# American Institute of Mathematical Sciences

May  2012, 17(3): 835-848. doi: 10.3934/dcdsb.2012.17.835

## Gravitational and electromagnetic properties of almost standing fields

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Received  June 2011 Revised  July 2011 Published  January 2012

For a scalar field propagating at light velocity $c$, kinematic properties of standing waves with constant frequency $\omega{}$ and velocity $v$, are formally identical with mechanic properties of isolated matter. They are both described by equations with the same mathematical structure, expressed by the Lorentz transformation with constant velocities $c$ and $v$. For almost standing waves, the variations of constant quantities lead to their dynamic properties. When they arise from adiabatic variations of the frequency $\Omega(x,t) = \omega \pm \delta\Omega(x,t)$, with $\omega{}$ constant, and $\delta\Omega(x,t) \ll \omega{}$, they lead to interactions which are formally identical with electromagnetic interactions. When they derive from variations of the field velocity $C(x,t) = c \pm \delta C(x,t)$, with $c$ constant, and $\delta C(x,t) \ll c$, they lead to interactions which are formally identical with gravitational interactions. The correspondence between almost standing waves of the field and matter, offers a common frame allowing an approach to investigate how gravitational and electromagnetic properties articulate together.
Citation: Claude Elbaz. Gravitational and electromagnetic properties of almost standing fields. Discrete and Continuous Dynamical Systems - B, 2012, 17 (3) : 835-848. doi: 10.3934/dcdsb.2012.17.835
##### References:
 [1] C. Elbaz, L'onde stationnaire et la transformation de Lorentz, C.R.Acad. Sc. Paris,. 298 (1984), 543-546. [2] C. Elbaz, Proprietes cinematiques des particules matérielles et des ondes stationnaires du champ, Annales de la Fondation Louis de Broglie, 11 (1986), 65-84. [3] C. Elbaz, Proprietes dynamiques des particules matérielles et des ondes stationnaires du champ, Annales de la Fondation Louis de Broglie, 14 (1989), 165-176. [4] A. Miranville and R. Temam, "Modelisation Mathematique des Milieux Continus," Springer Verlag, 2003. [5] R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. [6] G. I. Sivashinsky, The de Broglie soliton as a localized excitation of the action function, Phys. D, 240 (2011), 406-409. doi: 10.1016/j.physd.2010.10.002. [7] C. Elbaz, Classical mechanics of an extended material particle, Phys. Lett. A, 204 (1995), 229-235. doi: 10.1016/0375-9601(95)00470-N. [8] C. Elbaz, Dynamic properties of almost monochromatic standing waves, Asymptotic Analysis, 68 (2010), 77-88. [9] L. Landau and E. Lifchitz, "The Classical Theory of Fields," Pergamon, 1962. [10] M. Born and E. Wolf, "Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light," With contributions by A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman and W. L. Wilcock, Third revised edition, Pergamon Press, Oxford-New York-Paris, 1965. [11] C. Elbaz, Optical properties of the Compton effect, J. Phys. Math. Gen., 20 (1987), 279. doi: 10.1088/0305-4470/20/5/004. [12] C. Elbaz, On self-field electromagnetic properties for extended material particles, Phys. Lett. A, 127 (1988), 308-314. doi: 10.1016/0375-9601(88)90574-9. [13] A. Einstein, Lichtgeswindigkeit und Statik des Gravitationsfeldes, Annalen der Physik, 38 (1912), 355-369. doi: 10.1002/andp.19123430704. [14] G. C. Tannoudji and S. Hudlet, A new scientific revolution at the horizon?, in "L'Univers Invisible," Hermann, Paris, 2009. [15] T. Padmanabhan, "Gravitation-Foundations and Frontiers," Cambridge Univ. Press, Cambrige, U.K, 2010. [16] E. Verlinde, On the origin of gravity and the laws of Newton, arXiv:1001.0785, 2010. [17] R. C. Jennison and A. J. Drinkwater, An approach to the understanding of inertia, J. Phys. A, 10 (1977), 167. doi: 10.1088/0305-4470/10/2/005. [18] R. C. Jennison, The inertial mass and anomalous internal momentum of a cavity, J. Phys. A, 13 (1980), 2247. doi: 10.1088/0305-4470/13/6/043. [19] M. Molski, Extended wave-particle decription of longitudinal photons, J. Phys. A, 24 (1991), 5063. doi: 10.1088/0305-4470/24/21/018.

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##### References:
 [1] C. Elbaz, L'onde stationnaire et la transformation de Lorentz, C.R.Acad. Sc. Paris,. 298 (1984), 543-546. [2] C. Elbaz, Proprietes cinematiques des particules matérielles et des ondes stationnaires du champ, Annales de la Fondation Louis de Broglie, 11 (1986), 65-84. [3] C. Elbaz, Proprietes dynamiques des particules matérielles et des ondes stationnaires du champ, Annales de la Fondation Louis de Broglie, 14 (1989), 165-176. [4] A. Miranville and R. Temam, "Modelisation Mathematique des Milieux Continus," Springer Verlag, 2003. [5] R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997. [6] G. I. Sivashinsky, The de Broglie soliton as a localized excitation of the action function, Phys. D, 240 (2011), 406-409. doi: 10.1016/j.physd.2010.10.002. [7] C. Elbaz, Classical mechanics of an extended material particle, Phys. Lett. A, 204 (1995), 229-235. doi: 10.1016/0375-9601(95)00470-N. [8] C. Elbaz, Dynamic properties of almost monochromatic standing waves, Asymptotic Analysis, 68 (2010), 77-88. [9] L. Landau and E. Lifchitz, "The Classical Theory of Fields," Pergamon, 1962. [10] M. Born and E. Wolf, "Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light," With contributions by A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman and W. L. Wilcock, Third revised edition, Pergamon Press, Oxford-New York-Paris, 1965. [11] C. Elbaz, Optical properties of the Compton effect, J. Phys. Math. Gen., 20 (1987), 279. doi: 10.1088/0305-4470/20/5/004. [12] C. Elbaz, On self-field electromagnetic properties for extended material particles, Phys. Lett. A, 127 (1988), 308-314. doi: 10.1016/0375-9601(88)90574-9. [13] A. Einstein, Lichtgeswindigkeit und Statik des Gravitationsfeldes, Annalen der Physik, 38 (1912), 355-369. doi: 10.1002/andp.19123430704. [14] G. C. Tannoudji and S. Hudlet, A new scientific revolution at the horizon?, in "L'Univers Invisible," Hermann, Paris, 2009. [15] T. Padmanabhan, "Gravitation-Foundations and Frontiers," Cambridge Univ. Press, Cambrige, U.K, 2010. [16] E. Verlinde, On the origin of gravity and the laws of Newton, arXiv:1001.0785, 2010. [17] R. C. Jennison and A. J. Drinkwater, An approach to the understanding of inertia, J. Phys. A, 10 (1977), 167. doi: 10.1088/0305-4470/10/2/005. [18] R. C. Jennison, The inertial mass and anomalous internal momentum of a cavity, J. Phys. A, 13 (1980), 2247. doi: 10.1088/0305-4470/13/6/043. [19] M. Molski, Extended wave-particle decription of longitudinal photons, J. Phys. A, 24 (1991), 5063. doi: 10.1088/0305-4470/24/21/018.
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