The Longest Range Electric Field, and Gravity

The vector potential is A=(μo/4π)qv/r, from which B=∇×A. Upon any acceleration of the charge, one finds a long range electric field, E=− ∂A/∂t. The range of this 1/r field far exceeds that from a charge, which goes as 1/r2 or a dipole which goes as 1/r3. This E field differs from Hertz’ solution for an oscillating charge. Hertz’ finding of TEM waves from an oscillating charge is flawed by the implicit Galilean transformation of “retarded time”, t’=t−r/v. By relating all time to a clock sited at the source, the need for retarded time at the observer is avoided and one finds an E wave solution. The waves which result involve E and B fields, but only the E field is long range (1/r). These are classical waves which remain tied to the source, and carry away no energy. The electric field affects neutral bodies by the Stark effect, exchanging energy and leading to a weak force of attraction very like gravity. This suggests that gravity is founded in the electromagnetic force, and is not fundamental. ACCELERATION OF CHARGE A proper accounting for the effects of accelerated charge is important in electromagnetism. Currently, there is controversy as to the consequences of the acceleration of charge. Classical electromagnetism is very firm on the point. As Jackson puts it, “The motion of charged particles in external force fields necessarily involves the emission of radiation whenever the charges are accelerated.” (1) By radiation, he means Hertzian