004) MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Madelung, E.: Z. Phys. 40, 322 (1926) ADSGoogle Scholar
  24. 24.
    Nelson, E.: Phys. Rev. 150, 1079 (1966) ADSCrossRefGoogle Scholar
  25. 25.
    Hall, M.J.W., Reginatto, M.: Fortschr. Phys. 50, 646 (2002) MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Hall, M.J.W., Reginatto, M.: J. Phys. A 35, 3289 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Bohm, D.: Phys. Rev. 85, 166 (1952) MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Sciama, D.W.: Mon. Not. R. Astron. Soc. 113, 34 (1953) MathSciNetADSMATHGoogle Scholar
  29. 29.
    Sciama, D.W.: Sci. Am. 196, 99 (1957) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Bin Liu
    • 1
  • Yun-Chuan Dai
    • 1
  • Xian-Ru Hu
    • 1
  • Jian-Bo Deng
    • 1
  1. 1.Institute of Theoretical PhysicsLanzhou UniversityLanzhouPeople’s Republic of China

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