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. 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. Google Scholar

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C. Elbaz, Classical mechanics of an extended material particle,, Phys. Lett. A, 204 (1995), 229. 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. 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, (1965). Google Scholar

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

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C. Elbaz, On self-field electromagnetic properties for extended material particles,, Phys. Lett. A, 127 (1988), 308. doi: 10.1016/0375-9601(88)90574-9. Google Scholar

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

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E. Verlinde, On the origin of gravity and the laws of Newton,, \arXiv{1001.0785}, (2010). Google Scholar

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R. C. Jennison and A. J. Drinkwater, An approach to the understanding of inertia,, J. Phys. A, 10 (1977). doi: 10.1088/0305-4470/10/2/005. Google Scholar

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R. C. Jennison, The inertial mass and anomalous internal momentum of a cavity,, J. Phys. A, 13 (1980). doi: 10.1088/0305-4470/13/6/043. Google Scholar

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M. Molski, Extended wave-particle decription of longitudinal photons,, J. Phys. A, 24 (1991). 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. 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. 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. 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, 68 (1997). Google Scholar

[6]

G. I. Sivashinsky, The de Broglie soliton as a localized excitation of the action function,, Phys. D, 240 (2011), 406. 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. 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. 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, (1965). Google Scholar

[11]

C. Elbaz, Optical properties of the Compton effect,, J. Phys. Math. Gen., 20 (1987). 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. doi: 10.1016/0375-9601(88)90574-9. Google Scholar

[13]

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

[14]

G. C. Tannoudji and S. Hudlet, A new scientific revolution at the horizon?,, in, (2009). Google Scholar

[15]

T. Padmanabhan, "Gravitation-Foundations and Frontiers,", Cambridge Univ. Press, (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). 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). 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). doi: 10.1088/0305-4470/24/21/018. Google Scholar

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