A THEORY OF ELECTROMAGNETIC AND GRAVITATIONAL-FIELDS

Careful calculations using classical field theory show that if a macroscopic ball with uniform surface charge (say, a billiard ball with 1E6 excess electrons) is released near the surface of the earth, it will almost instantaneously accelerate to relativistic speed and blow a hole in the ground. This absurd prediction is just the macroscopic version of the self-force problem for charged particles [1]. Furthermore, if one attempts to develop from electromagnetism a parallel theory for gravitation [2], the result is the same, self-acceleration. The basis of the new theory is a measure of energy density for any wave equation [3-5]. Given any solution of any four-vector wave equation in spacetime (for example, the potentials (c-1 phi, A) = (A0, A1, A2, A3) in electromagnetism), one can form the 16 first order partial derivatives of the vector components, with respect to the time and space variables (ct, x) = (x0, x1, x2, x3). The sum of the squares of the 16 terms is a natural energy function [6, p. 283] (satisfying a conservation law partial derivative of u with respect to t = -DELTA.S). Such energy functions are routinely utilized by mathematicians as Lyapunov functions in the theory of stability of waves with conditions. A Lagrangian using this sum leads to a new energy tensor for electromagnetic and gravitational fields, an alternative to that in [7].