Correction of Maxwell's Equations for Signals I

Electromagnetic wave theory has been based on the concept of infinitely extended periodic sinusoidal waves ever since Maxwell published his theory a century ago. On the practical level this worked very well, but on the theoretical level we always had an indication that something was amiss. There was never a satisfactory concept of propagation velocity of signals within the framework of Maxwell's theory. The often-mentioned group velocity fails on two accounts, one being that it is almost always larger than the velocity of light in radio transmission through the atmosphere; the other being that its derivation implies a transmission rate of information equal to zero. A closer study shows that Maxwell's equations fail for waves with nonnegligible relative frequency bandwidth propagating in a medium with nonnegligible losses. The reason is singularities encountered in the course of calculation. The remedy is the addition of a magnetic current density which may be chosen zero after one has reached the last singularity but not before.