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Simulation of the Hydrogen Ground State in Stochastic Electrodynamics-2: Inclusion of Relativistic Corrections

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In a recent paper the authors studied numerically the hydrogen ground state in stochastic electrodynamics (SED) within the the non-relativistic approximation. In quantum theory the leading non-relativistic corrections to the ground state energy dominate the Lamb shift related to the photon cloud that should cause the quantum-like behaviour of SED. The present work takes these corrections into account in the numerical modelling. It is found that they have little effect; the self-ionisation that occurs without them remains present. It is speculated that the point-charge approximation for the electron is the cause of the failure.

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References

  1. de la Peña, L., Cetto, A.M.: The Quantum Dice: An Introduction to Stochastic Electrodynamics. Kluwer, Dordrecht (1996)

    Book  Google Scholar 

  2. de la Peña, L., Cetto, A.M., Valdés Hernández, A.: The Emerging Quantum: The Physics Behind Quantum Mechanics. Springer, Berlin (2014)

    Google Scholar 

  3. Nieuwenhuizen, ThM: Is the contextuality loophole fatal for the derivation of Bell inequalities? Found. Phys. 41, 580 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  4. de la Peña, L., Cetto, A.M., Valdés-Hernándes, A.: Quantum behaviour derived as an essentially stochastic behaviour. Phys. Scr. T 151, 014008 (2012)

    Article  ADS  Google Scholar 

  5. França, H.M., Kamimura, A., Barreto, G.A.: The Schrödinger equation, the zero-point electromagnetic radiation and the photoelectric effect. (2012) arXiv:1207.4076

  6. Cetto, A.M., de la Peña, L.: Radiative corrections for the matter-zeropoint field system: establishing contact with quantum electrodynamics. Phys. Scr. T 151, 014009 (2012)

    Article  ADS  Google Scholar 

  7. Nieuwenhuizen, T.M.: The Pullback mechanism in stochastic electrodynamics. AIP Conf. Proc. 962, 148 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  8. Nieuwenhuizen, T.M.: A subquantum arrow of time. J. Phys. 504, 012008 (2014)

    Google Scholar 

  9. Claverie, P., Soto, F.: Nonrecurrence of the stochastic process for the hydrogen atom problem in stochastic electrodynamics. J. Math. Phys. 23, 753 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  10. Puthoff, H.E.: Ground state of hydrogen as a zero-point-fluctuation-determined state. Phys. Rev. D 35, 3266 (1987)

    Article  ADS  Google Scholar 

  11. Cole, D.C., Zou, Y.: Quantum mechanical ground state of hydrogen obtained from classical electrodynamics. Phys. Lett. A 317, 14 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Nieuwenhuizen, Th. M., and Liska, M. T. P.: Simulation of the hydrogen ground state in stochastic electrodynamics, (2014). Phys. Scr. to appear (2015). arXiv:1502.06856

  13. Nieuwenhuizen, T.M.: Classical phase space density for the relativistic hydrogen atom. AIP Conf. Proc. 810, 198 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  14. Boyer, T.H.: Comments on Cole and Zou’s calculation of the hydrogen ground state in classical physics. Found. Phys. Lett. 16, 613 (2003)

    Article  Google Scholar 

  15. Boyer, T.H.: Unfamiliar trajectories for a relativistic particle in a Kepler or Coulomb potential. Am. J. Phys. 72, 992 (2004)

    Article  MATH  ADS  Google Scholar 

  16. de la Peña, L., Jáuregui, A.: Stochastic electrodynamics for the free particle. J. Math. Phys. 24, 2751 (1983)

    Article  MathSciNet  ADS  Google Scholar 

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Acknowledgments

It is a pleasure to thank Erik van Heusden for discussion.

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Institute for Theoretical Physics, P.O. Box 94485, 1098 XH, Amsterdam, The Netherlands

    Theodorus M. Nieuwenhuizen & Matthew T. P. Liska

  2. International Institute of Physics, UFRG, Av. O. Gomes de Lima, 1722, Natal, RN, 59078-400, Brazil

    Theodorus M. Nieuwenhuizen

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  1. Theodorus M. Nieuwenhuizen
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  2. Matthew T. P. Liska
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Correspondence to Theodorus M. Nieuwenhuizen.

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Nieuwenhuizen, T.M., Liska, M.T.P. Simulation of the Hydrogen Ground State in Stochastic Electrodynamics-2: Inclusion of Relativistic Corrections. Found Phys 45, 1190–1202 (2015). https://doi.org/10.1007/s10701-015-9919-0

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  • DOI: https://doi.org/10.1007/s10701-015-9919-0

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