Note concerning gravitation and electromagnetism |
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Authors: | C C Leiby Jr |
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Institution: | (1) Leghorn Laboratories, Bedford, Mass., USA |
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Abstract: | The Maxwell equations for gravitational fields previously assumed by Sciama are derived from elementary considerations. The
Lagrangian for a gravitating mass in a non-inertial coordinate system yields equations of motion leading to force definitions
for a gravitational field intensity and a gravitational induction field. The non-inertial velocity of the coordinate system
plays the role of a vector potential contributing to the generalized momenta of bodies moving in the system. A Lagrangian
density constructed from the force-defined fields then lead to the source definitions of gravitational fields. It is found
that positive field energy densities require repulsive gravitational forces, whereas attractive forces imply the violation
of the conservation of energy. This paradox is resolved by representing gravitational quantities as pure-imaginary entities.
Thus characterized, the equations which define gravitational fields become identical to Maxwell's equations but are pure-imaginary.
This suggests a combined representation for gravitational and electromagnetic fields which, in covariant form, indicates both
the well known equivalence of mass and energy and a possible equivalence of charge and energy. From orthogonality considerations,
it is conjectured that this latter energy is gravitational, and that, whereas gravitational fields interact with electromagnetic
energy, electromagnetic fields interact with gravitational energy.
Parts of this work were completed at Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A. |
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