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

Gravitational and electromagnetic properties of almost standing fields

1. 

5 Allée des sophoras, 92330, Sceaux, France

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 & 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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[4]

A. Miranville and R. Temam, "Modelisation Mathematique des Milieux Continus," Springer Verlag, 2003. Google Scholar

[5]

R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[8]

C. Elbaz, Dynamic properties of almost monochromatic standing waves, Asymptotic Analysis, 68 (2010), 77-88. Google Scholar

[9]

L. Landau and E. Lifchitz, "The Classical Theory of Fields," Pergamon, 1962. Google Scholar

[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.  Google Scholar

[11]

C. Elbaz, Optical properties of the Compton effect, J. Phys. Math. Gen., 20 (1987), 279. doi: 10.1088/0305-4470/20/5/004.  Google Scholar

[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.  Google Scholar

[13]

A. Einstein, Lichtgeswindigkeit und Statik des Gravitationsfeldes, Annalen der Physik, 38 (1912), 355-369. doi: 10.1002/andp.19123430704.  Google Scholar

[14]

G. C. Tannoudji and S. Hudlet, A new scientific revolution at the horizon?, in "L'Univers Invisible," Hermann, Paris, 2009. Google Scholar

[15]

T. Padmanabhan, "Gravitation-Foundations and Frontiers," Cambridge Univ. Press, Cambrige, U.K, 2010. Google Scholar

[16]

E. Verlinde, On the origin of gravity and the laws of Newton, arXiv:1001.0785, 2010. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

M. Molski, Extended wave-particle decription of longitudinal photons, J. Phys. A, 24 (1991), 5063. doi: 10.1088/0305-4470/24/21/018.  Google Scholar

show all references

References:
[1]

C. Elbaz, L'onde stationnaire et la transformation de Lorentz, C.R.Acad. Sc. Paris,. 298 (1984), 543-546. Google Scholar

[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. Google Scholar

[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. Google Scholar

[4]

A. Miranville and R. Temam, "Modelisation Mathematique des Milieux Continus," Springer Verlag, 2003. Google Scholar

[5]

R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Second edition, Applied Mathematical Sciences, 68, Springer-Verlag, New York, 1997.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[8]

C. Elbaz, Dynamic properties of almost monochromatic standing waves, Asymptotic Analysis, 68 (2010), 77-88. Google Scholar

[9]

L. Landau and E. Lifchitz, "The Classical Theory of Fields," Pergamon, 1962. Google Scholar

[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.  Google Scholar

[11]

C. Elbaz, Optical properties of the Compton effect, J. Phys. Math. Gen., 20 (1987), 279. doi: 10.1088/0305-4470/20/5/004.  Google Scholar

[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.  Google Scholar

[13]

A. Einstein, Lichtgeswindigkeit und Statik des Gravitationsfeldes, Annalen der Physik, 38 (1912), 355-369. doi: 10.1002/andp.19123430704.  Google Scholar

[14]

G. C. Tannoudji and S. Hudlet, A new scientific revolution at the horizon?, in "L'Univers Invisible," Hermann, Paris, 2009. Google Scholar

[15]

T. Padmanabhan, "Gravitation-Foundations and Frontiers," Cambridge Univ. Press, Cambrige, U.K, 2010. Google Scholar

[16]

E. Verlinde, On the origin of gravity and the laws of Newton, arXiv:1001.0785, 2010. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

M. Molski, Extended wave-particle decription of longitudinal photons, J. Phys. A, 24 (1991), 5063. doi: 10.1088/0305-4470/24/21/018.  Google Scholar

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