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Classical Charged Particle Models Derived from Complex Shift Methods

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Abstract

Extended charged objects embedded in complex space-time are proposed using the double-copy or complex shift method. Most of the objects studied are 3D strings in different shapes. The static-charged open string can be interpreted as purely electromagnetic. It exhibits the same relation between charge, mass, angular momentum, and magnetic moment as the Dirac equation and the Kerr-Newman metric. Its spin is purely electromagnetic, as is its mass. A gyromagnetic ratio of 2 is obtained. The fields in this case are multi-valued, and their singularities can be arranged to be on an unphysical Riemann sheet with a judicious selection of Riemann cut surfaces. The calculations of mass and angular momentum are done numerically using multi-precision algorithms included as a Python script. The mass calculation agrees with the measured electron mass. Particles for knotted or linked strings in 3 space dimensions are also proposed. A liquid drop model with complex shift is discussed. The multi-valued behavior of the solutions, related to that of the Kerr-Newman metric, can be thought of as the origin of the Einstein-Rosen bridge, and the conjectures that this is the origin of quantum entanglement, ER=EPR, is therefore supported in this theory. So we have here a classical theory that has some properties of quantum mechanics. Hopefully it can offer a new phenomenological application of string theory as a semiclassical model for elementary particles, nuclei, and solitons in condensed matter, fluids, and gases.

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References

  1. Lynden-Bell, D. , in Stellar Astrophysical Fluid Dynamics. pp. 369–375 (2003)

  2. Pekeris, C.L., Frankowski, K.: The electromagnetic field of a Kerr-Newman source. Phys. Rev. A 36(11), 5118 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  3. Adamo, T., Newman, E.T.: The Kerr-Newman metric: A Review. Tech, Rep (2016). arXiv:1410.6626

    Google Scholar 

  4. Bah, I., Dempsey, R., Weck, P.: Kerr-Schild double copy and complex worldlines. J. High Energy Phys. 2, 180 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Newman, E.T.: Heaven and its properties. General Relativity and Gravitation 7(1), 107–111 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  6. Newman, E.T. Classical, geometric origin of magnetic moments, spin-angular momentum, and the Dirac gyromagnetic ratio. Phys Rev D 65(10),104(2002)

  7. Born, M., Infeld, L., Foundations of the New Field Theory. Nature 132(3348), 1004–1004 (1933). Number: 3348 Publisher: Nature Publishing Group

  8. Bopp, F. Eine lineare Theorie des Elektrons. Annalen der Physik 430(5), 345–384 (1940). https://onlinelibrary.wiley.com/doi/pdf/10.1002/andp.19404300504

  9. Podolsky, B., A Generalized Electrodynamics Part I—Non-Quantum. Phys Rev 62(1-2), 68–71 (1942). American Physical Society

  10. Pearle, P. in Electromagnetism, ed. by D. Teplitz (Springer US, 1982), pp. 211–295

  11. Coleman, S. in Electromagnetism: Paths to Research. Teplitz, D. (eds) pp. 183–210 Springer US, Boston (1982)

  12. Rohrlich, F.: Classical Charged Particles, 3rd edn. World Scientific Publishing Company, Singapore; Hackensack (2007)

    Book  MATH  Google Scholar 

  13. Bialynicki-Birula, I., Classical Model of the Electron. Exactly Soluble Example. Phys Rev D 28(8), 2114–2117 (1983). American Physical Society

  14. Boyer, T.H., Classical model of the electron and the definition of electromagnetic field momentum. Phys Rev D 25(12), 3246–3250 (1982). American Physical Society

  15. Rohrlich, F., Comment on the preceding paper by T. H. Boyer. Phys Rev D 25(12), 3251–3255 (1982). American Physical Society

  16. Burinskii, A.: The Dirac – Kerr-Newman electron. Gravit Cosmo 14, 109–122 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Campos, N., Jiménez, N.: Comment on the 4/3 problem in the electromagnetic mass and the Boyer-Rohrlich controversy. Phys Rev. D Part Fields 33(2), 607–610 (1986)

    Article  ADS  Google Scholar 

  18. Rosquist, K. Gravitationally induced electromagnetism at the Compton scale. Classic Quantum Grav.23(9), 3111–3122 (2006). IOP Publishing

  19. Einstein, A., A Generalization of the Relativistic Theory of Gravitation. Ann Mathemat 46(4), 578–584 (1945). Annals of Mathematics

  20. Einstein, A., Straus, E.G. A Generalization of the Relativistic Theory of Gravitation, II. Ann Mathematics 47(4), 731–741 (1946). Annals of Mathematics

  21. Einstein, A. A Generalized Theory of Gravitation. Rev Modern Phys 20(1), 35–39 (1948). American Physical Society

  22. Brown, E.H. On the Complex Structure of the Universe. J Math Phys 7(3), 417–425 (1966). American Institute of Physics

  23. Chamseddine, A.: Hermitian Geometry and Complex Space-Time. Comm Math Phys 264(2), 291–302 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Das, A. Complex Space-Time and Classical Field Theory. I. J. Math Phys. 7(1), 45–51 (1966). American Institute of Physics

  25. Debergh, N., D’Agostini , G., Petit, J.P. On the Poincaré Algebra in a Complex Space-Time Manifold. J Modern Phys 12(3), 218–228 (2021). Scientific Research Publishing

  26. Esposito, G., Complex General Relativity (1995). Journal Abbreviation: Complex General Relativity: , Fundamental Theories of Physics, Volume 69. ISBN 978-0-7923-3340-1. Kluwer Academic Publishers, 2002 Publication Title: Complex General Relativity: , Fundamental Theories of Physics, Volume 69. ISBN 978-0-7923-3340-1. Kluwer Academic Publishers, 2002

  27. Kaiser, G. Quantum Physics, Relativity, and Complex Spacetime: Towards a New Synthesis North-Holland, Amsterdam ; New York : New York, N.Y., U.S.A (1990)

  28. Mantz, C., Prokopec, T., Hermitian Gravity and Cosmology. Tech. Rep. arXiv:0804.0213, arXiv (2008). [astro-ph, physics:gr-qc, physics:hep-th] type: article arXiv:0804.0213

  29. E.A. Rauscher, J.J. Hurtak, D.E. Hurtak, The ontological basis of quantum theory, nonlocality and local realism. J Phys Conf Ser 1251(1), 012,042 (2019). Publisher: IOP Publishing

  30. Witten, E. Space-Time and Topological Orbifolds. Phys Rev Lett 61(6), 670–673 (1988). American Physical Society

  31. Newman, E.T.: Maxwell’s equations and complex Minkowski space. J. Math. Phys 14(1), 102 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  32. Newman, E.T.: Heaven and its properties. Gen. Relat. Grav 7(1), 107–111 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  33. Burinskii, A. Stringlike structures in the real and complex Kerr-Schild geometry. J Phys. Conf. Ser 532(1), 012,004 (2014). https://doi.org/10.1088/1742-6596/532/1/012004

  34. Yang, C.D., Han, S.Y. Extending Quantum Probability from Real Axis to Complex Plane. Entropy 23(2), 210 (2021). Multidisciplinary Digital Publishing Institute

  35. Maldacena, J., Susskind, L. Cool horizons for entangled black holes. Fortsch. Phys. 61, 781–811 (2013). 1306.0533

  36. Toben, B., Sarfatti, J., Wolf, F.A.: Space-time and Beyond: Toward an Explanation of the Unexplainable (Dutton. Google-Books-ID, RLUKPwAACAAJ (1975)

    Google Scholar 

  37. Kaiser, D. How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival W.W. Norton & Company, (2012). Google-Books-ID: uSOfvQEACAAJ

  38. Sen, S. Galaxy Rotation Curve Anomaly and Complex Spacetime. J Lasers Opt Photon 0(0), 7–7 (2020). https://www.hilarispublisher.com/abstract/galaxy-rotation-curve-anomaly-and-complex-spacetime-50348.html. Hilaris SRL

  39. Sen, S. Non-gravitational Effects of the Metric Field over Complex Manifolds (2021). https://doi.org/10.21203/rs.3.rs-163617/v1, https://www.researchsquare.com

  40. Misner, C.W., Wheeler, J.A.: Classical physics as geometry. Ann Phys 2(6), 525–603 (1957). https://doi.org/10.1016/0003-4916(57)90049-0, https://www.sciencedirect.com/science/article/pii/0003491657900490

  41. Bialynicki-Birula, I., Bialynicka-Birula, Z., The role of the Riemann–Silberstein vector in classical and quantum theories of electromagnetism. J Phys A Math Theoretical 46(5), 053,001 (2013). Publisher: IOP Publishing

  42. Einstein, A., Rosen, N., The Particle Problem in the General Theory of Relativity. Phys Rev 48(1), 73–77 (1935). American Physical Society

  43. Burinskii, A.Y.: Microgeon with a Kerr metric. Soviet Phys J 17(8), 1068–1071 (1974)

    Article  ADS  Google Scholar 

  44. Burinskii, A.: Spinning Particle as Kerr-Newman ‘Black Hole’ Phys Part Nuclei Lett 17(5), 724–729 (2020)

  45. Newman, E.T. Classical, geometric origin of magnetic moments, spin-angular momentum, and the Dirac gyromagnetic ratio. Phys Rev D 65(10), 104,005 (2002)

  46. Davidson, M.: The Lorentz-Dirac equation in complex space-time. Gen Relativ Grav 44(11), 2939–2964 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Davidson, M.: Bohmian Trajectories for Kerr-Newman Particles in Complex Space-Time. Found Phys 48(11), 1590–1616 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Mori, M.: Discovery of the Double Exponential Transformation and Its Developments. Publ Res Instit Math Sci 41(4), 897–935 (2005). https://doi.org/10.2977/prims/1145474600, https://ems.press/journals/prims/articles/2317

  49. Bailey, D. (2006). https://www.semanticscholar.org/paper/Tanh-Sinh-High-Precision-Quadrature-Bailey/bed60098313492afba381db8fe78311f219a53e6

  50. Hanneke, D., Fogwell Hoogerheide, S., Gabrielse, G. Cavity control of a single-electron quantum cyclotron: Measuring the electron magnetic moment. Phys Rev A 83(5), 052,122 (2011). https://doi.org/10.1103/PhysRevA.83.052122. American Physical Society

  51. Wheeler, J.A. Geons. Phys Rev 97(2), 511–536 (1955). American Physical Society

  52. Polyakov, A.M.: Quantum geometry of bosonic strings. Phys Lett B 103(3), 207–210 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  53. Suleymanov, M., Horwitz, L., Yahalom, A. Second quantization of a covariant relativistic spacetime string in Steuckelberg–Horwitz–Piron theory. Front Phys 12(3), 121,103 (2017)

  54. Davidson, M. Relativistic quantum mechanics, by Lawrence P. Horwitz. Contemp Phys 57(3), 452–453 (2016). Taylor & Francis https://doi.org/10.1080/00107514.2016.1188856

  55. Marnelius, R. Action Principle and Nonlocal Field Theories. Phys Rev D 8(8), 2472–2495 (1973). American Physical Society

  56. Eliezer, D.A., Woodard, R.P.: The problem of nonlocality in string theory. Nucl Phys B 325(2), 389–469 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  57. Heredia, C., Llosa, J., Nonlocal Lagrangian fields: Noether’s theorem and Hamiltonian formalism. Phys Rev D 105(12), 126,002 (2022). American Physical Society

  58. Lindell, I.V., Nikoskinen, K.I. Time-Domain Green Function Corresponding to a Time-Harmonic Point Source in Complex Space. Electromagnetics 10(3), 313–325 (1990). Taylor & Francis https://doi.org/10.1080/02726349008908246

  59. Lindell, I.V.: Delta function expansions, complex delta functions and the steepest descent method. Am J Phys 61, 438–442 (1993)

    Article  ADS  Google Scholar 

  60. Brewster, R.A., Franson, J.D. Generalized delta functions and their use in quantum optics. J Math Phys 59(1), 012,102 (2018). American Institute of Physics

  61. Brewster, R.A. , Franson, J.D. Generalized Delta Functions and Their Use in Quasi-Probability Distributions. (2016). arXiv:1605.04321

  62. Giulini, D.: Electron spin or classically non-describable two-valuedness. Stud History Philo Sci B Stud History Philo Modern Phys 39(3), 557–578 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  63. Bopp, F.W.: Time Symmetric Quantum Mechanics and Causal Classical Physics. Found Phys 47(4), 490–504 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. Einstein, A.: Physics and reality. J Franklin Inst 221(3), 349–382 (1936). https://doi.org/10.1016/S0016-0032(36)91047-5, https://www.sciencedirect.com/science/article/pii/S0016003236910475

  65. Adler, S.L.Quantum theory as an emergent phenomenon: the statistical mechanics of matrix models as the precursor of quantum field theory Cambridge University Press (2004)

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    Mark Davidson

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Appendix A: Python script

Appendix A: Python script

 

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Davidson, M. Classical Charged Particle Models Derived from Complex Shift Methods. Int J Theor Phys 62, 154 (2023). https://doi.org/10.1007/s10773-023-05411-y

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