Electrostatics, the study of the effects of stationary electric charges, is well established. Electrodynamics, the study of what happens when the charges are moving, has not been free from difficulties. The special theory of relativity is commonly supposed to be used to bridge the gap between the static and dynamic situations. However, that theory involves some notions, such as the contraction of lengths and the dilation of times, which are not well established experimentally. Moreover, it leads to some seemingly absurd results such as the notorious twin paradox. In the present article, the authors use the idea of feedback, in which changing electrical fields cause magnetic effects and vice versa. These facts have been established experimentally for a long time. In that way a theory of what happens with moving charges is established. The results agree with those from the previous theory; but they are obtained in a way which seems physically more meaningful, and which does not require one to assume effects for which there is no experimental evidence.